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< a href = "one__tree__lower__bound_8h.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a name = "l00001" > < / a > < span class = "lineno" > 1< / span >   < span class = "comment" > // Copyright 2010-2021 Google LLC< / span > < / div >
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< div class = "line" > < a name = "l00002" > < / a > < span class = "lineno" > 2< / span >   < span class = "comment" > // Licensed under the Apache License, Version 2.0 (the " License" );< / span > < / div >
< div class = "line" > < a name = "l00003" > < / a > < span class = "lineno" > 3< / span >   < span class = "comment" > // you may not use this file except in compliance with the License.< / span > < / div >
< div class = "line" > < a name = "l00004" > < / a > < span class = "lineno" > 4< / span >   < span class = "comment" > // You may obtain a copy of the License at< / span > < / div >
< div class = "line" > < a name = "l00005" > < / a > < span class = "lineno" > 5< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00006" > < / a > < span class = "lineno" > 6< / span >   < span class = "comment" > // http://www.apache.org/licenses/LICENSE-2.0< / span > < / div >
< div class = "line" > < a name = "l00007" > < / a > < span class = "lineno" > 7< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00008" > < / a > < span class = "lineno" > 8< / span >   < span class = "comment" > // Unless required by applicable law or agreed to in writing, software< / span > < / div >
< div class = "line" > < a name = "l00009" > < / a > < span class = "lineno" > 9< / span >   < span class = "comment" > // distributed under the License is distributed on an " AS IS" BASIS,< / span > < / div >
< div class = "line" > < a name = "l00010" > < / a > < span class = "lineno" > 10< / span >   < span class = "comment" > // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.< / span > < / div >
< div class = "line" > < a name = "l00011" > < / a > < span class = "lineno" > 11< / span >   < span class = "comment" > // See the License for the specific language governing permissions and< / span > < / div >
< div class = "line" > < a name = "l00012" > < / a > < span class = "lineno" > 12< / span >   < span class = "comment" > // limitations under the License.< / span > < / div >
< div class = "line" > < a name = "l00013" > < / a > < span class = "lineno" > 13< / span >   < / div >
< div class = "line" > < a name = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "comment" > // An implementation of the Held-Karp symmetric Traveling Salesman (TSP) lower< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "comment" > // bound algorithm, inspired by " Estimating the Held-Karp lower bound for the< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < span class = "comment" > // geometric TSP" by Christine L. Valenzuela and Antonia J. Jones, European< / span > < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "comment" > // Journal of Operational Research, Volume 102, Issue 1, 1 October 1997,< / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < span class = "comment" > // Pages 157-175.< / span > < / div >
< div class = "line" > < a name = "l00019" > < / a > < span class = "lineno" > 19< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00020" > < / a > < span class = "lineno" > 20< / span >   < span class = "comment" > // The idea is to compute minimum 1-trees to evaluate a lower bound to the< / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < span class = "comment" > // corresponding TSP. A minimum 1-tree is a minimum spanning tree on all nodes< / span > < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < span class = "comment" > // but one, to which are added the two shortest edges from the left-out node to< / span > < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "comment" > // the nodes of the spanning tree. The sum of the cost of the edges of the< / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < span class = "comment" > // minimum 1-tree is a lower bound to the cost of the TSP.< / span > < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "comment" > // In order to improve (increase) this lower bound, the idea is to add weights< / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < span class = "comment" > // to each nodes, weights which are added to the cost function used when< / span > < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < span class = "comment" > // computing the 1-tree. If weight[i] is the weight of node i, the cost function< / span > < / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < span class = "comment" > // therefore becomes weighed_cost(i,j) = cost(i,j) + weight[i] + weight[j]. One< / span > < / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < span class = "comment" > // can see that w = weighed_cost(minimum 1-tree) - Sum(2 * weight[i])< / span > < / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "comment" > // = cost(minimum 1-tree) + Sum(weight[i] * (degree[i] - 2))< / span > < / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "comment" > // is a valid lower bound to the TSP:< / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < span class = "comment" > // 1) let T be the set of 1-trees on the nodes;< / span > < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < span class = "comment" > // 2) let U be the set of tours on the nodes; U is a subset of T (tours are< / span > < / div >
< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > 34< / span >   < span class = "comment" > // 1-trees with all degrees equal to 2), therefore:< / span > < / div >
< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   < span class = "comment" > // min(t in T) Cost(t) < = min(t in U) Cost(t)< / span > < / div >
< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < span class = "comment" > // and< / span > < / div >
< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < span class = "comment" > // min(t in T) WeighedCost(t) < = min(t in U) WeighedCost(t)< / span > < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "comment" > // 3) weighed_cost(i,j) = cost(i,j) + weight[i] + weight[j], therefore:< / span > < / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   < span class = "comment" > // for all t in T, WeighedCost(t) = Cost(t) + Sum(weight[i] * degree[i])< / span > < / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > 40< / span >   < span class = "comment" > // and< / span > < / div >
< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > 41< / span >   < span class = "comment" > // for all i in U, WeighedCost(t) = Cost(t) + Sum(weight[i] * 2)< / span > < / div >
< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < span class = "comment" > // 4) let t* in U s.t. WeighedCost(t*) = min(t in U) WeighedCost(t), therefore:< / span > < / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < span class = "comment" > // min(t in T) (Cost(t) + Sum(weight[i] * degree[i]))< / span > < / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "comment" > // < = Cost(t*) + Sum(weight[i] * 2)< / span > < / div >
< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   < span class = "comment" > // and< / span > < / div >
< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   < span class = "comment" > // min(t in T) (Cost(t) + Sum(weight[i] * (degree[i] - 2))) < = Cost(t*)< / span > < / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < span class = "comment" > // and< / span > < / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < span class = "comment" > // cost(minimum 1-tree) + Sum(weight[i] * (degree[i] - 2)) < = Cost(t*)< / span > < / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   < span class = "comment" > // and< / span > < / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < span class = "comment" > // w < = Cost(t*)< / span > < / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "comment" > // 5) because t* is also the tour minimizing Cost(t) with t in U (weights do not< / span > < / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "comment" > // affect the optimality of a tour), Cost(t*) is the cost of the optimal< / span > < / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   < span class = "comment" > // solution to the TSP and w is a lower bound to this cost.< / span > < / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   < span class = "comment" > // The best lower bound is the one for which weights maximize w. Intuitively as< / span > < / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   < span class = "comment" > // degrees get closer to 2 the minimum 1-trees gets closer to a tour.< / span > < / div >
< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "comment" > // At each iteration m, weights are therefore updated as follows:< / span > < / div >
< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   < span class = "comment" > // weight(m+1)[i] = weight(m)[i] + step(m) * (degree(m)[i] - 2)< / span > < / div >
< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   < span class = "comment" > // where degree(m)[i] is the degree of node i in the 1-tree at iteration i,< / span > < / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   < span class = "comment" > // step(m) is a subgradient optimization step.< / span > < / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < span class = "comment" > // This implementation uses two variants of Held-Karp' s initial subgradient< / span > < / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   < span class = "comment" > // optimization iterative estimation approach described in " The< / span > < / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   < span class = "comment" > // traveling-salesman problem and minimum spanning trees: Part I and II" , by< / span > < / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   < span class = "comment" > // Michael Held and Richard M. Karp, Operations Research Vol. 18,< / span > < / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   < span class = "comment" > // No. 6 (Nov. - Dec., 1970), pp. 1138-1162 and Mathematical Programming (1971).< / span > < / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   < span class = "comment" > // The first variant comes from Volgenant, T., and Jonker, R. (1982), " A branch< / span > < / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < span class = "comment" > // and bound algorithm for the symmetric traveling salesman problem based on the< / span > < / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   < span class = "comment" > // 1-tree relaxation" , European Journal of Operational Research. 9:83-89." .< / span > < / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   < span class = "comment" > // It suggests using< / span > < / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   < span class = "comment" > // step(m) = (1.0 * (m - 1) * (2 * M - 5) / (2 * (M - 1))) * step1< / span > < / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > 74< / span >   < span class = "comment" > // - (m - 2) * step1< / span > < / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   < span class = "comment" > // + (0.5 * (m - 1) * (m - 2) / ((M - 1) * (M - 2))) * step1< / span > < / div >
< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   < span class = "comment" > // where M is the maximum number of iterations and step1 is initially set to< / span > < / div >
< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < span class = "comment" > // L / (2 * number of nodes), where L is the un-weighed cost of the 1-tree;< / span > < / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   < span class = "comment" > // step1 is updated each time a better w is found. The intuition is to have a< / span > < / div >
< div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > 79< / span >   < span class = "comment" > // positive decreasing step which is equal to 0 after M iterations; Volgenant< / span > < / div >
< div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   < span class = "comment" > // and Jonker suggest that:< / span > < / div >
< div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   < span class = "comment" > // step(m) - 2 * step(m-1) + t(m-2) = constant,< / span > < / div >
< div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   < span class = "comment" > // step(M) = 0< / span > < / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   < span class = "comment" > // and< / span > < / div >
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   < span class = "comment" > // step(1) - step(2) = 3 * (step(M-1) - step(M)).< / span > < / div >
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "comment" > // The step(m) formula above derives from this recursive formulation.< / span > < / div >
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "comment" > // This is the default algorithm used in this implementation.< / span > < / div >
< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < span class = "comment" > // The second variant comes from Held, M., Wolfe, P., and Crowder, H. P. (1974),< / span > < / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   < span class = "comment" > // " Validation of subgradient optimization" , Mathematical Programming 6:62-88.< / span > < / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < span class = "comment" > // It derives from the original Held-Karp formulation:< / span > < / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   < span class = "comment" > // step(m) = lambda(m) * (wlb - w(m)) / Sum((degree[i] - 2)^2),< / span > < / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "comment" > // where wlb is a lower bound to max(w(m)) and lambda(m) in [0, 2].< / span > < / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   < span class = "comment" > // Help-Karp prove that< / span > < / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   < span class = "comment" > // if w(m' ) > w(m) and 0 < step < 2 * (w(m' ) - w(m))/norm(degree(m) - 2)^2,< / span > < / div >
< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > 95< / span >   < span class = "comment" > // then weight(m+1) is closer to w' than w from which they derive the above< / span > < / div >
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   < span class = "comment" > // formula.< / span > < / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   < span class = "comment" > // Held-Wolfe-Crowder show that using an overestimate UB is as effective as< / span > < / div >
< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   < span class = "comment" > // using the underestimate wlb while UB is easier to compute. The resulting< / span > < / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   < span class = "comment" > // formula is:< / span > < / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   < span class = "comment" > // step(m) = lambda(m) * (UB - w(m)) / Sum((degree[i] - 2)^2),< / span > < / div >
< div class = "line" > < a name = "l00101" > < / a > < span class = "lineno" > 101< / span >   < span class = "comment" > // where UB is an upper bound to the TSP (here computed with the Christofides< / span > < / div >
< div class = "line" > < a name = "l00102" > < / a > < span class = "lineno" > 102< / span >   < span class = "comment" > // algorithm), and lambda(m) in [0, 2] initially set to 2. Held-Wolfe-Crowder< / span > < / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   < span class = "comment" > // suggest running the algorithm for M = 2 * number of nodes iterations, then< / span > < / div >
< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   < span class = "comment" > // dividing lambda and M by 2 until M is small enough (less than 2 in this< / span > < / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   < span class = "comment" > // implementation).< / span > < / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > 106< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > 107< / span >   < span class = "comment" > // To speed up the computation, minimum spanning trees are actually computed on< / span > < / div >
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < span class = "comment" > // a graph limited to the nearest neighbors of each node. Valenzuela-Jones 1997< / span > < / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < span class = "comment" > // experiments have shown that this does not harm the lower bound computation< / span > < / div >
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   < span class = "comment" > // significantly. At the end of the algorithm a last iteration is run on the< / span > < / div >
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   < span class = "comment" > // complete graph to ensure the bound is correct (the cost of a minimum 1-tree< / span > < / div >
< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   < span class = "comment" > // on a partial graph is an upper bound to the one on a complete graph).< / span > < / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   < span class = "comment" > // Usage:< / span > < / div >
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< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < span class = "comment" > // std::function< int64_t(int,int)> cost_function =...;< / span > < / div >
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< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > 116< / span >   < span class = "comment" > // const double lower_bound =< / span > < / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > 117< / span >   < span class = "comment" > // ComputeOneTreeLowerBound(number_of_nodes, cost_function);< / span > < / div >
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   < span class = "comment" > // where number_of_nodes is the number of nodes in the TSP and cost_function< / span > < / div >
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > 119< / span >   < span class = "comment" > // is a function returning the cost between two nodes.< / span > < / div >
< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   < / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   < span class = "preprocessor" > #ifndef OR_TOOLS_GRAPH_ONE_TREE_LOWER_BOUND_H_< / span > < / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   < span class = "preprocessor" > #define OR_TOOLS_GRAPH_ONE_TREE_LOWER_BOUND_H_< / span > < / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > 123< / span >   < / div >
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > 124< / span >   < span class = "preprocessor" > #include < math.h> < / span > < / div >
< div class = "line" > < a name = "l00125" > < / a > < span class = "lineno" > 125< / span >   < / div >
< div class = "line" > < a name = "l00126" > < / a > < span class = "lineno" > 126< / span >   < span class = "preprocessor" > #include < limits> < / span > < / div >
< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   < span class = "preprocessor" > #include < set> < / span > < / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > 128< / span >   < / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > 129< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "integral__types_8h.html" > ortools/base/integral_types.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00130" > < / a > < span class = "lineno" > 130< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "christofides_8h.html" > ortools/graph/christofides.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00131" > < / a > < span class = "lineno" > 131< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "minimum__spanning__tree_8h.html" > ortools/graph/minimum_spanning_tree.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < / div >
< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   < span class = "keyword" > namespace < / span > < a class = "code" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   < / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   < span class = "comment" > // Implementation of algorithms computing Held-Karp bounds. They have to provide< / span > < / div >
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   < span class = "comment" > // the following methods:< / span > < / div >
< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < span class = "comment" > // - bool Next(): returns false when the algorithm must stop;< / span > < / div >
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > 138< / span >   < span class = "comment" > // - double GetStep(): returns the current step computed by the algorithm;< / span > < / div >
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   < span class = "comment" > // - void OnOneTree(CostType one_tree_cost,< / span > < / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > 140< / span >   < span class = "comment" > // double w,< / span > < / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   < span class = "comment" > // const std::vector< int> & degrees):< / span > < / div >
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   < span class = "comment" > // called each time a new minimum 1-tree is computed;< / span > < / div >
< div class = "line" > < a name = "l00143" > < / a > < span class = "lineno" > 143< / span >   < span class = "comment" > // - one_tree_cost: the un-weighed cost of the 1-tree,< / span > < / div >
< div class = "line" > < a name = "l00144" > < / a > < span class = "lineno" > 144< / span >   < span class = "comment" > // - w the current value of w,< / span > < / div >
< div class = "line" > < a name = "l00145" > < / a > < span class = "lineno" > 145< / span >   < span class = "comment" > // - degrees: the degree of nodes in the 1-tree.< / span > < / div >
< div class = "line" > < a name = "l00146" > < / a > < span class = "lineno" > 146< / span >   < span class = "comment" > // - OnNewWMax(CostType one_tree_cost): called when a better value of w is< / span > < / div >
< div class = "line" > < a name = "l00147" > < / a > < span class = "lineno" > 147< / span >   < span class = "comment" > // found, one_tree_cost being the un-weighed cost of the corresponding< / span > < / div >
< div class = "line" > < a name = "l00148" > < / a > < span class = "lineno" > 148< / span >   < span class = "comment" > // minimum 1-tree.< / span > < / div >
< div class = "line" > < a name = "l00149" > < / a > < span class = "lineno" > 149< / span >   < / div >
< div class = "line" > < a name = "l00150" > < / a > < span class = "lineno" > 150< / span >   < span class = "comment" > // Implementation of the Volgenant Jonker algorithm (see the comments at the< / span > < / div >
< div class = "line" > < a name = "l00151" > < / a > < span class = "lineno" > 151< / span >   < span class = "comment" > // head of the file for explanations).< / span > < / div >
< div class = "line" > < a name = "l00152" > < / a > < span class = "lineno" > 152< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType> < / div >
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< div class = "line" > < a name = "l00153" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html" > 153< / a > < / span >   < span class = "keyword" > class < / span > < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html" > VolgenantJonkerEvaluator< / a > {< / div >
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< div class = "line" > < a name = "l00154" > < / a > < span class = "lineno" > 154< / span >   < span class = "keyword" > public< / span > :< / div >
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< div class = "line" > < a name = "l00155" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a24cfa064cc97e776b361abdba5488673" > 155< / a > < / span >   < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a24cfa064cc97e776b361abdba5488673" > VolgenantJonkerEvaluator< / a > (< span class = "keywordtype" > int< / span > number_of_nodes, < span class = "keywordtype" > int< / span > max_iterations)< / div >
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< div class = "line" > < a name = "l00156" > < / a > < span class = "lineno" > 156< / span >   : step1_initialized_(false),< / div >
< div class = "line" > < a name = "l00157" > < / a > < span class = "lineno" > 157< / span >   step1_(0),< / div >
< div class = "line" > < a name = "l00158" > < / a > < span class = "lineno" > 158< / span >   iteration_(0),< / div >
< div class = "line" > < a name = "l00159" > < / a > < span class = "lineno" > 159< / span >   max_iterations_(max_iterations > 0 ? max_iterations< / div >
< div class = "line" > < a name = "l00160" > < / a > < span class = "lineno" > 160< / span >   : MaxIterations(number_of_nodes)),< / div >
< div class = "line" > < a name = "l00161" > < / a > < span class = "lineno" > 161< / span >   number_of_nodes_(number_of_nodes) {}< / div >
< div class = "line" > < a name = "l00162" > < / a > < span class = "lineno" > 162< / span >   < / div >
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< div class = "line" > < a name = "l00163" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a3947d19ac087ef2cd68c2409920339c4" > 163< / a > < / span >   < span class = "keywordtype" > bool< / span > < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a3947d19ac087ef2cd68c2409920339c4" > Next< / a > () { < span class = "keywordflow" > return< / span > iteration_++ < max_iterations_; }< / div >
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< div class = "line" > < a name = "l00164" > < / a > < span class = "lineno" > 164< / span >   < / div >
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< div class = "line" > < a name = "l00165" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a61aed6a943277e531b904cfdc3616890" > 165< / a > < / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a61aed6a943277e531b904cfdc3616890" > GetStep< / a > ()< span class = "keyword" > const < / span > {< / div >
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< div class = "line" > < a name = "l00166" > < / a > < span class = "lineno" > 166< / span >   < span class = "keywordflow" > return< / span > (1.0 * (iteration_ - 1) * (2 * max_iterations_ - 5) /< / div >
< div class = "line" > < a name = "l00167" > < / a > < span class = "lineno" > 167< / span >   (2 * (max_iterations_ - 1))) *< / div >
< div class = "line" > < a name = "l00168" > < / a > < span class = "lineno" > 168< / span >   step1_ -< / div >
< div class = "line" > < a name = "l00169" > < / a > < span class = "lineno" > 169< / span >   (iteration_ - 2) * step1_ +< / div >
