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< a href = "lagrangian__relaxation_8cc.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a id = "l00001" name = "l00001" > < / a > < span class = "lineno" > 1< / span > < span class = "comment" > // Copyright 2010-2021 Google LLC< / span > < / div >
< div class = "line" > < a id = "l00002" 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 id = "l00003" 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 id = "l00004" 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 id = "l00005" name = "l00005" > < / a > < span class = "lineno" > 5< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00006" 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 id = "l00007" name = "l00007" > < / a > < span class = "lineno" > 7< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00008" 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 id = "l00009" 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 id = "l00010" 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 id = "l00011" 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 id = "l00012" name = "l00012" > < / a > < span class = "lineno" > 12< / span > < span class = "comment" > // limitations under the License.< / span > < / div >
< div class = "line" > < a id = "l00013" name = "l00013" > < / a > < span class = "lineno" > 13< / span > < / div >
< div class = "line" > < a id = "l00014" name = "l00014" > < / a > < span class = "lineno" > 14< / span > < span class = "comment" > // Solves a constrained shortest path problem via Lagrangian Relaxation. The< / span > < / div >
< div class = "line" > < a id = "l00015" name = "l00015" > < / a > < span class = "lineno" > 15< / span > < span class = "comment" > // Lagrangian dual is solved with subgradient ascent.< / span > < / div >
< div class = "line" > < a id = "l00016" name = "l00016" > < / a > < span class = "lineno" > 16< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00017" name = "l00017" > < / a > < span class = "lineno" > 17< / span > < span class = "comment" > // Problem data:< / span > < / div >
< div class = "line" > < a id = "l00018" name = "l00018" > < / a > < span class = "lineno" > 18< / span > < span class = "comment" > // * N: set of nodes.< / span > < / div >
< div class = "line" > < a id = "l00019" name = "l00019" > < / a > < span class = "lineno" > 19< / span > < span class = "comment" > // * A: set of arcs.< / span > < / div >
< div class = "line" > < a id = "l00020" name = "l00020" > < / a > < span class = "lineno" > 20< / span > < span class = "comment" > // * R: set of resources.< / span > < / div >
< div class = "line" > < a id = "l00021" name = "l00021" > < / a > < span class = "lineno" > 21< / span > < span class = "comment" > // * c_(i,j): cost of traversing arc (i,j) in A.< / span > < / div >
< div class = "line" > < a id = "l00022" name = "l00022" > < / a > < span class = "lineno" > 22< / span > < span class = "comment" > // * r_(i,j,k): resource k spent by traversing arc (i,j) in A, for all k in R.< / span > < / div >
< div class = "line" > < a id = "l00023" name = "l00023" > < / a > < span class = "lineno" > 23< / span > < span class = "comment" > // * b_i: flow balance at node i in N (+1 at the source, -1 at the sink, and 0< / span > < / div >
< div class = "line" > < a id = "l00024" name = "l00024" > < / a > < span class = "lineno" > 24< / span > < span class = "comment" > // otherwise).< / span > < / div >
< div class = "line" > < a id = "l00025" name = "l00025" > < / a > < span class = "lineno" > 25< / span > < span class = "comment" > // * r_max_k: availability of resource k for a path, for all k in R.< / span > < / div >
< div class = "line" > < a id = "l00026" name = "l00026" > < / a > < span class = "lineno" > 26< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00027" name = "l00027" > < / a > < span class = "lineno" > 27< / span > < span class = "comment" > // Decision variables:< / span > < / div >
< div class = "line" > < a id = "l00028" name = "l00028" > < / a > < span class = "lineno" > 28< / span > < span class = "comment" > // * x_(i,j): flow through arc (i,j) in A.< / span > < / div >
< div class = "line" > < a id = "l00029" name = "l00029" > < / a > < span class = "lineno" > 29< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00030" name = "l00030" > < / a > < span class = "lineno" > 30< / span > < span class = "comment" > // Formulation:< / span > < / div >
< div class = "line" > < a id = "l00031" name = "l00031" > < / a > < span class = "lineno" > 31< / span > < span class = "comment" > // Z = min sum(c_(i,j) * x_(i,j): (i,j) in A)< / span > < / div >
< div class = "line" > < a id = "l00032" name = "l00032" > < / a > < span class = "lineno" > 32< / span > < span class = "comment" > // s.t.< / span > < / div >
< div class = "line" > < a id = "l00033" name = "l00033" > < / a > < span class = "lineno" > 33< / span > < span class = "comment" > // sum(x_(i,j): (i,j) in A) - sum(x_(j,i): (j,i) in A) = b_i for all i in N,< / span > < / div >
< div class = "line" > < a id = "l00034" name = "l00034" > < / a > < span class = "lineno" > 34< / span > < span class = "comment" > // sum(r_(i,j,k) * x_(i,j): (i,j) in A) < = r_max_k for all k in R,< / span > < / div >
< div class = "line" > < a id = "l00035" name = "l00035" > < / a > < span class = "lineno" > 35< / span > < span class = "comment" > // x_(i,j) in {0,1} for all (i,j) in A.< / span > < / div >
< div class = "line" > < a id = "l00036" name = "l00036" > < / a > < span class = "lineno" > 36< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00037" name = "l00037" > < / a > < span class = "lineno" > 37< / span > < span class = "comment" > // Upon dualizing a subset of the constraints (here we chose to relax some or< / span > < / div >
< div class = "line" > < a id = "l00038" name = "l00038" > < / a > < span class = "lineno" > 38< / span > < span class = "comment" > // all of the knapsack constraints), we obtaing a subproblem parameterized by< / span > < / div >
< div class = "line" > < a id = "l00039" name = "l00039" > < / a > < span class = "lineno" > 39< / span > < span class = "comment" > // dual variables mu (one per dualized constraint). We refer to this as the< / span > < / div >
< div class = "line" > < a id = "l00040" name = "l00040" > < / a > < span class = "lineno" > 40< / span > < span class = "comment" > // Lagrangian subproblem. Let R+ be the set of knapsack constraints that we< / span > < / div >
< div class = "line" > < a id = "l00041" name = "l00041" > < / a > < span class = "lineno" > 41< / span > < span class = "comment" > // keep, and R- the set of knapsack constraints that get dualized. The< / span > < / div >
< div class = "line" > < a id = "l00042" name = "l00042" > < / a > < span class = "lineno" > 42< / span > < span class = "comment" > // Lagrangian subproblem follows:< / span > < / div >
< div class = "line" > < a id = "l00043" name = "l00043" > < / a > < span class = "lineno" > 43< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00044" name = "l00044" > < / a > < span class = "lineno" > 44< / span > < span class = "comment" > // z(mu) = min sum(< / span > < / div >
< div class = "line" > < a id = "l00045" name = "l00045" > < / a > < span class = "lineno" > 45< / span > < span class = "comment" > // (c_(i,j) - sum(mu_k * r_(i,j,k): k in R)) * x_(i,j): (i,j) in A)< / span > < / div >
< div class = "line" > < a id = "l00046" name = "l00046" > < / a > < span class = "lineno" > 46< / span > < span class = "comment" > // + sum(mu_k * r_max_k: k in R-)< / span > < / div >
< div class = "line" > < a id = "l00047" name = "l00047" > < / a > < span class = "lineno" > 47< / span > < span class = "comment" > // s.t.< / span > < / div >
< div class = "line" > < a id = "l00048" name = "l00048" > < / a > < span class = "lineno" > 48< / span > < span class = "comment" > // sum(x_(i,j): (i,j) in A) - sum(x_(j,i): (j,i) in A) = b_i for all i in N,< / span > < / div >
< div class = "line" > < a id = "l00049" name = "l00049" > < / a > < span class = "lineno" > 49< / span > < span class = "comment" > // sum(r_(i,j,k) * x_(i,j): (i,j) in A) < = r_max_k for all k in R+,< / span > < / div >
< div class = "line" > < a id = "l00050" name = "l00050" > < / a > < span class = "lineno" > 50< / span > < span class = "comment" > // x_(i,j) in {0,1} for all (i,j) in A.< / span > < / div >
< div class = "line" > < a id = "l00051" name = "l00051" > < / a > < span class = "lineno" > 51< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00052" name = "l00052" > < / a > < span class = "lineno" > 52< / span > < span class = "comment" > // We seek to solve the Lagrangian dual, which is of the form:< / span > < / div >
< div class = "line" > < a id = "l00053" name = "l00053" > < / a > < span class = "lineno" > 53< / span > < span class = "comment" > // Z_D = max{ z(mu) : mu < =0 }. Concavity of z(mu) allows us to solve the< / span > < / div >
< div class = "line" > < a id = "l00054" name = "l00054" > < / a > < span class = "lineno" > 54< / span > < span class = "comment" > // Lagrangian dual with the iterates:< / span > < / div >
< div class = "line" > < a id = "l00055" name = "l00055" > < / a > < span class = "lineno" > 55< / span > < span class = "comment" > // mu_(t+1) = mu_t + step_size_t * grad_mu_t, where< / span > < / div >
< div class = "line" > < a id = "l00056" name = "l00056" > < / a > < span class = "lineno" > 56< / span > < span class = "comment" > // grad_mu_t = r_max - sum(t_(i,j) * x_(i,j)^t: (i,j) in A) is a subgradient of< / span > < / div >
< div class = "line" > < a id = "l00057" name = "l00057" > < / a > < span class = "lineno" > 57< / span > < span class = "comment" > // z(mu_t) and x^t is an optimal solution to the problem induced by z(mu_t).< / span > < / div >
< div class = "line" > < a id = "l00058" name = "l00058" > < / a > < span class = "lineno" > 58< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00059" name = "l00059" > < / a > < span class = "lineno" > 59< / span > < span class = "comment" > // In general we have that Z_D < = Z. For convex problems, Z_D = Z. For MIPs,< / span > < / div >