< div class = "line" > < a name = "l00170" > < / a > < span class = "lineno" > 170< / span >   (0.5 * (iteration_ - 1) * (iteration_ - 2) /< / div >
< div class = "line" > < a name = "l00171" > < / a > < span class = "lineno" > 171< / span >   ((max_iterations_ - 1) * (max_iterations_ - 2))) *< / div >
< div class = "line" > < a name = "l00172" > < / a > < span class = "lineno" > 172< / span >   step1_;< / div >
< div class = "line" > < a name = "l00173" > < / a > < span class = "lineno" > 173< / span >   }< / div >
< div class = "line" > < a name = "l00174" > < / a > < span class = "lineno" > 174< / span >   < / div >
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< div class = "line" > < a name = "l00175" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a33c2c5b8d838c77c2701a538f7f30ae4" > 175< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a33c2c5b8d838c77c2701a538f7f30ae4" > OnOneTree< / a > (CostType one_tree_cost, < span class = "keywordtype" > double< / span > w,< / div >
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< div class = "line" > < a name = "l00176" > < / a > < span class = "lineno" > 176< / span >   < span class = "keyword" > const< / span > std::vector< int> & degrees) {< / div >
< div class = "line" > < a name = "l00177" > < / a > < span class = "lineno" > 177< / span >   < span class = "keywordflow" > if< / span > (!step1_initialized_) {< / div >
< div class = "line" > < a name = "l00178" > < / a > < span class = "lineno" > 178< / span >   step1_initialized_ = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00179" > < / a > < span class = "lineno" > 179< / span >   UpdateStep(one_tree_cost);< / div >
< div class = "line" > < a name = "l00180" > < / a > < span class = "lineno" > 180< / span >   }< / div >
< div class = "line" > < a name = "l00181" > < / a > < span class = "lineno" > 181< / span >   }< / div >
< div class = "line" > < a name = "l00182" > < / a > < span class = "lineno" > 182< / span >   < / div >
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< div class = "line" > < a name = "l00183" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a2ad04ff9537d97fcabc58c86183890c3" > 183< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a2ad04ff9537d97fcabc58c86183890c3" > OnNewWMax< / a > (CostType one_tree_cost) { UpdateStep(one_tree_cost); }< / div >
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< div class = "line" > < a name = "l00184" > < / a > < span class = "lineno" > 184< / span >   < / div >
< div class = "line" > < a name = "l00185" > < / a > < span class = "lineno" > 185< / span >   < span class = "keyword" > private< / span > :< / div >
< div class = "line" > < a name = "l00186" > < / a > < span class = "lineno" > 186< / span >   < span class = "comment" > // Automatic computation of the number of iterations based on empirical< / span > < / div >
< div class = "line" > < a name = "l00187" > < / a > < span class = "lineno" > 187< / span >   < span class = "comment" > // results given in Valenzuela-Jones 1997.< / span > < / div >
< div class = "line" > < a name = "l00188" > < / a > < span class = "lineno" > 188< / span >   < span class = "keyword" > static< / span > < span class = "keywordtype" > int< / span > MaxIterations(< span class = "keywordtype" > int< / span > number_of_nodes) {< / div >
< div class = "line" > < a name = "l00189" > < / a > < span class = "lineno" > 189< / span >   < span class = "keywordflow" > return< / span > < span class = "keyword" > static_cast< < / span > < span class = "keywordtype" > int< / span > < span class = "keyword" > > < / span > (28 * std::pow(number_of_nodes, 0.62));< / div >
< div class = "line" > < a name = "l00190" > < / a > < span class = "lineno" > 190< / span >   }< / div >
< div class = "line" > < a name = "l00191" > < / a > < span class = "lineno" > 191< / span >   < / div >
< div class = "line" > < a name = "l00192" > < / a > < span class = "lineno" > 192< / span >   < span class = "keywordtype" > void< / span > UpdateStep(CostType one_tree_cost) {< / div >
< div class = "line" > < a name = "l00193" > < / a > < span class = "lineno" > 193< / span >   step1_ = one_tree_cost / (2 * number_of_nodes_);< / div >
< div class = "line" > < a name = "l00194" > < / a > < span class = "lineno" > 194< / span >   }< / div >
< div class = "line" > < a name = "l00195" > < / a > < span class = "lineno" > 195< / span >   < / div >
< div class = "line" > < a name = "l00196" > < / a > < span class = "lineno" > 196< / span >   < span class = "keywordtype" > bool< / span > step1_initialized_;< / div >
< div class = "line" > < a name = "l00197" > < / a > < span class = "lineno" > 197< / span >   < span class = "keywordtype" > double< / span > step1_;< / div >
< div class = "line" > < a name = "l00198" > < / a > < span class = "lineno" > 198< / span >   < span class = "keywordtype" > int< / span > iteration_;< / div >
< div class = "line" > < a name = "l00199" > < / a > < span class = "lineno" > 199< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > max_iterations_;< / div >
< div class = "line" > < a name = "l00200" > < / a > < span class = "lineno" > 200< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > number_of_nodes_;< / div >
< div class = "line" > < a name = "l00201" > < / a > < span class = "lineno" > 201< / span >   };< / div >
< div class = "line" > < a name = "l00202" > < / a > < span class = "lineno" > 202< / span >   < / div >
< div class = "line" > < a name = "l00203" > < / a > < span class = "lineno" > 203< / span >   < span class = "comment" > // Implementation of the Held-Wolfe-Crowder algorithm (see the comments at the< / span > < / div >
< div class = "line" > < a name = "l00204" > < / a > < span class = "lineno" > 204< / span >   < span class = "comment" > // head of the file for explanations).< / span > < / div >
< div class = "line" > < a name = "l00205" > < / a > < span class = "lineno" > 205< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostType, < span class = "keyword" > typename< / span > CostFunction> < / div >
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< div class = "line" > < a name = "l00206" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html" > 206< / a > < / span >   < span class = "keyword" > class < / span > < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html" > HeldWolfeCrowderEvaluator< / a > {< / div >
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< div class = "line" > < a name = "l00207" > < / a > < span class = "lineno" > 207< / span >   < span class = "keyword" > public< / span > :< / div >
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< div class = "line" > < a name = "l00208" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#adb1dee05e699715da68918f6b19d3e6d" > 208< / a > < / span >   < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#adb1dee05e699715da68918f6b19d3e6d" > HeldWolfeCrowderEvaluator< / a > (< span class = "keywordtype" > int< / span > number_of_nodes, < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > )< / div >
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< div class = "line" > < a name = "l00209" > < / a > < span class = "lineno" > 209< / span >   : iteration_(0),< / div >
< div class = "line" > < a name = "l00210" > < / a > < span class = "lineno" > 210< / span >   number_of_iterations_(2 * number_of_nodes),< / div >
< div class = "line" > < a name = "l00211" > < / a > < span class = "lineno" > 211< / span >   upper_bound_(0),< / div >
< div class = "line" > < a name = "l00212" > < / a > < span class = "lineno" > 212< / span >   lambda_(2.0),< / div >
< div class = "line" > < a name = "l00213" > < / a > < span class = "lineno" > 213< / span >   step_(0) {< / div >
< div class = "line" > < a name = "l00214" > < / a > < span class = "lineno" > 214< / span >   < span class = "comment" > // TODO(user): Improve upper bound with some local search; tighter upper< / span > < / div >
< div class = "line" > < a name = "l00215" > < / a > < span class = "lineno" > 215< / span >   < span class = "comment" > // bounds lead to faster convergence.< / span > < / div >
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< div class = "line" > < a name = "l00216" > < / a > < span class = "lineno" > 216< / span >   < a class = "code" href = "classoperations__research_1_1_christofides_path_solver.html" > ChristofidesPathSolver< CostType, int64_t, int, CostFunction> < / a > solver(< / div >
< div class = "line" > < a name = "l00217" > < / a > < span class = "lineno" > 217< / span >   number_of_nodes, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > );< / div >
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< div class = "line" > < a name = "l00218" > < / a > < span class = "lineno" > 218< / span >   upper_bound_ = solver.< a class = "code" href = "classoperations__research_1_1_christofides_path_solver.html#ab558649a26fef3a74f0909ef5af45e90" > TravelingSalesmanCost< / a > ();< / div >
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< div class = "line" > < a name = "l00219" > < / a > < span class = "lineno" > 219< / span >   }< / div >
< div class = "line" > < a name = "l00220" > < / a > < span class = "lineno" > 220< / span >   < / div >
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< div class = "line" > < a name = "l00221" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a3947d19ac087ef2cd68c2409920339c4" > 221< / a > < / span >   < span class = "keywordtype" > bool< / span > < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a3947d19ac087ef2cd68c2409920339c4" > Next< / a > () {< / div >
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< div class = "line" > < a name = "l00222" > < / a > < span class = "lineno" > 222< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > min_iterations = 2;< / div >
< div class = "line" > < a name = "l00223" > < / a > < span class = "lineno" > 223< / span >   < span class = "keywordflow" > if< / span > (iteration_ > = number_of_iterations_) {< / div >
< div class = "line" > < a name = "l00224" > < / a > < span class = "lineno" > 224< / span >   number_of_iterations_ /= 2;< / div >
< div class = "line" > < a name = "l00225" > < / a > < span class = "lineno" > 225< / span >   < span class = "keywordflow" > if< / span > (number_of_iterations_ < min_iterations) < span class = "keywordflow" > return< / span > < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a name = "l00226" > < / a > < span class = "lineno" > 226< / span >   iteration_ = 0;< / div >
< div class = "line" > < a name = "l00227" > < / a > < span class = "lineno" > 227< / span >   lambda_ /= 2;< / div >
< div class = "line" > < a name = "l00228" > < / a > < span class = "lineno" > 228< / span >   } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a name = "l00229" > < / a > < span class = "lineno" > 229< / span >   ++iteration_;< / div >
< div class = "line" > < a name = "l00230" > < / a > < span class = "lineno" > 230< / span >   }< / div >
< div class = "line" > < a name = "l00231" > < / a > < span class = "lineno" > 231< / span >   < span class = "keywordflow" > return< / span > < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a name = "l00232" > < / a > < span class = "lineno" > 232< / span >   }< / div >
< div class = "line" > < a name = "l00233" > < / a > < span class = "lineno" > 233< / span >   < / div >
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< div class = "line" > < a name = "l00234" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a61aed6a943277e531b904cfdc3616890" > 234< / a > < / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a61aed6a943277e531b904cfdc3616890" > GetStep< / a > ()< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > step_; }< / div >
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< div class = "line" > < a name = "l00235" > < / a > < span class = "lineno" > 235< / span >   < / div >
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< div class = "line" > < a name = "l00236" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a33c2c5b8d838c77c2701a538f7f30ae4" > 236< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a33c2c5b8d838c77c2701a538f7f30ae4" > OnOneTree< / a > (CostType one_tree_cost, < span class = "keywordtype" > double< / span > w,< / div >
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< div class = "line" > < a name = "l00237" > < / a > < span class = "lineno" > 237< / span >   < span class = "keyword" > const< / span > std::vector< int> & degrees) {< / div >
< div class = "line" > < a name = "l00238" > < / a > < span class = "lineno" > 238< / span >   < span class = "keywordtype" > double< / span > norm = 0;< / div >
< div class = "line" > < a name = "l00239" > < / a > < span class = "lineno" > 239< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > degree : degrees) {< / div >
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< div class = "line" > < a name = "l00240" > < / a > < span class = "lineno" > 240< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > < a class = "code" href = "resource_8cc.html#af12056bc2a8e3ec563f0940d87abbd2e" > delta< / a > = degree - 2;< / div >