< div class = "line" > < a id = "l00060" name = "l00060" > < / a > < span class = "lineno" > 60< / span > < span class = "comment" > // Z_LP < = Z_D < = Z, where Z_LP is the linear relaxation of the original< / span > < / div >
< div class = "line" > < a id = "l00061" name = "l00061" > < / a > < span class = "lineno" > 61< / span > < span class = "comment" > // problem.< / span > < / div >
< div class = "line" > < a id = "l00062" name = "l00062" > < / a > < span class = "lineno" > 62< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00063" name = "l00063" > < / a > < span class = "lineno" > 63< / span > < span class = "comment" > // In this particular example, we use two resource constraints. Either< / span > < / div >
< div class = "line" > < a id = "l00064" name = "l00064" > < / a > < span class = "lineno" > 64< / span > < span class = "comment" > // constraint or both can be dualized via the flags `dualize_resource_1` and< / span > < / div >
< div class = "line" > < a id = "l00065" name = "l00065" > < / a > < span class = "lineno" > 65< / span > < span class = "comment" > // `dualize_resource_2`. If both constraints are dualized, we have that Z_LP =< / span > < / div >
< div class = "line" > < a id = "l00066" name = "l00066" > < / a > < span class = "lineno" > 66< / span > < span class = "comment" > // Z_D because the resulting Lagrangian subproblem can be solved as a linear< / span > < / div >
< div class = "line" > < a id = "l00067" name = "l00067" > < / a > < span class = "lineno" > 67< / span > < span class = "comment" > // program (i.e., the problem becomes a pure shortest path problem upon< / span > < / div >
< div class = "line" > < a id = "l00068" name = "l00068" > < / a > < span class = "lineno" > 68< / span > < span class = "comment" > // dualizing all the side constraints). When only one of the side constraints is< / span > < / div >
< div class = "line" > < a id = "l00069" name = "l00069" > < / a > < span class = "lineno" > 69< / span > < span class = "comment" > // dualized, we can have Z_LP < = Z_D because the resulting Lagrangian subproblem< / span > < / div >
< div class = "line" > < a id = "l00070" name = "l00070" > < / a > < span class = "lineno" > 70< / span > < span class = "comment" > // needs to be solved as an MIP. For the particular data used in this example,< / span > < / div >
< div class = "line" > < a id = "l00071" name = "l00071" > < / a > < span class = "lineno" > 71< / span > < span class = "comment" > // dualizing only the first resource constraint leads to Z_LP < Z_D, while< / span > < / div >
< div class = "line" > < a id = "l00072" name = "l00072" > < / a > < span class = "lineno" > 72< / span > < span class = "comment" > // dualizing only the second resource constraint leads to Z_LP = Z_D. In either< / span > < / div >
< div class = "line" > < a id = "l00073" name = "l00073" > < / a > < span class = "lineno" > 73< / span > < span class = "comment" > // case, solving the Lagrandual dual also provides an upper bound to Z.< / span > < / div >
< div class = "line" > < a id = "l00074" name = "l00074" > < / a > < span class = "lineno" > 74< / span > < span class = "comment" > //< / span > < / div >
< div class = "line" > < a id = "l00075" name = "l00075" > < / a > < span class = "lineno" > 75< / span > < span class = "comment" > // Usage: blaze build -c opt< / span > < / div >
< div class = "line" > < a id = "l00076" name = "l00076" > < / a > < span class = "lineno" > 76< / span > < span class = "comment" > // ortools/math_opt/examples:lagrangian_relaxation< / span > < / div >
< div class = "line" > < a id = "l00077" name = "l00077" > < / a > < span class = "lineno" > 77< / span > < span class = "comment" > // blaze-bin/ortools/math_opt/examples/lagrangian_relaxation< / span > < / div >
< div class = "line" > < a id = "l00078" name = "l00078" > < / a > < span class = "lineno" > 78< / span > < / div >
< div class = "line" > < a id = "l00079" name = "l00079" > < / a > < span class = "lineno" > 79< / span > < span class = "preprocessor" > #include < math.h> < / span > < / div >
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< div class = "line" > < a id = "l00081" name = "l00081" > < / a > < span class = "lineno" > 81< / span > < span class = "preprocessor" > #include < algorithm> < / span > < / div >
< div class = "line" > < a id = "l00082" name = "l00082" > < / a > < span class = "lineno" > 82< / span > < span class = "preprocessor" > #include < iostream> < / span > < / div >
< div class = "line" > < a id = "l00083" name = "l00083" > < / a > < span class = "lineno" > 83< / span > < span class = "preprocessor" > #include < limits> < / span > < / div >
< div class = "line" > < a id = "l00084" name = "l00084" > < / a > < span class = "lineno" > 84< / span > < span class = "preprocessor" > #include < memory> < / span > < / div >
< div class = "line" > < a id = "l00085" name = "l00085" > < / a > < span class = "lineno" > 85< / span > < span class = "preprocessor" > #include < string> < / span > < / div >
< div class = "line" > < a id = "l00086" name = "l00086" > < / a > < span class = "lineno" > 86< / span > < span class = "preprocessor" > #include < vector> < / span > < / div >
< div class = "line" > < a id = "l00087" name = "l00087" > < / a > < span class = "lineno" > 87< / span > < / div >
< div class = "line" > < a id = "l00088" name = "l00088" > < / a > < span class = "lineno" > 88< / span > < span class = "preprocessor" > #include " absl/flags/flag.h" < / span > < / div >
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< div class = "line" > < a id = "l00089" name = "l00089" > < / a > < span class = "lineno" > 89< / span > < span class = "preprocessor" > #include " absl/memory/memory.h" < / span > < / div >
< div class = "line" > < a id = "l00090" name = "l00090" > < / a > < span class = "lineno" > 90< / span > < span class = "preprocessor" > #include " absl/status/status.h" < / span > < / div >
< div class = "line" > < a id = "l00091" name = "l00091" > < / a > < span class = "lineno" > 91< / span > < span class = "preprocessor" > #include " absl/status/statusor.h" < / span > < / div >
< div class = "line" > < a id = "l00092" name = "l00092" > < / a > < span class = "lineno" > 92< / span > < span class = "preprocessor" > #include " absl/strings/str_format.h" < / span > < / div >
< div class = "line" > < a id = "l00093" name = "l00093" > < / a > < span class = "lineno" > 93< / span > < span class = "preprocessor" > #include " absl/strings/string_view.h" < / span > < / div >
< div class = "line" > < a id = "l00094" name = "l00094" > < / a > < span class = "lineno" > 94< / span > < span class = "preprocessor" > #include " < a class = "code" href = "container__logging_8h.html" > ortools/base/container_logging.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00095" name = "l00095" > < / a > < span class = "lineno" > 95< / span > < span class = "preprocessor" > #include " < a class = "code" href = "init__google_8h.html" > ortools/base/init_google.h< / a > " < / span > < / div >
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< div class = "line" > < a id = "l00096" name = "l00096" > < / a > < span class = "lineno" > 96< / span > < span class = "preprocessor" > #include " < a class = "code" href = "base_2logging_8h.html" > ortools/base/logging.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00097" name = "l00097" > < / a > < span class = "lineno" > 97< / span > < span class = "preprocessor" > #include " < a class = "code" href = "mathutil_8h.html" > ortools/base/mathutil.h< / a > " < / span > < / div >
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< div class = "line" > < a id = "l00098" name = "l00098" > < / a > < span class = "lineno" > 98< / span > < span class = "preprocessor" > #include " < a class = "code" href = "status__builder_8h.html" > ortools/base/status_builder.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00099" name = "l00099" > < / a > < span class = "lineno" > 99< / span > < span class = "preprocessor" > #include " < a class = "code" href = "base_2status__macros_8h.html" > ortools/base/status_macros.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00100" name = "l00100" > < / a > < span class = "lineno" > 100< / span > < span class = "preprocessor" > #include " < a class = "code" href = "math__opt_8h.html" > ortools/math_opt/cpp/math_opt.h< / a > " < / span > < / div >
< div class = "line" > < a id = "l00101" name = "l00101" > < / a > < span class = "lineno" > 101< / span > < / div >
< div class = "line" > < a id = "l00102" name = "l00102" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > 102< / a > < / span > < a class = "code hl_function" href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > ABSL_FLAG< / a > (< span class = "keywordtype" > double< / span > , step_size, 0.95,< / div >
< div class = "line" > < a id = "l00103" name = "l00103" > < / a > < span class = "lineno" > 103< / span > < span class = "stringliteral" > " Stepsize for gradient ascent, determined as step_size^t." < / span > );< / div >
< div class = "line" > < a id = "l00104" name = "l00104" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#a38044bbf977275409524d07163ab3276" > 104< / a > < / span > < a class = "code hl_function" href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > ABSL_FLAG< / a > (< span class = "keywordtype" > int< / span > , max_iterations, 1000,< / div >
< div class = "line" > < a id = "l00105" name = "l00105" > < / a > < span class = "lineno" > 105< / span > < span class = "stringliteral" > " Max number of iterations for gradient ascent." < / span > );< / div >
< div class = "line" > < a id = "l00106" name = "l00106" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#a54d9cccfffed73a64555e2d29363fd57" > 106< / a > < / span > < a class = "code hl_function" href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > ABSL_FLAG< / a > (< span class = "keywordtype" > bool< / span > , dualize_resource_1, < span class = "keyword" > true< / span > ,< / div >
< div class = "line" > < a id = "l00107" name = "l00107" > < / a > < span class = "lineno" > 107< / span > < span class = "stringliteral" > " If true, the side constraint associated to resource 1 is dualized." < / span > );< / div >