< div class = "line" > < a name = "l00241" > < / a > < span class = "lineno" > 241< / span >   norm += < a class = "code" href = "resource_8cc.html#af12056bc2a8e3ec563f0940d87abbd2e" > delta< / a > * < a class = "code" href = "resource_8cc.html#af12056bc2a8e3ec563f0940d87abbd2e" > delta< / a > ;< / div >
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< div class = "line" > < a name = "l00242" > < / a > < span class = "lineno" > 242< / span >   }< / div >
< div class = "line" > < a name = "l00243" > < / a > < span class = "lineno" > 243< / span >   step_ = lambda_ * (upper_bound_ - w) / norm;< / div >
< div class = "line" > < a name = "l00244" > < / a > < span class = "lineno" > 244< / span >   }< / div >
< div class = "line" > < a name = "l00245" > < / a > < span class = "lineno" > 245< / span >   < / div >
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< div class = "line" > < a name = "l00246" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a2ad04ff9537d97fcabc58c86183890c3" > 246< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a2ad04ff9537d97fcabc58c86183890c3" > OnNewWMax< / a > (CostType one_tree_cost) {}< / div >
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< div class = "line" > < a name = "l00247" > < / a > < span class = "lineno" > 247< / span >   < / div >
< div class = "line" > < a name = "l00248" > < / a > < span class = "lineno" > 248< / span >   < span class = "keyword" > private< / span > :< / div >
< div class = "line" > < a name = "l00249" > < / a > < span class = "lineno" > 249< / span >   < span class = "keywordtype" > int< / span > iteration_;< / div >
< div class = "line" > < a name = "l00250" > < / a > < span class = "lineno" > 250< / span >   < span class = "keywordtype" > int< / span > number_of_iterations_;< / div >
< div class = "line" > < a name = "l00251" > < / a > < span class = "lineno" > 251< / span >   CostType upper_bound_;< / div >
< div class = "line" > < a name = "l00252" > < / a > < span class = "lineno" > 252< / span >   < span class = "keywordtype" > double< / span > lambda_;< / div >
< div class = "line" > < a name = "l00253" > < / a > < span class = "lineno" > 253< / span >   < span class = "keywordtype" > double< / span > step_;< / div >
< div class = "line" > < a name = "l00254" > < / a > < span class = "lineno" > 254< / span >   };< / div >
< div class = "line" > < a name = "l00255" > < / a > < span class = "lineno" > 255< / span >   < / div >
< div class = "line" > < a name = "l00256" > < / a > < span class = "lineno" > 256< / span >   < span class = "comment" > // Computes the nearest neighbors of each node for the given cost function.< / span > < / div >
< div class = "line" > < a name = "l00257" > < / a > < span class = "lineno" > 257< / span >   < span class = "comment" > // The ith element of the returned vector contains the indices of the nearest< / span > < / div >
< div class = "line" > < a name = "l00258" > < / a > < span class = "lineno" > 258< / span >   < span class = "comment" > // nodes to node i. Note that these indices contain the number_of_neighbors< / span > < / div >
< div class = "line" > < a name = "l00259" > < / a > < span class = "lineno" > 259< / span >   < span class = "comment" > // nearest neighbors as well as all the nodes for which i is a nearest< / span > < / div >
< div class = "line" > < a name = "l00260" > < / a > < span class = "lineno" > 260< / span >   < span class = "comment" > // neighbor.< / span > < / div >
< div class = "line" > < a name = "l00261" > < / a > < span class = "lineno" > 261< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00262" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a078701f3ce8570abe24e8157029c8abf" > 262< / a > < / span >   std::set< std::pair< int, int> > < a class = "code" href = "namespaceoperations__research.html#a078701f3ce8570abe24e8157029c8abf" > NearestNeighbors< / a > (< span class = "keywordtype" > int< / span > number_of_nodes,< / div >
< div class = "line" > < a name = "l00263" > < / a > < span class = "lineno" > 263< / span >   < span class = "keywordtype" > int< / span > number_of_neighbors,< / div >
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< div class = "line" > < a name = "l00264" > < / a > < span class = "lineno" > 264< / span >   < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ) {< / div >
< div class = "line" > < a name = "l00265" > < / a > < span class = "lineno" > 265< / span >   < span class = "keyword" > using< / span > CostType = decltype(< a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (0, 0));< / div >
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< div class = "line" > < a name = "l00266" > < / a > < span class = "lineno" > 266< / span >   std::set< std::pair< int, int> > nearest;< / div >
< div class = "line" > < a name = "l00267" > < / a > < span class = "lineno" > 267< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > i = 0; i < number_of_nodes; ++i) {< / div >
< div class = "line" > < a name = "l00268" > < / a > < span class = "lineno" > 268< / span >   std::vector< std::pair< CostType, int> > neighbors;< / div >
< div class = "line" > < a name = "l00269" > < / a > < span class = "lineno" > 269< / span >   neighbors.reserve(number_of_nodes - 1);< / div >
< div class = "line" > < a name = "l00270" > < / a > < span class = "lineno" > 270< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > j = 0; j < number_of_nodes; ++j) {< / div >
< div class = "line" > < a name = "l00271" > < / a > < span class = "lineno" > 271< / span >   < span class = "keywordflow" > if< / span > (i != j) {< / div >
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< div class = "line" > < a name = "l00272" > < / a > < span class = "lineno" > 272< / span >   neighbors.emplace_back(< a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (i, j), j);< / div >
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< div class = "line" > < a name = "l00273" > < / a > < span class = "lineno" > 273< / span >   }< / div >
< div class = "line" > < a name = "l00274" > < / a > < span class = "lineno" > 274< / span >   }< / div >
< div class = "line" > < a name = "l00275" > < / a > < span class = "lineno" > 275< / span >   < span class = "keywordtype" > int< / span > size = neighbors.size();< / div >
< div class = "line" > < a name = "l00276" > < / a > < span class = "lineno" > 276< / span >   < span class = "keywordflow" > if< / span > (number_of_neighbors < size) {< / div >
< div class = "line" > < a name = "l00277" > < / a > < span class = "lineno" > 277< / span >   std::nth_element(neighbors.begin(),< / div >
< div class = "line" > < a name = "l00278" > < / a > < span class = "lineno" > 278< / span >   neighbors.begin() + number_of_neighbors - 1,< / div >
< div class = "line" > < a name = "l00279" > < / a > < span class = "lineno" > 279< / span >   neighbors.end());< / div >
< div class = "line" > < a name = "l00280" > < / a > < span class = "lineno" > 280< / span >   size = number_of_neighbors;< / div >
< div class = "line" > < a name = "l00281" > < / a > < span class = "lineno" > 281< / span >   }< / div >
< div class = "line" > < a name = "l00282" > < / a > < span class = "lineno" > 282< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > j = 0; j < size; ++j) {< / div >
< div class = "line" > < a name = "l00283" > < / a > < span class = "lineno" > 283< / span >   nearest.insert({i, neighbors[j].second});< / div >
< div class = "line" > < a name = "l00284" > < / a > < span class = "lineno" > 284< / span >   nearest.insert({neighbors[j].second, i});< / div >
< div class = "line" > < a name = "l00285" > < / a > < span class = "lineno" > 285< / span >   }< / div >
< div class = "line" > < a name = "l00286" > < / a > < span class = "lineno" > 286< / span >   }< / div >
< div class = "line" > < a name = "l00287" > < / a > < span class = "lineno" > 287< / span >   < span class = "keywordflow" > return< / span > nearest;< / div >
< div class = "line" > < a name = "l00288" > < / a > < span class = "lineno" > 288< / span >   }< / div >
< div class = "line" > < a name = "l00289" > < / a > < span class = "lineno" > 289< / span >   < / div >
< div class = "line" > < a name = "l00290" > < / a > < span class = "lineno" > 290< / span >   < span class = "comment" > // Let G be the complete graph on nodes in [0, number_of_nodes - 1]. Adds arcs< / span > < / div >
< div class = "line" > < a name = "l00291" > < / a > < span class = "lineno" > 291< / span >   < span class = "comment" > // from the minimum spanning tree of G to the arcs set argument.< / span > < / div >
< div class = "line" > < a name = "l00292" > < / a > < span class = "lineno" > 292< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00293" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#adfc52ee652f25f3a2f249ffb830f2e8a" > 293< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "namespaceoperations__research.html#adfc52ee652f25f3a2f249ffb830f2e8a" > AddArcsFromMinimumSpanningTree< / a > (< span class = "keywordtype" > int< / span > number_of_nodes,< / div >
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< div class = "line" > < a name = "l00294" > < / a > < span class = "lineno" > 294< / span >   < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ,< / div >
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< div class = "line" > < a name = "l00295" > < / a > < span class = "lineno" > 295< / span >   std::set< std::pair< int, int> > * arcs) {< / div >
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< div class = "line" > < a name = "l00296" > < / a > < span class = "lineno" > 296< / span >   < a class = "code" href = "classutil_1_1_complete_graph.html" > util::CompleteGraph< int, int> < / a > graph(number_of_nodes);< / div >
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< div class = "line" > < a name = "l00297" > < / a > < span class = "lineno" > 297< / span >   < span class = "keyword" > const< / span > std::vector< int> mst =< / div >
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< div class = "line" > < a name = "l00298" > < / a > < span class = "lineno" > 298< / span >   < a class = "code" href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > BuildPrimMinimumSpanningTree< / a > (graph, [& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , & graph](< span class = "keywordtype" > int< / span > arc) {< / div >
< div class = "line" > < a name = "l00299" > < / a > < span class = "lineno" > 299< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (graph.< a class = "code" href = "classutil_1_1_complete_graph.html#a2eeae3a8497dc3942e3db3128a10d41c" > Tail< / a > (arc), graph.< a class = "code" href = "classutil_1_1_complete_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955" > Head< / a > (arc));< / div >
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< div class = "line" > < a name = "l00300" > < / a > < span class = "lineno" > 300< / span >   });< / div >
< div class = "line" > < a name = "l00301" > < / a > < span class = "lineno" > 301< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > arc : mst) {< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00302" > < / a > < span class = "lineno" > 302< / span >   arcs-> insert({graph.< a class = "code" href = "classutil_1_1_complete_graph.html#a2eeae3a8497dc3942e3db3128a10d41c" > Tail< / a > (arc), graph.< a class = "code" href = "classutil_1_1_complete_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955" > Head< / a > (arc)});< / div >
< div class = "line" > < a name = "l00303" > < / a > < span class = "lineno" > 303< / span >   arcs-> insert({graph.< a class = "code" href = "classutil_1_1_complete_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955" > Head< / a > (arc), graph.< a class = "code" href = "classutil_1_1_complete_graph.html#a2eeae3a8497dc3942e3db3128a10d41c" > Tail< / a > (arc)});< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00304" > < / a > < span class = "lineno" > 304< / span >   }< / div >
< div class = "line" > < a name = "l00305" > < / a > < span class = "lineno" > 305< / span >   }< / div >
< div class = "line" > < a name = "l00306" > < / a > < span class = "lineno" > 306< / span >   < / div >
< div class = "line" > < a name = "l00307" > < / a > < span class = "lineno" > 307< / span >   < span class = "comment" > // Returns the index of the node in graph which minimizes cost(node, source)< / span > < / div >
< div class = "line" > < a name = "l00308" > < / a > < span class = "lineno" > 308< / span >   < span class = "comment" > // with the constraint that accept(node) is true.< / span > < / div >
< div class = "line" > < a name = "l00309" > < / a > < span class = "lineno" > 309< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction, < span class = "keyword" > typename< / span > GraphType, < span class = "keyword" > typename< / span > AcceptFunction> < / div >
< div class = "line" > < a name = "l00310" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aeae6cf89ac4d73d2e95cffaa0edbd687" > 310< / a > < / span >   < span class = "keywordtype" > int< / span > < a class = "code" href = "namespaceoperations__research.html#aeae6cf89ac4d73d2e95cffaa0edbd687" > GetNodeMinimizingEdgeCostToSource< / a > (< span class = "keyword" > const< / span > GraphType& graph, < span class = "keywordtype" > int< / span > source,< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00311" > < / a > < span class = "lineno" > 311< / span >   < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ,< / div >
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< div class = "line" > < a name = "l00312" > < / a > < span class = "lineno" > 312< / span >   AcceptFunction accept) {< / div >
< div class = "line" > < a name = "l00313" > < / a > < span class = "lineno" > 313< / span >   < span class = "keywordtype" > int< / span > best_node = -1;< / div >
< div class = "line" > < a name = "l00314" > < / a > < span class = "lineno" > 314< / span >   < span class = "keywordtype" > double< / span > best_edge_cost = 0;< / div >
< div class = "line" > < a name = "l00315" > < / a > < span class = "lineno" > 315< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > node : graph.AllNodes()) {< / div >
< div class = "line" > < a name = "l00316" > < / a > < span class = "lineno" > 316< / span >   < span class = "keywordflow" > if< / span > (accept(node)) {< / div >
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< div class = "line" > < a name = "l00317" > < / a > < span class = "lineno" > 317< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > edge_cost = < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (node, source);< / div >
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< div class = "line" > < a name = "l00318" > < / a > < span class = "lineno" > 318< / span >   < span class = "keywordflow" > if< / span > (best_node == -1 || edge_cost < best_edge_cost) {< / div >
< div class = "line" > < a name = "l00319" > < / a > < span class = "lineno" > 319< / span >   best_node = node;< / div >
< div class = "line" > < a name = "l00320" > < / a > < span class = "lineno" > 320< / span >   best_edge_cost = edge_cost;< / div >
< div class = "line" > < a name = "l00321" > < / a > < span class = "lineno" > 321< / span >   }< / div >
< div class = "line" > < a name = "l00322" > < / a > < span class = "lineno" > 322< / span >   }< / div >
< div class = "line" > < a name = "l00323" > < / a > < span class = "lineno" > 323< / span >   }< / div >
< div class = "line" > < a name = "l00324" > < / a > < span class = "lineno" > 324< / span >   < span class = "keywordflow" > return< / span > best_node;< / div >
< div class = "line" > < a name = "l00325" > < / a > < span class = "lineno" > 325< / span >   }< / div >
< div class = "line" > < a name = "l00326" > < / a > < span class = "lineno" > 326< / span >   < / div >
< div class = "line" > < a name = "l00327" > < / a > < span class = "lineno" > 327< / span >   < span class = "comment" > // Computes a 1-tree for the given graph, cost function and node weights.< / span > < / div >
< div class = "line" > < a name = "l00328" > < / a > < span class = "lineno" > 328< / span >   < span class = "comment" > // Returns the degree of each node in the 1-tree and the un-weighed cost of the< / span > < / div >
< div class = "line" > < a name = "l00329" > < / a > < span class = "lineno" > 329< / span >   < span class = "comment" > // 1-tree.< / span > < / div >
< div class = "line" > < a name = "l00330" > < / a > < span class = "lineno" > 330< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction, < span class = "keyword" > typename< / span > GraphType, < span class = "keyword" > typename< / span > CostType> < / div >
< div class = "line" > < a name = "l00331" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#aa29730f0377a3408590f4e621af966eb" > 331< / a > < / span >   std::vector< int> < a class = "code" href = "namespaceoperations__research.html#aa29730f0377a3408590f4e621af966eb" > ComputeOneTree< / a > (< span class = "keyword" > const< / span > GraphType& graph,< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00332" > < / a > < span class = "lineno" > 332< / span >   < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ,< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00333" > < / a > < span class = "lineno" > 333< / span >   < span class = "keyword" > const< / span > std::vector< double> & weights,< / div >
< div class = "line" > < a name = "l00334" > < / a > < span class = "lineno" > 334< / span >   < span class = "keyword" > const< / span > std::vector< int> & sorted_arcs,< / div >
< div class = "line" > < a name = "l00335" > < / a > < span class = "lineno" > 335< / span >   CostType* one_tree_cost) {< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00336" > < / a > < span class = "lineno" > 336< / span >   < span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > weighed_cost = [& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , & weights](< span class = "keywordtype" > int< / span > from, < span class = "keywordtype" > int< / span > to) {< / div >
< div class = "line" > < a name = "l00337" > < / a > < span class = "lineno" > 337< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (from, to) + weights[from] + weights[to];< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00338" > < / a > < span class = "lineno" > 338< / span >   };< / div >
< div class = "line" > < a name = "l00339" > < / a > < span class = "lineno" > 339< / span >   < span class = "comment" > // Compute MST on graph.< / span > < / div >
< div class = "line" > < a name = "l00340" > < / a > < span class = "lineno" > 340< / span >   std::vector< int> mst;< / div >
< div class = "line" > < a name = "l00341" > < / a > < span class = "lineno" > 341< / span >   < span class = "keywordflow" > if< / span > (!sorted_arcs.empty()) {< / div >
< div class = "line" > < a name = "l00342" > < / a > < span class = "lineno" > 342< / span >   mst = BuildKruskalMinimumSpanningTreeFromSortedArcs< GraphType> (graph,< / div >
< div class = "line" > < a name = "l00343" > < / a > < span class = "lineno" > 343< / span >   sorted_arcs);< / div >
< div class = "line" > < a name = "l00344" > < / a > < span class = "lineno" > 344< / span >   } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a name = "l00345" > < / a > < span class = "lineno" > 345< / span >   mst = BuildPrimMinimumSpanningTree< GraphType> (< / div >
< div class = "line" > < a name = "l00346" > < / a > < span class = "lineno" > 346< / span >   graph, [& weighed_cost, & graph](< span class = "keywordtype" > int< / span > arc) {< / div >
< div class = "line" > < a name = "l00347" > < / a > < span class = "lineno" > 347< / span >   < span class = "keywordflow" > return< / span > weighed_cost(graph.Tail(arc), graph.Head(arc));< / div >
< div class = "line" > < a name = "l00348" > < / a > < span class = "lineno" > 348< / span >   });< / div >
< div class = "line" > < a name = "l00349" > < / a > < span class = "lineno" > 349< / span >   }< / div >
< div class = "line" > < a name = "l00350" > < / a > < span class = "lineno" > 350< / span >   std::vector< int> degrees(graph.num_nodes() + 1, 0);< / div >
< div class = "line" > < a name = "l00351" > < / a > < span class = "lineno" > 351< / span >   *one_tree_cost = 0;< / div >
< div class = "line" > < a name = "l00352" > < / a > < span class = "lineno" > 352< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > arc : mst) {< / div >
< div class = "line" > < a name = "l00353" > < / a > < span class = "lineno" > 353< / span >   degrees[graph.Head(arc)]++;< / div >
< div class = "line" > < a name = "l00354" > < / a > < span class = "lineno" > 354< / span >   degrees[graph.Tail(arc)]++;< / div >
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< div class = "line" > < a name = "l00355" > < / a > < span class = "lineno" > 355< / span >   *one_tree_cost += < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (graph.Tail(arc), graph.Head(arc));< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00356" > < / a > < span class = "lineno" > 356< / span >   }< / div >
< div class = "line" > < a name = "l00357" > < / a > < span class = "lineno" > 357< / span >   < span class = "comment" > // Add 2 cheapest edges from the nodes in the graph to the extra node not in< / span > < / div >
< div class = "line" > < a name = "l00358" > < / a > < span class = "lineno" > 358< / span >   < span class = "comment" > // the graph.< / span > < / div >
< div class = "line" > < a name = "l00359" > < / a > < span class = "lineno" > 359< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > extra_node = graph.num_nodes();< / div >
< div class = "line" > < a name = "l00360" > < / a > < span class = "lineno" > 360< / span >   < span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > update_one_tree = [extra_node, one_tree_cost, & degrees,< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00361" > < / a > < span class = "lineno" > 361< / span >   & < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ](< span class = "keywordtype" > int< / span > node) {< / div >
< div class = "line" > < a name = "l00362" > < / a > < span class = "lineno" > 362< / span >   *one_tree_cost += < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (node, extra_node);< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00363" > < / a > < span class = "lineno" > 363< / span >   degrees.back()++;< / div >
< div class = "line" > < a name = "l00364" > < / a > < span class = "lineno" > 364< / span >   degrees[node]++;< / div >
< div class = "line" > < a name = "l00365" > < / a > < span class = "lineno" > 365< / span >   };< / div >
< div class = "line" > < a name = "l00366" > < / a > < span class = "lineno" > 366< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > node = < a class = "code" href = "namespaceoperations__research.html#aeae6cf89ac4d73d2e95cffaa0edbd687" > GetNodeMinimizingEdgeCostToSource< / a > (< / div >
< div class = "line" > < a name = "l00367" > < / a > < span class = "lineno" > 367< / span >   graph, extra_node, weighed_cost,< / div >
< div class = "line" > < a name = "l00368" > < / a > < span class = "lineno" > 368< / span >   [extra_node](< span class = "keywordtype" > int< / span > n) { < span class = "keywordflow" > return< / span > n != extra_node; });< / div >
< div class = "line" > < a name = "l00369" > < / a > < span class = "lineno" > 369< / span >   update_one_tree(node);< / div >
< div class = "line" > < a name = "l00370" > < / a > < span class = "lineno" > 370< / span >   update_one_tree(< a class = "code" href = "namespaceoperations__research.html#aeae6cf89ac4d73d2e95cffaa0edbd687" > GetNodeMinimizingEdgeCostToSource< / a > (< / div >
< div class = "line" > < a name = "l00371" > < / a > < span class = "lineno" > 371< / span >   graph, extra_node, weighed_cost,< / div >
< div class = "line" > < a name = "l00372" > < / a > < span class = "lineno" > 372< / span >   [extra_node, node](< span class = "keywordtype" > int< / span > n) { < span class = "keywordflow" > return< / span > n != extra_node & & n != node; }));< / div >
< div class = "line" > < a name = "l00373" > < / a > < span class = "lineno" > 373< / span >   < span class = "keywordflow" > return< / span > degrees;< / div >
< div class = "line" > < a name = "l00374" > < / a > < span class = "lineno" > 374< / span >   }< / div >
< div class = "line" > < a name = "l00375" > < / a > < span class = "lineno" > 375< / span >   < / div >
< div class = "line" > < a name = "l00376" > < / a > < span class = "lineno" > 376< / span >   < span class = "comment" > // Computes the lower bound of a TSP using a given subgradient algorithm.< / span > < / div >
< div class = "line" > < a name = "l00377" > < / a > < span class = "lineno" > 377< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction, < span class = "keyword" > typename< / span > Algorithm> < / div >
< div class = "line" > < a name = "l00378" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a3ed3d609fa06ad508b3d21119f94a560" > 378< / a > < / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "namespaceoperations__research.html#a3ed3d609fa06ad508b3d21119f94a560" > ComputeOneTreeLowerBoundWithAlgorithm< / a > (< span class = "keywordtype" > int< / span > number_of_nodes,< / div >
< div class = "line" > < a name = "l00379" > < / a > < span class = "lineno" > 379< / span >   < span class = "keywordtype" > int< / span > nearest_neighbors,< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00380" > < / a > < span class = "lineno" > 380< / span >   < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ,< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00381" > < / a > < span class = "lineno" > 381< / span >   Algorithm* algorithm) {< / div >
< div class = "line" > < a name = "l00382" > < / a > < span class = "lineno" > 382< / span >   < span class = "keywordflow" > if< / span > (number_of_nodes < 2) < span class = "keywordflow" > return< / span > 0;< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00383" > < / a > < span class = "lineno" > 383< / span >   < span class = "keywordflow" > if< / span > (number_of_nodes == 2) < span class = "keywordflow" > return< / span > < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (0, 1) + < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (1, 0);< / div >
< div class = "line" > < a name = "l00384" > < / a > < span class = "lineno" > 384< / span >   < span class = "keyword" > using< / span > CostType = decltype(< a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (0, 0));< / div >