< div class = "line" > < a id = "l00108" name = "l00108" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#af983917cd26cd3cc8e9de25abf287fe4" > 108< / a > < / span > < a class = "code hl_function" href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > ABSL_FLAG< / a > (< span class = "keywordtype" > bool< / span > , dualize_resource_2, < span class = "keyword" > false< / span > ,< / div >
< div class = "line" > < a id = "l00109" name = "l00109" > < / a > < span class = "lineno" > 109< / span > < span class = "stringliteral" > " If true, the side constraint associated to resource 2 is dualized." < / span > );< / div >
< div class = "line" > < a id = "l00110" name = "l00110" > < / a > < span class = "lineno" > 110< / span > < / div >
< div class = "line" > < a id = "l00111" name = "l00111" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#a69e141f2228adf5791514fd1632e6fd6" > 111< / a > < / span > < a class = "code hl_function" href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > ABSL_FLAG< / a > (< span class = "keywordtype" > bool< / span > , lagrangian_output, < span class = "keyword" > false< / span > ,< / div >
< div class = "line" > < a id = "l00112" name = "l00112" > < / a > < span class = "lineno" > 112< / span > < span class = "stringliteral" > " If true, shows the iteration log of the subgradient ascent " < / span > < / div >
< div class = "line" > < a id = "l00113" name = "l00113" > < / a > < span class = "lineno" > 113< / span > < span class = "stringliteral" > " procedure use to solve the Lagrangian problem" < / span > );< / div >
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< div class = "line" > < a id = "l00114" name = "l00114" > < / a > < span class = "lineno" > 114< / span > < / div >
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< div class = "line" > < a id = "l00115" name = "l00115" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41" > 115< / a > < / span > < span class = "keyword" > constexpr< / span > < span class = "keywordtype" > double< / span > < a class = "code hl_variable" href = "lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41" > kZeroTol< / a > = 1.0e-8;< / div >
< div class = "line" > < a id = "l00116" name = "l00116" > < / a > < span class = "lineno" > 116< / span > < / div >
< div class = "line" > < a id = "l00117" name = "l00117" > < / a > < span class = "lineno" > 117< / span > < span class = "keyword" > namespace < / span > {< / div >
< div class = "line" > < a id = "l00118" name = "l00118" > < / a > < span class = "lineno" > 118< / span > using ::operations_research::MathUtil;< / div >
< div class = "line" > < a id = "l00119" name = "l00119" > < / a > < span class = "lineno" > 119< / span > < / div >
< div class = "line" > < a id = "l00120" name = "l00120" > < / a > < span class = "lineno" > 120< / span > < span class = "keyword" > namespace < / span > < a class = "code hl_namespace" href = "namespaceoperations__research_1_1math__opt.html" > math_opt< / a > = ::operations_research::math_opt;< / div >
< div class = "line" > < a id = "l00121" name = "l00121" > < / a > < span class = "lineno" > 121< / span > < / div >
< div class = "line" > < a id = "l00122" name = "l00122" > < / a > < span class = "lineno" > 122< / span > < span class = "keyword" > struct < / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7deeae530369e107f9d91c1a189f451f" > Arc< / a > {< / div >
< div class = "line" > < a id = "l00123" name = "l00123" > < / a > < span class = "lineno" > 123< / span > < span class = "keywordtype" > int< / span > i;< / div >
< div class = "line" > < a id = "l00124" name = "l00124" > < / a > < span class = "lineno" > 124< / span > < span class = "keywordtype" > int< / span > j;< / div >
< div class = "line" > < a id = "l00125" name = "l00125" > < / a > < span class = "lineno" > 125< / span > < span class = "keywordtype" > double< / span > < a class = "code hl_variable" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ;< / div >
< div class = "line" > < a id = "l00126" name = "l00126" > < / a > < span class = "lineno" > 126< / span > < span class = "keywordtype" > double< / span > resource_1;< / div >
< div class = "line" > < a id = "l00127" name = "l00127" > < / a > < span class = "lineno" > 127< / span > < span class = "keywordtype" > double< / span > resource_2;< / div >
< div class = "line" > < a id = "l00128" name = "l00128" > < / a > < span class = "lineno" > 128< / span > };< / div >
< div class = "line" > < a id = "l00129" name = "l00129" > < / a > < span class = "lineno" > 129< / span > < / div >
< div class = "line" > < a id = "l00130" name = "l00130" > < / a > < span class = "lineno" > 130< / span > < span class = "keyword" > struct < / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > {< / div >
< div class = "line" > < a id = "l00131" name = "l00131" > < / a > < span class = "lineno" > 131< / span > < span class = "keywordtype" > int< / span > num_nodes;< / div >
< div class = "line" > < a id = "l00132" name = "l00132" > < / a > < span class = "lineno" > 132< / span > std::vector< Arc> arcs;< / div >
< div class = "line" > < a id = "l00133" name = "l00133" > < / a > < span class = "lineno" > 133< / span > < span class = "keywordtype" > int< / span > source;< / div >
< div class = "line" > < a id = "l00134" name = "l00134" > < / a > < span class = "lineno" > 134< / span > < span class = "keywordtype" > int< / span > sink;< / div >
< div class = "line" > < a id = "l00135" name = "l00135" > < / a > < span class = "lineno" > 135< / span > };< / div >
< div class = "line" > < a id = "l00136" name = "l00136" > < / a > < span class = "lineno" > 136< / span > < / div >
< div class = "line" > < a id = "l00137" name = "l00137" > < / a > < span class = "lineno" > 137< / span > < span class = "keyword" > struct < / span > FlowModel {< / div >
< div class = "line" > < a id = "l00138" name = "l00138" > < / a > < span class = "lineno" > 138< / span > FlowModel() : < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > (std::make_unique< math_opt::Model> (< span class = "stringliteral" > " LagrangianProblem" < / span > )) {}< / div >
< div class = "line" > < a id = "l00139" name = "l00139" > < / a > < span class = "lineno" > 139< / span > std::unique_ptr< math_opt::Model> < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > ;< / div >
< div class = "line" > < a id = "l00140" name = "l00140" > < / a > < span class = "lineno" > 140< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > < a class = "code hl_variable" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ;< / div >
< div class = "line" > < a id = "l00141" name = "l00141" > < / a > < span class = "lineno" > 141< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > resource_1;< / div >
< div class = "line" > < a id = "l00142" name = "l00142" > < / a > < span class = "lineno" > 142< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > resource_2;< / div >
< div class = "line" > < a id = "l00143" name = "l00143" > < / a > < span class = "lineno" > 143< / span > std::vector< math_opt::Variable> flow_vars;< / div >
< div class = "line" > < a id = "l00144" name = "l00144" > < / a > < span class = "lineno" > 144< / span > };< / div >
< div class = "line" > < a id = "l00145" name = "l00145" > < / a > < span class = "lineno" > 145< / span > < / div >
< div class = "line" > < a id = "l00146" name = "l00146" > < / a > < span class = "lineno" > 146< / span > < span class = "comment" > // Populates `model` with variables and constraints of a shortest path problem.< / span > < / div >
< div class = "line" > < a id = "l00147" name = "l00147" > < / a > < span class = "lineno" > 147< / span > FlowModel CreateShortestPathModel(< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > graph) {< / div >
< div class = "line" > < a id = "l00148" name = "l00148" > < / a > < span class = "lineno" > 148< / span > FlowModel flow_model;< / div >
< div class = "line" > < a id = "l00149" name = "l00149" > < / a > < span class = "lineno" > 149< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_model.html" > math_opt::Model< / a > & < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > = *flow_model.model;< / div >
< div class = "line" > < a id = "l00150" name = "l00150" > < / a > < span class = "lineno" > 150< / span > < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7deeae530369e107f9d91c1a189f451f" > Arc< / a > & < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > : graph.arcs) {< / div >
< div class = "line" > < a id = "l00151" name = "l00151" > < / a > < span class = "lineno" > 151< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_variable.html" > math_opt::Variable< / a > < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > = < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddContinuousVariable(< / div >
< div class = "line" > < a id = "l00152" name = "l00152" > < / a > < span class = "lineno" > 152< / span > < span class = "comment" > /*lower_bound=*/< / span > 0, < span class = "comment" > /*upper_bound=*/< / span > 1,< / div >
< div class = "line" > < a id = "l00153" name = "l00153" > < / a > < span class = "lineno" > 153< / span > < span class = "comment" > /*name=*/< / span > absl::StrFormat(< span class = "stringliteral" > " x_%d_%d" < / span > , < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .i, < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .j));< / div >
< div class = "line" > < a id = "l00154" name = "l00154" > < / a > < span class = "lineno" > 154< / span > flow_model.cost += < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .cost * < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > ;< / div >
< div class = "line" > < a id = "l00155" name = "l00155" > < / a > < span class = "lineno" > 155< / span > flow_model.resource_1 += < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .resource_1 * < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > ;< / div >
< div class = "line" > < a id = "l00156" name = "l00156" > < / a > < span class = "lineno" > 156< / span > flow_model.resource_2 += < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .resource_2 * < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > ;< / div >
< div class = "line" > < a id = "l00157" name = "l00157" > < / a > < span class = "lineno" > 157< / span > flow_model.flow_vars.push_back(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > );< / div >
< div class = "line" > < a id = "l00158" name = "l00158" > < / a > < span class = "lineno" > 158< / span > }< / div >
< div class = "line" > < a id = "l00159" name = "l00159" > < / a > < span class = "lineno" > 159< / span > < / div >
< div class = "line" > < a id = "l00160" name = "l00160" > < / a > < span class = "lineno" > 160< / span > < span class = "comment" > // Flow balance constraints< / span > < / div >
< div class = "line" > < a id = "l00161" name = "l00161" > < / a > < span class = "lineno" > 161< / span > std::vector< math_opt::LinearExpression> out_flow(graph.num_nodes);< / div >
< div class = "line" > < a id = "l00162" name = "l00162" > < / a > < span class = "lineno" > 162< / span > std::vector< math_opt::LinearExpression> in_flow(graph.num_nodes);< / div >
< div class = "line" > < a id = "l00163" name = "l00163" > < / a > < span class = "lineno" > 163< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > arc_index = 0; arc_index < graph.arcs.size(); ++arc_index) {< / div >
< div class = "line" > < a id = "l00164" name = "l00164" > < / a > < span class = "lineno" > 164< / span > out_flow[graph.arcs[arc_index].i] += flow_model.flow_vars[arc_index];< / div >
< div class = "line" > < a id = "l00165" name = "l00165" > < / a > < span class = "lineno" > 165< / span > in_flow[graph.arcs[arc_index].j] += flow_model.flow_vars[arc_index];< / div >
< div class = "line" > < a id = "l00166" name = "l00166" > < / a > < span class = "lineno" > 166< / span > }< / div >
< div class = "line" > < a id = "l00167" name = "l00167" > < / a > < span class = "lineno" > 167< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > node_index = 0; node_index < graph.num_nodes; ++node_index) {< / div >
< div class = "line" > < a id = "l00168" name = "l00168" > < / a > < span class = "lineno" > 168< / span > < span class = "keywordtype" > int< / span > rhs = node_index == graph.source ? 1< / div >
< div class = "line" > < a id = "l00169" name = "l00169" > < / a > < span class = "lineno" > 169< / span > : node_index == graph.sink ? -1< / div >
< div class = "line" > < a id = "l00170" name = "l00170" > < / a > < span class = "lineno" > 170< / span > : 0;< / div >
< div class = "line" > < a id = "l00171" name = "l00171" > < / a > < span class = "lineno" > 171< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddLinearConstraint(out_flow[node_index] - in_flow[node_index] ==< / div >
< div class = "line" > < a id = "l00172" name = "l00172" > < / a > < span class = "lineno" > 172< / span > rhs);< / div >
< div class = "line" > < a id = "l00173" name = "l00173" > < / a > < span class = "lineno" > 173< / span > }< / div >
< div class = "line" > < a id = "l00174" name = "l00174" > < / a > < span class = "lineno" > 174< / span > < / div >
< div class = "line" > < a id = "l00175" name = "l00175" > < / a > < span class = "lineno" > 175< / span > < span class = "keywordflow" > return< / span > flow_model;< / div >
< div class = "line" > < a id = "l00176" name = "l00176" > < / a > < span class = "lineno" > 176< / span > }< / div >
< div class = "line" > < a id = "l00177" name = "l00177" > < / a > < span class = "lineno" > 177< / span > < / div >
< div class = "line" > < a id = "l00178" name = "l00178" > < / a > < span class = "lineno" > 178< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > CreateSampleNetwork() {< / div >
< div class = "line" > < a id = "l00179" name = "l00179" > < / a > < span class = "lineno" > 179< / span > std::vector< Arc> arcs;< / div >
< div class = "line" > < a id = "l00180" name = "l00180" > < / a > < span class = "lineno" > 180< / span > arcs.push_back(< / div >
< div class = "line" > < a id = "l00181" name = "l00181" > < / a > < span class = "lineno" > 181< / span > {.i = 0, .j = 1, .cost = 12, .resource_1 = 1, .resource_2 = 1});< / div >
< div class = "line" > < a id = "l00182" name = "l00182" > < / a > < span class = "lineno" > 182< / span > arcs.push_back(< / div >
< div class = "line" > < a id = "l00183" name = "l00183" > < / a > < span class = "lineno" > 183< / span > {.i = 0, .j = 2, .cost = 3, .resource_1 = 2.5, .resource_2 = 1});< / div >
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< div class = "line" > < a id = "l00184" name = "l00184" > < / a > < span class = "lineno" > 184< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00185" name = "l00185" > < / a > < span class = "lineno" > 185< / span > {.i = 1, .j = 3, .cost = 5, .resource_1 = 1, .resource_2 = 1.5});< / div >
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< div class = "line" > < a id = "l00186" name = "l00186" > < / a > < span class = "lineno" > 186< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00187" name = "l00187" > < / a > < span class = "lineno" > 187< / span > {.i = 1, .j = 4, .cost = 5, .resource_1 = 2.5, .resource_2 = 1});< / div >
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< div class = "line" > < a id = "l00188" name = "l00188" > < / a > < span class = "lineno" > 188< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00189" name = "l00189" > < / a > < span class = "lineno" > 189< / span > {.i = 2, .j = 1, .cost = 7, .resource_1 = 2.5, .resource_2 = 1});< / div >
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< div class = "line" > < a id = "l00190" name = "l00190" > < / a > < span class = "lineno" > 190< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00191" name = "l00191" > < / a > < span class = "lineno" > 191< / span > {.i = 2, .j = 3, .cost = 5, .resource_1 = 7, .resource_2 = 2.5});< / div >
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< div class = "line" > < a id = "l00192" name = "l00192" > < / a > < span class = "lineno" > 192< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00193" name = "l00193" > < / a > < span class = "lineno" > 193< / span > {.i = 2, .j = 4, .cost = 1, .resource_1 = 6.5, .resource_2 = 1});< / div >
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< div class = "line" > < a id = "l00194" name = "l00194" > < / a > < span class = "lineno" > 194< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00195" name = "l00195" > < / a > < span class = "lineno" > 195< / span > {.i = 3, .j = 5, .cost = 6, .resource_1 = 1, .resource_2 = 2.0});< / div >
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< div class = "line" > < a id = "l00196" name = "l00196" > < / a > < span class = "lineno" > 196< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00197" name = "l00197" > < / a > < span class = "lineno" > 197< / span > {.i = 4, .j = 3, .cost = 3, .resource_1 = 1, .resource_2 = 0.5});< / div >
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< div class = "line" > < a id = "l00198" name = "l00198" > < / a > < span class = "lineno" > 198< / span > arcs.push_back(< / div >
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< div class = "line" > < a id = "l00199" name = "l00199" > < / a > < span class = "lineno" > 199< / span > {.i = 4, .j = 5, .cost = 5, .resource_1 = 2.5, .resource_2 = 1});< / div >
< div class = "line" > < a id = "l00200" name = "l00200" > < / a > < span class = "lineno" > 200< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > graph = {.num_nodes = 6, .arcs = arcs, .source = 0, .sink = 5};< / div >
< div class = "line" > < a id = "l00201" name = "l00201" > < / a > < span class = "lineno" > 201< / span > < / div >
< div class = "line" > < a id = "l00202" name = "l00202" > < / a > < span class = "lineno" > 202< / span > < span class = "keywordflow" > return< / span > graph;< / div >
< div class = "line" > < a id = "l00203" name = "l00203" > < / a > < span class = "lineno" > 203< / span > }< / div >
< div class = "line" > < a id = "l00204" name = "l00204" > < / a > < span class = "lineno" > 204< / span > < / div >
< div class = "line" > < a id = "l00205" name = "l00205" > < / a > < span class = "lineno" > 205< / span > < span class = "comment" > // Solves the constrained shortest path as an MIP.< / span > < / div >
< div class = "line" > < a id = "l00206" name = "l00206" > < / a > < span class = "lineno" > 206< / span > absl::StatusOr< FlowModel> SolveMip(< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > graph,< / div >
< div class = "line" > < a id = "l00207" name = "l00207" > < / a > < span class = "lineno" > 207< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_1,< / div >
< div class = "line" > < a id = "l00208" name = "l00208" > < / a > < span class = "lineno" > 208< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_2) {< / div >
< div class = "line" > < a id = "l00209" name = "l00209" > < / a > < span class = "lineno" > 209< / span > FlowModel flow_model;< / div >
< div class = "line" > < a id = "l00210" name = "l00210" > < / a > < span class = "lineno" > 210< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_model.html" > math_opt::Model< / a > & < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > = *flow_model.model;< / div >
< div class = "line" > < a id = "l00211" name = "l00211" > < / a > < span class = "lineno" > 211< / span > < span class = "keywordflow" > for< / span > (< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceoperations__research.html#a7deeae530369e107f9d91c1a189f451f" > Arc< / a > & < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > : graph.arcs) {< / div >
< div class = "line" > < a id = "l00212" name = "l00212" > < / a > < span class = "lineno" > 212< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_variable.html" > math_opt::Variable< / a > < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > = < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddBinaryVariable(< / div >
< div class = "line" > < a id = "l00213" name = "l00213" > < / a > < span class = "lineno" > 213< / span > < span class = "comment" > /*name=*/< / span > absl::StrFormat(< span class = "stringliteral" > " x_%d_%d" < / span > , < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .i, < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .j));< / div >