< div class = "line" > < a name = "l00385" > < / a > < span class = "lineno" > 385< / span >   < span class = "keyword" > auto< / span > nearest = < a class = "code" href = "namespaceoperations__research.html#a078701f3ce8570abe24e8157029c8abf" > NearestNeighbors< / a > (number_of_nodes - 1, nearest_neighbors, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > );< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00386" > < / a > < span class = "lineno" > 386< / span >   < span class = "comment" > // Ensure nearest arcs result in a connected graph by adding arcs from the< / span > < / div >
< div class = "line" > < a name = "l00387" > < / a > < span class = "lineno" > 387< / span >   < span class = "comment" > // minimum spanning tree; this will add arcs which are likely to be " good" < / span > < / div >
< div class = "line" > < a name = "l00388" > < / a > < span class = "lineno" > 388< / span >   < span class = "comment" > // 1-tree arcs.< / span > < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00389" > < / a > < span class = "lineno" > 389< / span >   < a class = "code" href = "namespaceoperations__research.html#adfc52ee652f25f3a2f249ffb830f2e8a" > AddArcsFromMinimumSpanningTree< / a > (number_of_nodes - 1, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , & nearest);< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00390" > < / a > < span class = "lineno" > 390< / span >   < a class = "code" href = "classutil_1_1_list_graph.html" > util::ListGraph< int, int> < / a > graph(number_of_nodes - 1, nearest.size());< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00391" > < / a > < span class = "lineno" > 391< / span >   < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < span class = "keyword" > auto< / span > & arc : nearest) {< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00392" > < / a > < span class = "lineno" > 392< / span >   graph.< a class = "code" href = "classutil_1_1_list_graph.html#a7b505ba4a01bce342d049f5a8674da72" > AddArc< / a > (arc.first, arc.second);< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00393" > < / a > < span class = "lineno" > 393< / span >   }< / div >
< div class = "line" > < a name = "l00394" > < / a > < span class = "lineno" > 394< / span >   std::vector< double> weights(number_of_nodes, 0);< / div >
< div class = "line" > < a name = "l00395" > < / a > < span class = "lineno" > 395< / span >   std::vector< double> best_weights(number_of_nodes, 0);< / div >
< div class = "line" > < a name = "l00396" > < / a > < span class = "lineno" > 396< / span >   < span class = "keywordtype" > double< / span > max_w = -std::numeric_limits< double> ::infinity();< / div >
< div class = "line" > < a name = "l00397" > < / a > < span class = "lineno" > 397< / span >   < span class = "keywordtype" > double< / span > w = 0;< / div >
< div class = "line" > < a name = "l00398" > < / a > < span class = "lineno" > 398< / span >   < span class = "comment" > // Iteratively compute lower bound using a partial graph.< / span > < / div >
< div class = "line" > < a name = "l00399" > < / a > < span class = "lineno" > 399< / span >   < span class = "keywordflow" > while< / span > (algorithm-> Next()) {< / div >
< div class = "line" > < a name = "l00400" > < / a > < span class = "lineno" > 400< / span >   CostType one_tree_cost = 0;< / div >
< div class = "line" > < a name = "l00401" > < / a > < span class = "lineno" > 401< / span >   < span class = "keyword" > const< / span > std::vector< int> degrees =< / div >
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< div class = "line" > < a name = "l00402" > < / a > < span class = "lineno" > 402< / span >   < a class = "code" href = "namespaceoperations__research.html#aa29730f0377a3408590f4e621af966eb" > ComputeOneTree< / a > (graph, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , weights, {}, & one_tree_cost);< / div >
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< div class = "line" > < a name = "l00403" > < / a > < span class = "lineno" > 403< / span >   algorithm-> OnOneTree(one_tree_cost, w, degrees);< / div >
< div class = "line" > < a name = "l00404" > < / a > < span class = "lineno" > 404< / span >   w = one_tree_cost;< / div >
< div class = "line" > < a name = "l00405" > < / a > < span class = "lineno" > 405< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > j = 0; j < number_of_nodes; ++j) {< / div >
< div class = "line" > < a name = "l00406" > < / a > < span class = "lineno" > 406< / span >   w += weights[j] * (degrees[j] - 2);< / div >
< div class = "line" > < a name = "l00407" > < / a > < span class = "lineno" > 407< / span >   }< / div >
< div class = "line" > < a name = "l00408" > < / a > < span class = "lineno" > 408< / span >   < span class = "keywordflow" > if< / span > (w > max_w) {< / div >
< div class = "line" > < a name = "l00409" > < / a > < span class = "lineno" > 409< / span >   max_w = w;< / div >
< div class = "line" > < a name = "l00410" > < / a > < span class = "lineno" > 410< / span >   best_weights = weights;< / div >
< div class = "line" > < a name = "l00411" > < / a > < span class = "lineno" > 411< / span >   algorithm-> OnNewWMax(one_tree_cost);< / div >
< div class = "line" > < a name = "l00412" > < / a > < span class = "lineno" > 412< / span >   }< / div >
< div class = "line" > < a name = "l00413" > < / a > < span class = "lineno" > 413< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > step = algorithm-> GetStep();< / div >
< div class = "line" > < a name = "l00414" > < / a > < span class = "lineno" > 414< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > j = 0; j < number_of_nodes; ++j) {< / div >
< div class = "line" > < a name = "l00415" > < / a > < span class = "lineno" > 415< / span >   weights[j] += step * (degrees[j] - 2);< / div >
< div class = "line" > < a name = "l00416" > < / a > < span class = "lineno" > 416< / span >   }< / div >
< div class = "line" > < a name = "l00417" > < / a > < span class = "lineno" > 417< / span >   }< / div >
< div class = "line" > < a name = "l00418" > < / a > < span class = "lineno" > 418< / span >   < span class = "comment" > // Compute lower bound using the complete graph on the best weights. This is< / span > < / div >
< div class = "line" > < a name = "l00419" > < / a > < span class = "lineno" > 419< / span >   < span class = "comment" > // necessary as the MSTs computed on nearest neighbors is not guaranteed to< / span > < / div >
< div class = "line" > < a name = "l00420" > < / a > < span class = "lineno" > 420< / span >   < span class = "comment" > // lead to a lower bound.< / span > < / div >
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< div class = "line" > < a name = "l00421" > < / a > < span class = "lineno" > 421< / span >   < a class = "code" href = "classutil_1_1_complete_graph.html" > util::CompleteGraph< int, int> < / a > complete_graph(number_of_nodes - 1);< / div >
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< div class = "line" > < a name = "l00422" > < / a > < span class = "lineno" > 422< / span >   CostType one_tree_cost = 0;< / div >
< div class = "line" > < a name = "l00423" > < / a > < span class = "lineno" > 423< / span >   < span class = "comment" > // TODO(user): We are not caching here since this would take O(n^2) memory;< / span > < / div >
< div class = "line" > < a name = "l00424" > < / a > < span class = "lineno" > 424< / span >   < span class = "comment" > // however the Kruskal algorithm will expand all arcs also consuming O(n^2)< / span > < / div >
< div class = "line" > < a name = "l00425" > < / a > < span class = "lineno" > 425< / span >   < span class = "comment" > // memory; investigate alternatives to expanding all arcs (Prim' s algorithm).< / span > < / div >
< div class = "line" > < a name = "l00426" > < / a > < span class = "lineno" > 426< / span >   < span class = "keyword" > const< / span > std::vector< int> degrees =< / div >
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< div class = "line" > < a name = "l00427" > < / a > < span class = "lineno" > 427< / span >   < a class = "code" href = "namespaceoperations__research.html#aa29730f0377a3408590f4e621af966eb" > ComputeOneTree< / a > (complete_graph, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , best_weights, {}, & one_tree_cost);< / div >
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< div class = "line" > < a name = "l00428" > < / a > < span class = "lineno" > 428< / span >   w = one_tree_cost;< / div >
< div class = "line" > < a name = "l00429" > < / a > < span class = "lineno" > 429< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > j = 0; j < number_of_nodes; ++j) {< / div >
< div class = "line" > < a name = "l00430" > < / a > < span class = "lineno" > 430< / span >   w += best_weights[j] * (degrees[j] - 2);< / div >
< div class = "line" > < a name = "l00431" > < / a > < span class = "lineno" > 431< / span >   }< / div >
< div class = "line" > < a name = "l00432" > < / a > < span class = "lineno" > 432< / span >   < span class = "keywordflow" > return< / span > w;< / div >
< div class = "line" > < a name = "l00433" > < / a > < span class = "lineno" > 433< / span >   }< / div >
< div class = "line" > < a name = "l00434" > < / a > < span class = "lineno" > 434< / span >   < / div >
< div class = "line" > < a name = "l00435" > < / a > < span class = "lineno" > 435< / span >   < span class = "comment" > // Parameters to configure the computation of the TSP lower bound.< / span > < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00436" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html" > 436< / a > < / span >   < span class = "keyword" > struct < / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html" > TravelingSalesmanLowerBoundParameters< / a > {< / div >
< div class = "line" > < a name = "l00437" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691" > 437< / a > < / span >   < span class = "keyword" > enum< / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691" > Algorithm< / a > {< / div >
< div class = "line" > < a name = "l00438" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691a324779d0e6f33b00553606d001821935" > 438< / a > < / span >   < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691a324779d0e6f33b00553606d001821935" > VolgenantJonker< / a > ,< / div >
< div class = "line" > < a name = "l00439" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691aab5026cdecee6d30b78813ed209bbba3" > 439< / a > < / span >   < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691aab5026cdecee6d30b78813ed209bbba3" > HeldWolfeCrowder< / a > ,< / div >
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< div class = "line" > < a name = "l00440" > < / a > < span class = "lineno" > 440< / span >   };< / div >
< div class = "line" > < a name = "l00441" > < / a > < span class = "lineno" > 441< / span >   < span class = "comment" > // Subgradient algorithm to use to compute the TSP lower bound.< / span > < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00442" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#acc4ba09a6333be056db50ed15007518c" > 442< / a > < / span >   < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691" > Algorithm< / a > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#acc4ba09a6333be056db50ed15007518c" > algorithm< / a > = < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691a324779d0e6f33b00553606d001821935" > VolgenantJonker< / a > ;< / div >
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< div class = "line" > < a name = "l00443" > < / a > < span class = "lineno" > 443< / span >   < span class = "comment" > // Number of iterations to use in the Volgenant-Jonker algorithm. Overrides< / span > < / div >
< div class = "line" > < a name = "l00444" > < / a > < span class = "lineno" > 444< / span >   < span class = "comment" > // automatic iteration computation if positive.< / span > < / div >
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< div class = "line" > < a name = "l00445" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#aa5624a1c87ea6c30028af3168aa6daf9" > 445< / a > < / span >   < span class = "keywordtype" > int< / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#aa5624a1c87ea6c30028af3168aa6daf9" > volgenant_jonker_iterations< / a > = 0;< / div >
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< div class = "line" > < a name = "l00446" > < / a > < span class = "lineno" > 446< / span >   < span class = "comment" > // Number of nearest neighbors to consider in the miminum spanning trees.< / span > < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00447" > < / a > < span class = "lineno" > < a class = "line" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#ac0c01b0297a60d1b72ac046280057e20" > 447< / a > < / span >   < span class = "keywordtype" > int< / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#ac0c01b0297a60d1b72ac046280057e20" > nearest_neighbors< / a > = 40;< / div >
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< div class = "line" > < a name = "l00448" > < / a > < span class = "lineno" > 448< / span >   };< / div >
< div class = "line" > < a name = "l00449" > < / a > < span class = "lineno" > 449< / span >   < / div >
< div class = "line" > < a name = "l00450" > < / a > < span class = "lineno" > 450< / span >   < span class = "comment" > // Computes the lower bound of a TSP using given parameters.< / span > < / div >