< div class = "line" > < a id = "l00214" name = "l00214" > < / a > < span class = "lineno" > 214< / span > flow_model.cost += < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .cost * < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > ;< / div >
< div class = "line" > < a id = "l00215" name = "l00215" > < / a > < span class = "lineno" > 215< / span > flow_model.resource_1 += +< a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .resource_1 * < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > ;< / div >
< div class = "line" > < a id = "l00216" name = "l00216" > < / a > < span class = "lineno" > 216< / span > flow_model.resource_2 += < a class = "code hl_variable" href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > .resource_2 * < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > ;< / div >
< div class = "line" > < a id = "l00217" name = "l00217" > < / a > < span class = "lineno" > 217< / span > flow_model.flow_vars.push_back(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > );< / div >
< div class = "line" > < a id = "l00218" name = "l00218" > < / a > < span class = "lineno" > 218< / span > }< / div >
< div class = "line" > < a id = "l00219" name = "l00219" > < / a > < span class = "lineno" > 219< / span > < / div >
< div class = "line" > < a id = "l00220" name = "l00220" > < / a > < span class = "lineno" > 220< / span > < span class = "comment" > // Flow balance constraints< / span > < / div >
< div class = "line" > < a id = "l00221" name = "l00221" > < / a > < span class = "lineno" > 221< / span > std::vector< math_opt::LinearExpression> out_flow(graph.num_nodes);< / div >
< div class = "line" > < a id = "l00222" name = "l00222" > < / a > < span class = "lineno" > 222< / span > std::vector< math_opt::LinearExpression> in_flow(graph.num_nodes);< / div >
< div class = "line" > < a id = "l00223" name = "l00223" > < / a > < span class = "lineno" > 223< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > arc_index = 0; arc_index < graph.arcs.size(); ++arc_index) {< / div >
< div class = "line" > < a id = "l00224" name = "l00224" > < / a > < span class = "lineno" > 224< / span > out_flow[graph.arcs[arc_index].i] += flow_model.flow_vars[arc_index];< / div >
< div class = "line" > < a id = "l00225" name = "l00225" > < / a > < span class = "lineno" > 225< / span > in_flow[graph.arcs[arc_index].j] += flow_model.flow_vars[arc_index];< / div >
< div class = "line" > < a id = "l00226" name = "l00226" > < / a > < span class = "lineno" > 226< / span > }< / div >
< div class = "line" > < a id = "l00227" name = "l00227" > < / a > < span class = "lineno" > 227< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > node_index = 0; node_index < graph.num_nodes; ++node_index) {< / div >
< div class = "line" > < a id = "l00228" name = "l00228" > < / a > < span class = "lineno" > 228< / span > < span class = "keywordtype" > int< / span > rhs = node_index == graph.source ? 1< / div >
< div class = "line" > < a id = "l00229" name = "l00229" > < / a > < span class = "lineno" > 229< / span > : node_index == graph.sink ? -1< / div >
< div class = "line" > < a id = "l00230" name = "l00230" > < / a > < span class = "lineno" > 230< / span > : 0;< / div >
< div class = "line" > < a id = "l00231" name = "l00231" > < / a > < span class = "lineno" > 231< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddLinearConstraint(out_flow[node_index] - in_flow[node_index] ==< / div >
< div class = "line" > < a id = "l00232" name = "l00232" > < / a > < span class = "lineno" > 232< / span > rhs);< / div >
< div class = "line" > < a id = "l00233" name = "l00233" > < / a > < span class = "lineno" > 233< / span > }< / div >
< div class = "line" > < a id = "l00234" name = "l00234" > < / a > < span class = "lineno" > 234< / span > < / div >
< div class = "line" > < a id = "l00235" name = "l00235" > < / a > < span class = "lineno" > 235< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddLinearConstraint(flow_model.resource_1 < = max_resource_1,< / div >
< div class = "line" > < a id = "l00236" name = "l00236" > < / a > < span class = "lineno" > 236< / span > < span class = "stringliteral" > " resource_ctr_1" < / span > );< / div >
< div class = "line" > < a id = "l00237" name = "l00237" > < / a > < span class = "lineno" > 237< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddLinearConstraint(flow_model.resource_2 < = max_resource_2,< / div >
< div class = "line" > < a id = "l00238" name = "l00238" > < / a > < span class = "lineno" > 238< / span > < span class = "stringliteral" > " resource_ctr_2" < / span > );< / div >
< div class = "line" > < a id = "l00239" name = "l00239" > < / a > < span class = "lineno" > 239< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .Minimize(flow_model.cost);< / div >
< div class = "line" > < a id = "l00240" name = "l00240" > < / a > < span class = "lineno" > 240< / span > < a class = "code hl_define" href = "base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011" > ASSIGN_OR_RETURN< / a > (< span class = "keyword" > const< / span > < a class = "code hl_struct" href = "structoperations__research_1_1math__opt_1_1_solve_result.html" > math_opt::SolveResult< / a > result,< / div >
< div class = "line" > < a id = "l00241" name = "l00241" > < / a > < span class = "lineno" > 241< / span > < a class = "code hl_function" href = "namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1" > Solve< / a > (< a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > , math_opt::SolverType::kGscip));< / div >
< div class = "line" > < a id = "l00242" name = "l00242" > < / a > < span class = "lineno" > 242< / span > < span class = "keywordflow" > switch< / span > (result.< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > termination< / a > .< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9" > reason< / a > ) {< / div >
< div class = "line" > < a id = "l00243" name = "l00243" > < / a > < span class = "lineno" > 243< / span > < span class = "keywordflow" > case< / span > math_opt::TerminationReason::kOptimal:< / div >
< div class = "line" > < a id = "l00244" name = "l00244" > < / a > < span class = "lineno" > 244< / span > < span class = "keywordflow" > case< / span > math_opt::TerminationReason::kFeasible:< / div >
< div class = "line" > < a id = "l00245" name = "l00245" > < / a > < span class = "lineno" > 245< / span > std::cout < < < span class = "stringliteral" > " MIP Solution with 2 side constraints" < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00246" name = "l00246" > < / a > < span class = "lineno" > 246< / span > std::cout < < absl::StrFormat(< span class = "stringliteral" > " MIP objective value: %6.3f" < / span > ,< / div >
< div class = "line" > < a id = "l00247" name = "l00247" > < / a > < span class = "lineno" > 247< / span > result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08" > objective_value< / a > ())< / div >
< div class = "line" > < a id = "l00248" name = "l00248" > < / a > < span class = "lineno" > 248< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00249" name = "l00249" > < / a > < span class = "lineno" > 249< / span > std::cout < < < span class = "stringliteral" > " Resource 1: " < / span > < / div >
< div class = "line" > < a id = "l00250" name = "l00250" > < / a > < span class = "lineno" > 250< / span > < < flow_model.resource_1.Evaluate(result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532" > variable_values< / a > ())< / div >
< div class = "line" > < a id = "l00251" name = "l00251" > < / a > < span class = "lineno" > 251< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00252" name = "l00252" > < / a > < span class = "lineno" > 252< / span > std::cout < < < span class = "stringliteral" > " Resource 2: " < / span > < / div >
< div class = "line" > < a id = "l00253" name = "l00253" > < / a > < span class = "lineno" > 253< / span > < < flow_model.resource_2.Evaluate(result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532" > variable_values< / a > ())< / div >
< div class = "line" > < a id = "l00254" name = "l00254" > < / a > < span class = "lineno" > 254< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00255" name = "l00255" > < / a > < span class = "lineno" > 255< / span > std::cout < < < span class = "stringliteral" > " ========================================" < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00256" name = "l00256" > < / a > < span class = "lineno" > 256< / span > < span class = "keywordflow" > return< / span > flow_model;< / div >
< div class = "line" > < a id = "l00257" name = "l00257" > < / a > < span class = "lineno" > 257< / span > < span class = "keywordflow" > default< / span > :< / div >
< div class = "line" > < a id = "l00258" name = "l00258" > < / a > < span class = "lineno" > 258< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648" > util::InternalErrorBuilder< / a > ()< / div >
< div class = "line" > < a id = "l00259" name = "l00259" > < / a > < span class = "lineno" > 259< / span > < < < span class = "stringliteral" > " model failed to solve: " < / span > < < result.< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > termination< / a > ;< / div >
< div class = "line" > < a id = "l00260" name = "l00260" > < / a > < span class = "lineno" > 260< / span > }< / div >
< div class = "line" > < a id = "l00261" name = "l00261" > < / a > < span class = "lineno" > 261< / span > }< / div >
< div class = "line" > < a id = "l00262" name = "l00262" > < / a > < span class = "lineno" > 262< / span > < / div >
< div class = "line" > < a id = "l00263" name = "l00263" > < / a > < span class = "lineno" > 263< / span > < span class = "comment" > // Solves the linear relaxation of a constrained shortest path problem< / span > < / div >
< div class = "line" > < a id = "l00264" name = "l00264" > < / a > < span class = "lineno" > 264< / span > < span class = "comment" > // formulated as an MIP.< / span > < / div >
< div class = "line" > < a id = "l00265" name = "l00265" > < / a > < span class = "lineno" > 265< / span > absl::Status SolveLinearRelaxation(FlowModel& flow_model, < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph,< / div >
< div class = "line" > < a id = "l00266" name = "l00266" > < / a > < span class = "lineno" > 266< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_1,< / div >
< div class = "line" > < a id = "l00267" name = "l00267" > < / a > < span class = "lineno" > 267< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_2) {< / div >
< div class = "line" > < a id = "l00268" name = "l00268" > < / a > < span class = "lineno" > 268< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_model.html" > math_opt::Model< / a > & < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > = *flow_model.model;< / div >
< div class = "line" > < a id = "l00269" name = "l00269" > < / a > < span class = "lineno" > 269< / span > < a class = "code hl_define" href = "base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011" > ASSIGN_OR_RETURN< / a > (< span class = "keyword" > const< / span > < a class = "code hl_struct" href = "structoperations__research_1_1math__opt_1_1_solve_result.html" > math_opt::SolveResult< / a > result,< / div >
< div class = "line" > < a id = "l00270" name = "l00270" > < / a > < span class = "lineno" > 270< / span > < a class = "code hl_function" href = "namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1" > Solve< / a > (< a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > , math_opt::SolverType::kGscip));< / div >
< div class = "line" > < a id = "l00271" name = "l00271" > < / a > < span class = "lineno" > 271< / span > < span class = "keywordflow" > switch< / span > (result.< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > termination< / a > .< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9" > reason< / a > ) {< / div >
< div class = "line" > < a id = "l00272" name = "l00272" > < / a > < span class = "lineno" > 272< / span > < span class = "keywordflow" > case< / span > math_opt::TerminationReason::kOptimal:< / div >
< div class = "line" > < a id = "l00273" name = "l00273" > < / a > < span class = "lineno" > 273< / span > < span class = "keywordflow" > case< / span > math_opt::TerminationReason::kFeasible:< / div >
< div class = "line" > < a id = "l00274" name = "l00274" > < / a > < span class = "lineno" > 274< / span > std::cout < < < span class = "stringliteral" > " LP relaxation with 2 side constraints" < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00275" name = "l00275" > < / a > < span class = "lineno" > 275< / span > std::cout < < absl::StrFormat(< span class = "stringliteral" > " LP objective value: %6.3f" < / span > ,< / div >
< div class = "line" > < a id = "l00276" name = "l00276" > < / a > < span class = "lineno" > 276< / span > result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08" > objective_value< / a > ())< / div >
< div class = "line" > < a id = "l00277" name = "l00277" > < / a > < span class = "lineno" > 277< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00278" name = "l00278" > < / a > < span class = "lineno" > 278< / span > std::cout < < < span class = "stringliteral" > " Resource 1: " < / span > < / div >
< div class = "line" > < a id = "l00279" name = "l00279" > < / a > < span class = "lineno" > 279< / span > < < flow_model.resource_1.Evaluate(result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532" > variable_values< / a > ())< / div >
< div class = "line" > < a id = "l00280" name = "l00280" > < / a > < span class = "lineno" > 280< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00281" name = "l00281" > < / a > < span class = "lineno" > 281< / span > std::cout < < < span class = "stringliteral" > " Resource 2: " < / span > < / div >
< div class = "line" > < a id = "l00282" name = "l00282" > < / a > < span class = "lineno" > 282< / span > < < flow_model.resource_2.Evaluate(result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532" > variable_values< / a > ())< / div >
< div class = "line" > < a id = "l00283" name = "l00283" > < / a > < span class = "lineno" > 283< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00284" name = "l00284" > < / a > < span class = "lineno" > 284< / span > std::cout < < < span class = "stringliteral" > " ========================================" < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00285" name = "l00285" > < / a > < span class = "lineno" > 285< / span > < span class = "keywordflow" > return< / span > absl::OkStatus();< / div >
< div class = "line" > < a id = "l00286" name = "l00286" > < / a > < span class = "lineno" > 286< / span > < span class = "keywordflow" > default< / span > :< / div >
< div class = "line" > < a id = "l00287" name = "l00287" > < / a > < span class = "lineno" > 287< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648" > util::InternalErrorBuilder< / a > ()< / div >
< div class = "line" > < a id = "l00288" name = "l00288" > < / a > < span class = "lineno" > 288< / span > < < < span class = "stringliteral" > " model failed to solve: " < / span > < < result.< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > termination< / a > ;< / div >
< div class = "line" > < a id = "l00289" name = "l00289" > < / a > < span class = "lineno" > 289< / span > }< / div >
< div class = "line" > < a id = "l00290" name = "l00290" > < / a > < span class = "lineno" > 290< / span > }< / div >
< div class = "line" > < a id = "l00291" name = "l00291" > < / a > < span class = "lineno" > 291< / span > < / div >
< div class = "line" > < a id = "l00292" name = "l00292" > < / a > < span class = "lineno" > 292< / span > absl::Status SolveLagrangianRelaxation(< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > graph,< / div >
< div class = "line" > < a id = "l00293" name = "l00293" > < / a > < span class = "lineno" > 293< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_1,< / div >
< div class = "line" > < a id = "l00294" name = "l00294" > < / a > < span class = "lineno" > 294< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_2) {< / div >
< div class = "line" > < a id = "l00295" name = "l00295" > < / a > < span class = "lineno" > 295< / span > < span class = "comment" > // Model, variables, and linear expressions.< / span > < / div >
< div class = "line" > < a id = "l00296" name = "l00296" > < / a > < span class = "lineno" > 296< / span > FlowModel flow_model = CreateShortestPathModel(graph);< / div >
< div class = "line" > < a id = "l00297" name = "l00297" > < / a > < span class = "lineno" > 297< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_model.html" > math_opt::Model< / a > & < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > = *flow_model.model;< / div >
< div class = "line" > < a id = "l00298" name = "l00298" > < / a > < span class = "lineno" > 298< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > & < a class = "code hl_variable" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > = flow_model.cost;< / div >
< div class = "line" > < a id = "l00299" name = "l00299" > < / a > < span class = "lineno" > 299< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > & resource_1 = flow_model.resource_1;< / div >
< div class = "line" > < a id = "l00300" name = "l00300" > < / a > < span class = "lineno" > 300< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > & resource_2 = flow_model.resource_2;< / div >
< div class = "line" > < a id = "l00301" name = "l00301" > < / a > < span class = "lineno" > 301< / span > < / div >
< div class = "line" > < a id = "l00302" name = "l00302" > < / a > < span class = "lineno" > 302< / span > < span class = "comment" > // Dualized constraints and dual variable iterates.< / span > < / div >
< div class = "line" > < a id = "l00303" name = "l00303" > < / a > < span class = "lineno" > 303< / span > std::vector< double> mu;< / div >
< div class = "line" > < a id = "l00304" name = "l00304" > < / a > < span class = "lineno" > 304< / span > std::vector< math_opt::LinearExpression> grad_mu;< / div >
< div class = "line" > < a id = "l00305" name = "l00305" > < / a > < span class = "lineno" > 305< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > bool< / span > dualized_resource_1 = absl::GetFlag(FLAGS_dualize_resource_1);< / div >
< div class = "line" > < a id = "l00306" name = "l00306" > < / a > < span class = "lineno" > 306< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > bool< / span > dualized_resource_2 = absl::GetFlag(FLAGS_dualize_resource_2);< / div >
< div class = "line" > < a id = "l00307" name = "l00307" > < / a > < span class = "lineno" > 307< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > bool< / span > lagrangian_output = absl::GetFlag(FLAGS_lagrangian_output);< / div >
< div class = "line" > < a id = "l00308" name = "l00308" > < / a > < span class = "lineno" > 308< / span > < a class = "code hl_define" href = "base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274" > CHECK< / a > (dualized_resource_1 || dualized_resource_2)< / div >
< div class = "line" > < a id = "l00309" name = "l00309" > < / a > < span class = "lineno" > 309< / span > < < < span class = "stringliteral" > " At least one of the side constraints should be dualized." < / span > ;< / div >
< div class = "line" > < a id = "l00310" name = "l00310" > < / a > < span class = "lineno" > 310< / span > < / div >
< div class = "line" > < a id = "l00311" name = "l00311" > < / a > < span class = "lineno" > 311< / span > < span class = "comment" > // Modify the lagrangian problem according to the constraints that are< / span > < / div >
< div class = "line" > < a id = "l00312" name = "l00312" > < / a > < span class = "lineno" > 312< / span > < span class = "comment" > // dualized. We use a initial dual value different from zero to prioritize< / span > < / div >
< div class = "line" > < a id = "l00313" name = "l00313" > < / a > < span class = "lineno" > 313< / span > < span class = "comment" > // finding a feasible solution.< / span > < / div >
< div class = "line" > < a id = "l00314" name = "l00314" > < / a > < span class = "lineno" > 314< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > initial_dual_value = -10;< / div >
< div class = "line" > < a id = "l00315" name = "l00315" > < / a > < span class = "lineno" > 315< / span > < span class = "keywordflow" > if< / span > (dualized_resource_1 & & !dualized_resource_2) {< / div >