< div class = "line" > < a name = "l00451" > < / a > < span class = "lineno" > 451< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction> < / div >
< div class = "line" > < a name = "l00452" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#a516a7ec8626d689aa84729fb6f358f89" > 452< / a > < / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "namespaceoperations__research.html#a516a7ec8626d689aa84729fb6f358f89" > ComputeOneTreeLowerBoundWithParameters< / a > (< / div >
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< div class = "line" > < a name = "l00453" > < / a > < span class = "lineno" > 453< / span >   < span class = "keywordtype" > int< / span > number_of_nodes, < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ,< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00454" > < / a > < span class = "lineno" > 454< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html" > TravelingSalesmanLowerBoundParameters< / a > & < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > ) {< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00455" > < / a > < span class = "lineno" > 455< / span >   < span class = "keyword" > using< / span > CostType = decltype(< a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > (0, 0));< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00456" > < / a > < span class = "lineno" > 456< / span >   < span class = "keywordflow" > switch< / span > (< a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > .algorithm) {< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00457" > < / a > < span class = "lineno" > 457< / span >   < span class = "keywordflow" > case< / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691a324779d0e6f33b00553606d001821935" > TravelingSalesmanLowerBoundParameters::VolgenantJonker< / a > : {< / div >
< div class = "line" > < a name = "l00458" > < / a > < span class = "lineno" > 458< / span >   < a class = "code" href = "classoperations__research_1_1_volgenant_jonker_evaluator.html" > VolgenantJonkerEvaluator< CostType> < / a > algorithm(< / div >
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< div class = "line" > < a name = "l00459" > < / a > < span class = "lineno" > 459< / span >   number_of_nodes, < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > .volgenant_jonker_iterations);< / div >
< div class = "line" > < a name = "l00460" > < / a > < span class = "lineno" > 460< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "namespaceoperations__research.html#a3ed3d609fa06ad508b3d21119f94a560" > ComputeOneTreeLowerBoundWithAlgorithm< / a > (< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00461" > < / a > < span class = "lineno" > 461< / span >   number_of_nodes, < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > .nearest_neighbors, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , & algorithm);< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00462" > < / a > < span class = "lineno" > 462< / span >   < span class = "keywordflow" > break< / span > ;< / div >
< div class = "line" > < a name = "l00463" > < / a > < span class = "lineno" > 463< / span >   }< / div >
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< div class = "line" > < a name = "l00464" > < / a > < span class = "lineno" > 464< / span >   < span class = "keywordflow" > case< / span > < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691aab5026cdecee6d30b78813ed209bbba3" > TravelingSalesmanLowerBoundParameters::HeldWolfeCrowder< / a > : {< / div >
< div class = "line" > < a name = "l00465" > < / a > < span class = "lineno" > 465< / span >   < a class = "code" href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html" > HeldWolfeCrowderEvaluator< CostType, CostFunction> < / a > algorithm(< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00466" > < / a > < span class = "lineno" > 466< / span >   number_of_nodes, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > );< / div >
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< div class = "line" > < a name = "l00467" > < / a > < span class = "lineno" > 467< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "namespaceoperations__research.html#a3ed3d609fa06ad508b3d21119f94a560" > ComputeOneTreeLowerBoundWithAlgorithm< / a > (< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00468" > < / a > < span class = "lineno" > 468< / span >   number_of_nodes, < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > .nearest_neighbors, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > , & algorithm);< / div >
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< div class = "line" > < a name = "l00469" > < / a > < span class = "lineno" > 469< / span >   }< / div >
< div class = "line" > < a name = "l00470" > < / a > < span class = "lineno" > 470< / span >   < span class = "keywordflow" > default< / span > :< / div >
2020-11-18 14:53:30 +01:00
< div class = "line" > < a name = "l00471" > < / a > < span class = "lineno" > 471< / span >   < a class = "code" href = "base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae" > LOG< / a > (< a class = "code" href = "log__severity_8h.html#ac9bcbe19995a8140cd4ec61773cd6e67" > ERROR< / a > ) < < < span class = "stringliteral" > " Unsupported algorithm: " < / span > < < < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > .algorithm;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00472" > < / a > < span class = "lineno" > 472< / span >   < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < a name = "l00473" > < / a > < span class = "lineno" > 473< / span >   }< / div >
< div class = "line" > < a name = "l00474" > < / a > < span class = "lineno" > 474< / span >   }< / div >
< div class = "line" > < a name = "l00475" > < / a > < span class = "lineno" > 475< / span >   < / div >
< div class = "line" > < a name = "l00476" > < / a > < span class = "lineno" > 476< / span >   < span class = "comment" > // Computes the lower bound of a TSP using default parameters (Volgenant-Jonker< / span > < / div >
< div class = "line" > < a name = "l00477" > < / a > < span class = "lineno" > 477< / span >   < span class = "comment" > // algorithm, 200 iterations and 40 nearest neighbors) which have turned out to< / span > < / div >
< div class = "line" > < a name = "l00478" > < / a > < span class = "lineno" > 478< / span >   < span class = "comment" > // give good results on the TSPLIB.< / span > < / div >
< div class = "line" > < a name = "l00479" > < / a > < span class = "lineno" > 479< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > CostFunction> < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00480" > < / a > < span class = "lineno" > < a class = "line" href = "namespaceoperations__research.html#ae9af26e7687cb65967941eb175148fe5" > 480< / a > < / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "namespaceoperations__research.html#ae9af26e7687cb65967941eb175148fe5" > ComputeOneTreeLowerBound< / a > (< span class = "keywordtype" > int< / span > number_of_nodes, < span class = "keyword" > const< / span > CostFunction& < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ) {< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00481" > < / a > < span class = "lineno" > 481< / span >   < a class = "code" href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html" > TravelingSalesmanLowerBoundParameters< / a > < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > ;< / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00482" > < / a > < span class = "lineno" > 482< / span >   < span class = "keywordflow" > return< / span > < a class = "code" href = "namespaceoperations__research.html#a516a7ec8626d689aa84729fb6f358f89" > ComputeOneTreeLowerBoundWithParameters< / a > (number_of_nodes, < a class = "code" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ,< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00483" > < / a > < span class = "lineno" > 483< / span >   < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > );< / div >
< div class = "line" > < a name = "l00484" > < / a > < span class = "lineno" > 484< / span >   }< / div >
< div class = "line" > < a name = "l00485" > < / a > < span class = "lineno" > 485< / span >   < / div >
< div class = "line" > < a name = "l00486" > < / a > < span class = "lineno" > 486< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00487" > < / a > < span class = "lineno" > 487< / span >   < / div >
2021-01-26 11:28:50 +01:00
< div class = "line" > < a name = "l00488" > < / a > < span class = "lineno" > 488< / span >   < span class = "preprocessor" > #endif < / span > < span class = "comment" > // OR_TOOLS_GRAPH_ONE_TREE_LOWER_BOUND_H_< / span > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "abase_2logging_8h_html_accad43a85d781d53381cd53a9894b6ae" > < div class = "ttname" > < a href = "base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae" > LOG< / a > < / div > < div class = "ttdeci" > #define LOG(severity)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00423" > base/logging.h:423< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "achristofides_8h_html" > < div class = "ttname" > < a href = "christofides_8h.html" > christofides.h< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_christofides_path_solver_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_christofides_path_solver.html" > operations_research::ChristofidesPathSolver< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00042" > christofides.h:42< / a > < / div > < / div >
2021-02-16 18:34:57 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_christofides_path_solver_html_ab558649a26fef3a74f0909ef5af45e90" > < div class = "ttname" > < a href = "classoperations__research_1_1_christofides_path_solver.html#ab558649a26fef3a74f0909ef5af45e90" > operations_research::ChristofidesPathSolver::TravelingSalesmanCost< / a > < / div > < div class = "ttdeci" > CostType TravelingSalesmanCost()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "christofides_8h_source.html#l00230" > christofides.h:230< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_held_wolfe_crowder_evaluator_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html" > operations_research::HeldWolfeCrowderEvaluator< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00206" > one_tree_lower_bound.h:206< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_held_wolfe_crowder_evaluator_html_a2ad04ff9537d97fcabc58c86183890c3" > < div class = "ttname" > < a href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a2ad04ff9537d97fcabc58c86183890c3" > operations_research::HeldWolfeCrowderEvaluator::OnNewWMax< / a > < / div > < div class = "ttdeci" > void OnNewWMax(CostType one_tree_cost)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00246" > one_tree_lower_bound.h:246< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_held_wolfe_crowder_evaluator_html_a33c2c5b8d838c77c2701a538f7f30ae4" > < div class = "ttname" > < a href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a33c2c5b8d838c77c2701a538f7f30ae4" > operations_research::HeldWolfeCrowderEvaluator::OnOneTree< / a > < / div > < div class = "ttdeci" > void OnOneTree(CostType one_tree_cost, double w, const std::vector< int > & degrees)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00236" > one_tree_lower_bound.h:236< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_held_wolfe_crowder_evaluator_html_a3947d19ac087ef2cd68c2409920339c4" > < div class = "ttname" > < a href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a3947d19ac087ef2cd68c2409920339c4" > operations_research::HeldWolfeCrowderEvaluator::Next< / a > < / div > < div class = "ttdeci" > bool Next()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00221" > one_tree_lower_bound.h:221< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_held_wolfe_crowder_evaluator_html_a61aed6a943277e531b904cfdc3616890" > < div class = "ttname" > < a href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#a61aed6a943277e531b904cfdc3616890" > operations_research::HeldWolfeCrowderEvaluator::GetStep< / a > < / div > < div class = "ttdeci" > double GetStep() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00234" > one_tree_lower_bound.h:234< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_held_wolfe_crowder_evaluator_html_adb1dee05e699715da68918f6b19d3e6d" > < div class = "ttname" > < a href = "classoperations__research_1_1_held_wolfe_crowder_evaluator.html#adb1dee05e699715da68918f6b19d3e6d" > operations_research::HeldWolfeCrowderEvaluator::HeldWolfeCrowderEvaluator< / a > < / div > < div class = "ttdeci" > HeldWolfeCrowderEvaluator(int number_of_nodes, const CostFunction & cost)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00208" > one_tree_lower_bound.h:208< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_volgenant_jonker_evaluator_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_volgenant_jonker_evaluator.html" > operations_research::VolgenantJonkerEvaluator< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00153" > one_tree_lower_bound.h:153< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_volgenant_jonker_evaluator_html_a24cfa064cc97e776b361abdba5488673" > < div class = "ttname" > < a href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a24cfa064cc97e776b361abdba5488673" > operations_research::VolgenantJonkerEvaluator::VolgenantJonkerEvaluator< / a > < / div > < div class = "ttdeci" > VolgenantJonkerEvaluator(int number_of_nodes, int max_iterations)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00155" > one_tree_lower_bound.h:155< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_volgenant_jonker_evaluator_html_a2ad04ff9537d97fcabc58c86183890c3" > < div class = "ttname" > < a href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a2ad04ff9537d97fcabc58c86183890c3" > operations_research::VolgenantJonkerEvaluator::OnNewWMax< / a > < / div > < div class = "ttdeci" > void OnNewWMax(CostType one_tree_cost)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00183" > one_tree_lower_bound.h:183< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1_volgenant_jonker_evaluator_html_a33c2c5b8d838c77c2701a538f7f30ae4" > < div class = "ttname" > < a href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a33c2c5b8d838c77c2701a538f7f30ae4" > operations_research::VolgenantJonkerEvaluator::OnOneTree< / a > < / div > < div class = "ttdeci" > void OnOneTree(CostType one_tree_cost, double w, const std::vector< int > & degrees)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00175" > one_tree_lower_bound.h:175< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_volgenant_jonker_evaluator_html_a3947d19ac087ef2cd68c2409920339c4" > < div class = "ttname" > < a href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a3947d19ac087ef2cd68c2409920339c4" > operations_research::VolgenantJonkerEvaluator::Next< / a > < / div > < div class = "ttdeci" > bool Next()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00163" > one_tree_lower_bound.h:163< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_volgenant_jonker_evaluator_html_a61aed6a943277e531b904cfdc3616890" > < div class = "ttname" > < a href = "classoperations__research_1_1_volgenant_jonker_evaluator.html#a61aed6a943277e531b904cfdc3616890" > operations_research::VolgenantJonkerEvaluator::GetStep< / a > < / div > < div class = "ttdeci" > double GetStep() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00165" > one_tree_lower_bound.h:165< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassutil_1_1_complete_graph_html" > < div class = "ttname" > < a href = "classutil_1_1_complete_graph.html" > util::CompleteGraph< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l02177" > graph.h:2177< / a > < / div > < / div >
< div class = "ttc" id = "aclassutil_1_1_complete_graph_html_a2eeae3a8497dc3942e3db3128a10d41c" > < div class = "ttname" > < a href = "classutil_1_1_complete_graph.html#a2eeae3a8497dc3942e3db3128a10d41c" > util::CompleteGraph::Tail< / a > < / div > < div class = "ttdeci" > NodeIndexType Tail(ArcIndexType arc) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l02211" > graph.h:2211< / a > < / div > < / div >
< div class = "ttc" id = "aclassutil_1_1_complete_graph_html_aceb0938bcb2e8e5f37986d4cf8e3a955" > < div class = "ttname" > < a href = "classutil_1_1_complete_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955" > util::CompleteGraph::Head< / a > < / div > < div class = "ttdeci" > NodeIndexType Head(ArcIndexType arc) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l02204" > graph.h:2204< / a > < / div > < / div >
< div class = "ttc" id = "aclassutil_1_1_list_graph_html" > < div class = "ttname" > < a href = "classutil_1_1_list_graph.html" > util::ListGraph< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l00299" > graph.h:299< / a > < / div > < / div >
< div class = "ttc" id = "aclassutil_1_1_list_graph_html_a7b505ba4a01bce342d049f5a8674da72" > < div class = "ttname" > < a href = "classutil_1_1_list_graph.html#a7b505ba4a01bce342d049f5a8674da72" > util::ListGraph::AddArc< / a > < / div > < div class = "ttdeci" > ArcIndexType AddArc(NodeIndexType tail, NodeIndexType head)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l01141" > graph.h:1141< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "acp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219" > < div class = "ttname" > < a href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > < / div > < div class = "ttdeci" > SatParameters parameters< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "cp__model__fz__solver_8cc_source.html#l00108" > cp_model_fz_solver.cc:108< / a > < / div > < / div >
< div class = "ttc" id = "aintegral__types_8h_html" > < div class = "ttname" > < a href = "integral__types_8h.html" > integral_types.h< / a > < / div > < / div >
< div class = "ttc" id = "alog__severity_8h_html_ac9bcbe19995a8140cd4ec61773cd6e67" > < div class = "ttname" > < a href = "log__severity_8h.html#ac9bcbe19995a8140cd4ec61773cd6e67" > ERROR< / a > < / div > < div class = "ttdeci" > const int ERROR< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "log__severity_8h_source.html#l00032" > log_severity.h:32< / a > < / div > < / div >
< div class = "ttc" id = "aminimum__spanning__tree_8h_html" > < div class = "ttname" > < a href = "minimum__spanning__tree_8h.html" > minimum_spanning_tree.h< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "anamespaceoperations__research_html" > < div class = "ttname" > < a href = "namespaceoperations__research.html" > operations_research< / a > < / div > < div class = "ttdoc" > Collection of objects used to extend the Constraint Solver library.< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "dense__doubly__linked__list_8h_source.html#l00021" > dense_doubly_linked_list.h:21< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html_a078701f3ce8570abe24e8157029c8abf" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a078701f3ce8570abe24e8157029c8abf" > operations_research::NearestNeighbors< / a > < / div > < div class = "ttdeci" > std::set< std::pair< int, int > > NearestNeighbors(int number_of_nodes, int number_of_neighbors, const CostFunction & cost)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00262" > one_tree_lower_bound.h:262< / a > < / div > < / div >
2020-11-18 14:53:30 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html_a33a2f4c26fd60cd0fa98257b571c974f" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a33a2f4c26fd60cd0fa98257b571c974f" > operations_research::BuildPrimMinimumSpanningTree< / a > < / div > < div class = "ttdeci" > std::vector< typename Graph::ArcIndex > BuildPrimMinimumSpanningTree(const Graph & graph, const ArcValue & arc_value)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "minimum__spanning__tree_8h_source.html#l00115" > minimum_spanning_tree.h:115< / a > < / div > < / div >
2020-09-02 09:42:51 +02:00
< div class = "ttc" id = "anamespaceoperations__research_html_a3ed3d609fa06ad508b3d21119f94a560" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a3ed3d609fa06ad508b3d21119f94a560" > operations_research::ComputeOneTreeLowerBoundWithAlgorithm< / a > < / div > < div class = "ttdeci" > double ComputeOneTreeLowerBoundWithAlgorithm(int number_of_nodes, int nearest_neighbors, const CostFunction & cost, Algorithm *algorithm)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00378" > one_tree_lower_bound.h:378< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html_a516a7ec8626d689aa84729fb6f358f89" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a516a7ec8626d689aa84729fb6f358f89" > operations_research::ComputeOneTreeLowerBoundWithParameters< / a > < / div > < div class = "ttdeci" > double ComputeOneTreeLowerBoundWithParameters(int number_of_nodes, const CostFunction & cost, const TravelingSalesmanLowerBoundParameters & parameters)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00452" > one_tree_lower_bound.h:452< / a > < / div > < / div >
2020-09-02 09:42:51 +02:00
< div class = "ttc" id = "anamespaceoperations__research_html_aa29730f0377a3408590f4e621af966eb" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aa29730f0377a3408590f4e621af966eb" > operations_research::ComputeOneTree< / a > < / div > < div class = "ttdeci" > std::vector< int > ComputeOneTree(const GraphType & graph, const CostFunction & cost, const std::vector< double > & weights, const std::vector< int > & sorted_arcs, CostType *one_tree_cost)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00331" > one_tree_lower_bound.h:331< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "anamespaceoperations__research_html_adfc52ee652f25f3a2f249ffb830f2e8a" > < div class = "ttname" > < a href = "namespaceoperations__research.html#adfc52ee652f25f3a2f249ffb830f2e8a" > operations_research::AddArcsFromMinimumSpanningTree< / a > < / div > < div class = "ttdeci" > void AddArcsFromMinimumSpanningTree(int number_of_nodes, const CostFunction & cost, std::set< std::pair< int, int > > *arcs)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00293" > one_tree_lower_bound.h:293< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_ae9af26e7687cb65967941eb175148fe5" > < div class = "ttname" > < a href = "namespaceoperations__research.html#ae9af26e7687cb65967941eb175148fe5" > operations_research::ComputeOneTreeLowerBound< / a > < / div > < div class = "ttdeci" > double ComputeOneTreeLowerBound(int number_of_nodes, const CostFunction & cost)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00480" > one_tree_lower_bound.h:480< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_html_aeae6cf89ac4d73d2e95cffaa0edbd687" > < div class = "ttname" > < a href = "namespaceoperations__research.html#aeae6cf89ac4d73d2e95cffaa0edbd687" > operations_research::GetNodeMinimizingEdgeCostToSource< / a > < / div > < div class = "ttdeci" > int GetNodeMinimizingEdgeCostToSource(const GraphType & graph, int source, const CostFunction & cost, AcceptFunction accept)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00310" > one_tree_lower_bound.h:310< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aresource_8cc_html_af12056bc2a8e3ec563f0940d87abbd2e" > < div class = "ttname" > < a href = "resource_8cc.html#af12056bc2a8e3ec563f0940d87abbd2e" > delta< / a > < / div > < div class = "ttdeci" > int64_t delta< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "resource_8cc_source.html#l01692" > resource.cc:1692< / a > < / div > < / div >
< div class = "ttc" id = "arouting__flow_8cc_html_a75d7b5e4cab1e156cc7a2c5eba1e16f1" > < div class = "ttname" > < a href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > < / div > < div class = "ttdeci" > int64_t cost< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "routing__flow_8cc_source.html#l00152" > routing_flow.cc:152< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html" > operations_research::TravelingSalesmanLowerBoundParameters< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00436" > one_tree_lower_bound.h:436< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html_a5e41188f16a381c8915a17a22228e691" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691" > operations_research::TravelingSalesmanLowerBoundParameters::Algorithm< / a > < / div > < div class = "ttdeci" > Algorithm< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00437" > one_tree_lower_bound.h:437< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html_a5e41188f16a381c8915a17a22228e691a324779d0e6f33b00553606d001821935" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691a324779d0e6f33b00553606d001821935" > operations_research::TravelingSalesmanLowerBoundParameters::VolgenantJonker< / a > < / div > < div class = "ttdeci" > @ VolgenantJonker< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00438" > one_tree_lower_bound.h:438< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html_a5e41188f16a381c8915a17a22228e691aab5026cdecee6d30b78813ed209bbba3" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#a5e41188f16a381c8915a17a22228e691aab5026cdecee6d30b78813ed209bbba3" > operations_research::TravelingSalesmanLowerBoundParameters::HeldWolfeCrowder< / a > < / div > < div class = "ttdeci" > @ HeldWolfeCrowder< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00439" > one_tree_lower_bound.h:439< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html_aa5624a1c87ea6c30028af3168aa6daf9" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#aa5624a1c87ea6c30028af3168aa6daf9" > operations_research::TravelingSalesmanLowerBoundParameters::volgenant_jonker_iterations< / a > < / div > < div class = "ttdeci" > int volgenant_jonker_iterations< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00445" > one_tree_lower_bound.h:445< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html_ac0c01b0297a60d1b72ac046280057e20" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#ac0c01b0297a60d1b72ac046280057e20" > operations_research::TravelingSalesmanLowerBoundParameters::nearest_neighbors< / a > < / div > < div class = "ttdeci" > int nearest_neighbors< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00447" > one_tree_lower_bound.h:447< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1_traveling_salesman_lower_bound_parameters_html_acc4ba09a6333be056db50ed15007518c" > < div class = "ttname" > < a href = "structoperations__research_1_1_traveling_salesman_lower_bound_parameters.html#acc4ba09a6333be056db50ed15007518c" > operations_research::TravelingSalesmanLowerBoundParameters::algorithm< / a > < / div > < div class = "ttdeci" > Algorithm algorithm< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "one__tree__lower__bound_8h_source.html#l00442" > one_tree_lower_bound.h:442< / a > < / div > < / div >
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