< div class = "line" > < a id = "l00316" name = "l00316" > < / a > < span class = "lineno" > 316< / span > mu.push_back(initial_dual_value);< / div >
< div class = "line" > < a id = "l00317" name = "l00317" > < / a > < span class = "lineno" > 317< / span > grad_mu.push_back(max_resource_1 - resource_1);< / div >
< div class = "line" > < a id = "l00318" name = "l00318" > < / a > < span class = "lineno" > 318< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddLinearConstraint(resource_2 < = max_resource_2);< / div >
< div class = "line" > < a id = "l00319" name = "l00319" > < / a > < span class = "lineno" > 319< / span > < span class = "keywordflow" > for< / span > (< a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_variable.html" > math_opt::Variable< / a > & < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > : flow_model.flow_vars) {< / div >
< div class = "line" > < a id = "l00320" name = "l00320" > < / a > < span class = "lineno" > 320< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .set_integer(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > );< / div >
< div class = "line" > < a id = "l00321" name = "l00321" > < / a > < span class = "lineno" > 321< / span > }< / div >
< div class = "line" > < a id = "l00322" name = "l00322" > < / a > < span class = "lineno" > 322< / span > } < span class = "keywordflow" > else< / span > < span class = "keywordflow" > if< / span > (!dualized_resource_1 & & dualized_resource_2) {< / div >
< div class = "line" > < a id = "l00323" name = "l00323" > < / a > < span class = "lineno" > 323< / span > mu.push_back(initial_dual_value);< / div >
< div class = "line" > < a id = "l00324" name = "l00324" > < / a > < span class = "lineno" > 324< / span > grad_mu.push_back(max_resource_2 - resource_2);< / div >
< div class = "line" > < a id = "l00325" name = "l00325" > < / a > < span class = "lineno" > 325< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .AddLinearConstraint(resource_1 < = max_resource_1);< / div >
< div class = "line" > < a id = "l00326" name = "l00326" > < / a > < span class = "lineno" > 326< / span > < span class = "keywordflow" > for< / span > (< a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_variable.html" > math_opt::Variable< / a > & < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > : flow_model.flow_vars) {< / div >
< div class = "line" > < a id = "l00327" name = "l00327" > < / a > < span class = "lineno" > 327< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .set_integer(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > );< / div >
< div class = "line" > < a id = "l00328" name = "l00328" > < / a > < span class = "lineno" > 328< / span > }< / div >
< div class = "line" > < a id = "l00329" name = "l00329" > < / a > < span class = "lineno" > 329< / span > } < span class = "keywordflow" > else< / span > {< / div >
< div class = "line" > < a id = "l00330" name = "l00330" > < / a > < span class = "lineno" > 330< / span > mu.push_back(initial_dual_value);< / div >
< div class = "line" > < a id = "l00331" name = "l00331" > < / a > < span class = "lineno" > 331< / span > mu.push_back(initial_dual_value);< / div >
< div class = "line" > < a id = "l00332" name = "l00332" > < / a > < span class = "lineno" > 332< / span > grad_mu.push_back(max_resource_1 - resource_1);< / div >
< div class = "line" > < a id = "l00333" name = "l00333" > < / a > < span class = "lineno" > 333< / span > grad_mu.push_back(max_resource_2 - resource_2);< / div >
< div class = "line" > < a id = "l00334" name = "l00334" > < / a > < span class = "lineno" > 334< / span > }< / div >
< div class = "line" > < a id = "l00335" name = "l00335" > < / a > < span class = "lineno" > 335< / span > < / div >
< div class = "line" > < a id = "l00336" name = "l00336" > < / a > < span class = "lineno" > 336< / span > < span class = "comment" > // Gradient ascent setup< / span > < / div >
< div class = "line" > < a id = "l00337" name = "l00337" > < / a > < span class = "lineno" > 337< / span > < span class = "keywordtype" > bool< / span > termination = < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a id = "l00338" name = "l00338" > < / a > < span class = "lineno" > 338< / span > < span class = "keywordtype" > int< / span > iterations = 1;< / div >
< div class = "line" > < a id = "l00339" name = "l00339" > < / a > < span class = "lineno" > 339< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > step_size = absl::GetFlag(FLAGS_step_size);< / div >
< div class = "line" > < a id = "l00340" name = "l00340" > < / a > < span class = "lineno" > 340< / span > < a class = "code hl_define" href = "base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6" > CHECK_GT< / a > (step_size, 0) < < < span class = "stringliteral" > " step_size must be strictly positive" < / span > ;< / div >
< div class = "line" > < a id = "l00341" name = "l00341" > < / a > < span class = "lineno" > 341< / span > < a class = "code hl_define" href = "base_2logging_8h.html#a4bd2e815ca2f702a4b6aa744b1ff3b82" > CHECK_LT< / a > (step_size, 1) < < < span class = "stringliteral" > " step_size must be strictly less than 1" < / span > ;< / div >
< div class = "line" > < a id = "l00342" name = "l00342" > < / a > < span class = "lineno" > 342< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > int< / span > max_iterations = absl::GetFlag(FLAGS_max_iterations);< / div >
< div class = "line" > < a id = "l00343" name = "l00343" > < / a > < span class = "lineno" > 343< / span > < a class = "code hl_define" href = "base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6" > CHECK_GT< / a > (max_iterations, 0)< / div >
< div class = "line" > < a id = "l00344" name = "l00344" > < / a > < span class = "lineno" > 344< / span > < < < span class = "stringliteral" > " Number of iterations must be strictly positive." < / span > ;< / div >
< div class = "line" > < a id = "l00345" name = "l00345" > < / a > < span class = "lineno" > 345< / span > < / div >
< div class = "line" > < a id = "l00346" name = "l00346" > < / a > < span class = "lineno" > 346< / span > < span class = "comment" > // Upper and lower bounds on the full problem.< / span > < / div >
< div class = "line" > < a id = "l00347" name = "l00347" > < / a > < span class = "lineno" > 347< / span > < span class = "keywordtype" > double< / span > < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > = std::numeric_limits< double> ::infinity();< / div >
< div class = "line" > < a id = "l00348" name = "l00348" > < / a > < span class = "lineno" > 348< / span > < span class = "keywordtype" > double< / span > < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > = -std::numeric_limits< double> ::infinity();< / div >
< div class = "line" > < a id = "l00349" name = "l00349" > < / a > < span class = "lineno" > 349< / span > < span class = "keywordtype" > double< / span > best_solution_resource_1 = 0;< / div >
< div class = "line" > < a id = "l00350" name = "l00350" > < / a > < span class = "lineno" > 350< / span > < span class = "keywordtype" > double< / span > best_solution_resource_2 = 0;< / div >
< div class = "line" > < a id = "l00351" name = "l00351" > < / a > < span class = "lineno" > 351< / span > < / div >
< div class = "line" > < a id = "l00352" name = "l00352" > < / a > < span class = "lineno" > 352< / span > < span class = "keywordflow" > if< / span > (lagrangian_output) {< / div >
< div class = "line" > < a id = "l00353" name = "l00353" > < / a > < span class = "lineno" > 353< / span > std::cout < < < span class = "stringliteral" > " Starting gradient ascent..." < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00354" name = "l00354" > < / a > < span class = "lineno" > 354< / span > std::cout < < absl::StrFormat(< span class = "stringliteral" > " %4s %6s %6s %9s %10s %10s" < / span > , < span class = "stringliteral" > " Iter" < / span > , < span class = "stringliteral" > " LB" < / span > ,< / div >
< div class = "line" > < a id = "l00355" name = "l00355" > < / a > < span class = "lineno" > 355< / span > < span class = "stringliteral" > " UB" < / span > , < span class = "stringliteral" > " Step size" < / span > , < span class = "stringliteral" > " mu_t" < / span > , < span class = "stringliteral" > " grad_mu_t" < / span > )< / div >
< div class = "line" > < a id = "l00356" name = "l00356" > < / a > < span class = "lineno" > 356< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00357" name = "l00357" > < / a > < span class = "lineno" > 357< / span > }< / div >
< div class = "line" > < a id = "l00358" name = "l00358" > < / a > < span class = "lineno" > 358< / span > < / div >
< div class = "line" > < a id = "l00359" name = "l00359" > < / a > < span class = "lineno" > 359< / span > < span class = "keywordflow" > while< / span > (!termination) {< / div >
< div class = "line" > < a id = "l00360" name = "l00360" > < / a > < span class = "lineno" > 360< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > math_opt::LinearExpression< / a > lagrangian_function;< / div >
< div class = "line" > < a id = "l00361" name = "l00361" > < / a > < span class = "lineno" > 361< / span > lagrangian_function += < a class = "code hl_variable" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > ;< / div >
< div class = "line" > < a id = "l00362" name = "l00362" > < / a > < span class = "lineno" > 362< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > k = 0; k < mu.size(); ++k) {< / div >
< div class = "line" > < a id = "l00363" name = "l00363" > < / a > < span class = "lineno" > 363< / span > lagrangian_function += mu[k] * grad_mu[k];< / div >
< div class = "line" > < a id = "l00364" name = "l00364" > < / a > < span class = "lineno" > 364< / span > }< / div >
< div class = "line" > < a id = "l00365" name = "l00365" > < / a > < span class = "lineno" > 365< / span > < a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > .Minimize(lagrangian_function);< / div >
< div class = "line" > < a id = "l00366" name = "l00366" > < / a > < span class = "lineno" > 366< / span > < a class = "code hl_define" href = "base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011" > ASSIGN_OR_RETURN< / a > (< a class = "code hl_struct" href = "structoperations__research_1_1math__opt_1_1_solve_result.html" > math_opt::SolveResult< / a > result,< / div >
< div class = "line" > < a id = "l00367" name = "l00367" > < / a > < span class = "lineno" > 367< / span > < a class = "code hl_function" href = "namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1" > Solve< / a > (< a class = "code hl_variable" href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > , math_opt::SolverType::kGscip));< / div >
< div class = "line" > < a id = "l00368" name = "l00368" > < / a > < span class = "lineno" > 368< / span > < span class = "keywordflow" > switch< / span > (result.< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > termination< / a > .< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9" > reason< / a > ) {< / div >
< div class = "line" > < a id = "l00369" name = "l00369" > < / a > < span class = "lineno" > 369< / span > < span class = "keywordflow" > case< / span > math_opt::TerminationReason::kOptimal:< / div >
< div class = "line" > < a id = "l00370" name = "l00370" > < / a > < span class = "lineno" > 370< / span > < span class = "keywordflow" > case< / span > math_opt::TerminationReason::kFeasible:< / div >
< div class = "line" > < a id = "l00371" name = "l00371" > < / a > < span class = "lineno" > 371< / span > < span class = "keywordflow" > break< / span > ;< / div >
< div class = "line" > < a id = "l00372" name = "l00372" > < / a > < span class = "lineno" > 372< / span > < span class = "keywordflow" > default< / span > :< / div >
< div class = "line" > < a id = "l00373" name = "l00373" > < / a > < span class = "lineno" > 373< / span > < span class = "keywordflow" > return< / span > < a class = "code hl_function" href = "namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648" > util::InternalErrorBuilder< / a > ()< / div >
< div class = "line" > < a id = "l00374" name = "l00374" > < / a > < span class = "lineno" > 374< / span > < < < span class = "stringliteral" > " failed to minimize lagrangian function: " < / span > < / div >
< div class = "line" > < a id = "l00375" name = "l00375" > < / a > < span class = "lineno" > 375< / span > < < result.< a class = "code hl_variable" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > termination< / a > ;< / div >
< div class = "line" > < a id = "l00376" name = "l00376" > < / a > < span class = "lineno" > 376< / span > }< / div >
< div class = "line" > < a id = "l00377" name = "l00377" > < / a > < span class = "lineno" > 377< / span > < / div >
< div class = "line" > < a id = "l00378" name = "l00378" > < / a > < span class = "lineno" > 378< / span > < span class = "keyword" > const< / span > < a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_id_map.html" > math_opt::VariableMap< double> < / a > & vars_val = result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532" > variable_values< / a > ();< / div >
< div class = "line" > < a id = "l00379" name = "l00379" > < / a > < span class = "lineno" > 379< / span > < span class = "keywordtype" > bool< / span > feasible = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a id = "l00380" name = "l00380" > < / a > < span class = "lineno" > 380< / span > < / div >
< div class = "line" > < a id = "l00381" name = "l00381" > < / a > < span class = "lineno" > 381< / span > < span class = "comment" > // Iterate update. Takes a step in the direction of the gradient (since the< / span > < / div >
< div class = "line" > < a id = "l00382" name = "l00382" > < / a > < span class = "lineno" > 382< / span > < span class = "comment" > // Lagrangian dual is a max problem), and projects onto {mu: mu < =0} to< / span > < / div >
< div class = "line" > < a id = "l00383" name = "l00383" > < / a > < span class = "lineno" > 383< / span > < span class = "comment" > // satisfy the sign of the dual variable. In general, convergence to an< / span > < / div >
< div class = "line" > < a id = "l00384" name = "l00384" > < / a > < span class = "lineno" > 384< / span > < span class = "comment" > // optimal solution requires diminishing step sizes satisfying:< / span > < / div >
< div class = "line" > < a id = "l00385" name = "l00385" > < / a > < span class = "lineno" > 385< / span > < span class = "comment" > // * sum(step_size_t: t=1...) = infinity and,< / span > < / div >
< div class = "line" > < a id = "l00386" name = "l00386" > < / a > < span class = "lineno" > 386< / span > < span class = "comment" > // * sum((step_size_t)^2: t=1...) < infinity< / span > < / div >
< div class = "line" > < a id = "l00387" name = "l00387" > < / a > < span class = "lineno" > 387< / span > < span class = "comment" > // See details in Prop 3.2.6 Bertsekas 2015, Convex Optimization Algorithms.< / span > < / div >
< div class = "line" > < a id = "l00388" name = "l00388" > < / a > < span class = "lineno" > 388< / span > < span class = "comment" > // Here we use step_size_t = step_size^t which does NOT satisfy the< / span > < / div >
< div class = "line" > < a id = "l00389" name = "l00389" > < / a > < span class = "lineno" > 389< / span > < span class = "comment" > // first condition, but is good enough for the purpose of this example.< / span > < / div >
< div class = "line" > < a id = "l00390" name = "l00390" > < / a > < span class = "lineno" > 390< / span > std::vector< double> grad_mu_vals;< / div >
< div class = "line" > < a id = "l00391" name = "l00391" > < / a > < span class = "lineno" > 391< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > step_size_t = MathUtil::IPow(step_size, iterations);< / div >
< div class = "line" > < a id = "l00392" name = "l00392" > < / a > < span class = "lineno" > 392< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > int< / span > k = 0; k < mu.size(); ++k) {< / div >
< div class = "line" > < a id = "l00393" name = "l00393" > < / a > < span class = "lineno" > 393< / span > < span class = "comment" > // Evaluate resource k and evaluate the gradient of z(mu).< / span > < / div >
< div class = "line" > < a id = "l00394" name = "l00394" > < / a > < span class = "lineno" > 394< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > grad_mu_val = grad_mu[k].Evaluate(vars_val);< / div >
< div class = "line" > < a id = "l00395" name = "l00395" > < / a > < span class = "lineno" > 395< / span > grad_mu_vals.push_back(grad_mu_val);< / div >
< div class = "line" > < a id = "l00396" name = "l00396" > < / a > < span class = "lineno" > 396< / span > mu[k] = < a class = "code hl_variable" href = "alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045" > std::min< / a > (0.0, mu[k] + step_size_t * grad_mu_val);< / div >
< div class = "line" > < a id = "l00397" name = "l00397" > < / a > < span class = "lineno" > 397< / span > < span class = "keywordflow" > if< / span > (grad_mu_val < 0) {< / div >
< div class = "line" > < a id = "l00398" name = "l00398" > < / a > < span class = "lineno" > 398< / span > feasible = < span class = "keyword" > false< / span > ;< / div >
< div class = "line" > < a id = "l00399" name = "l00399" > < / a > < span class = "lineno" > 399< / span > }< / div >
< div class = "line" > < a id = "l00400" name = "l00400" > < / a > < span class = "lineno" > 400< / span > }< / div >
< div class = "line" > < a id = "l00401" name = "l00401" > < / a > < span class = "lineno" > 401< / span > < span class = "comment" > // Bounds update< / span > < / div >
< div class = "line" > < a id = "l00402" name = "l00402" > < / a > < span class = "lineno" > 402< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > path_cost = < a class = "code hl_variable" href = "routing__flow_8cc.html#a75d7b5e4cab1e156cc7a2c5eba1e16f1" > cost< / a > .Evaluate(vars_val);< / div >
< div class = "line" > < a id = "l00403" name = "l00403" > < / a > < span class = "lineno" > 403< / span > < span class = "keywordflow" > if< / span > (feasible & & path_cost < < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > ) {< / div >
< div class = "line" > < a id = "l00404" name = "l00404" > < / a > < span class = "lineno" > 404< / span > best_solution_resource_1 = resource_1.< a class = "code hl_function" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html#a22c903e7b46f35670371e44edd8dc6b1" > Evaluate< / a > (vars_val);< / div >
< div class = "line" > < a id = "l00405" name = "l00405" > < / a > < span class = "lineno" > 405< / span > best_solution_resource_2 = resource_2.< a class = "code hl_function" href = "classoperations__research_1_1math__opt_1_1_linear_expression.html#a22c903e7b46f35670371e44edd8dc6b1" > Evaluate< / a > (vars_val);< / div >
< div class = "line" > < a id = "l00406" name = "l00406" > < / a > < span class = "lineno" > 406< / span > < span class = "keywordflow" > if< / span > (lagrangian_output) {< / div >
< div class = "line" > < a id = "l00407" name = "l00407" > < / a > < span class = "lineno" > 407< / span > std::cout < < < span class = "stringliteral" > " Feasible solution with" < / span > < / div >
< div class = "line" > < a id = "l00408" name = "l00408" > < / a > < span class = "lineno" > 408< / span > < < absl::StrFormat(< / div >
< div class = "line" > < a id = "l00409" name = "l00409" > < / a > < span class = "lineno" > 409< / span > < span class = "stringliteral" > " cost=%4.2f, resource_1=%4.2f, and resource_2=%4.2f. " < / span > ,< / div >
< div class = "line" > < a id = "l00410" name = "l00410" > < / a > < span class = "lineno" > 410< / span > path_cost, best_solution_resource_1,< / div >
< div class = "line" > < a id = "l00411" name = "l00411" > < / a > < span class = "lineno" > 411< / span > best_solution_resource_2)< / div >
< div class = "line" > < a id = "l00412" name = "l00412" > < / a > < span class = "lineno" > 412< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00413" name = "l00413" > < / a > < span class = "lineno" > 413< / span > }< / div >
< div class = "line" > < a id = "l00414" name = "l00414" > < / a > < span class = "lineno" > 414< / span > < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > = path_cost;< / div >
< div class = "line" > < a id = "l00415" name = "l00415" > < / a > < span class = "lineno" > 415< / span > }< / div >
< div class = "line" > < a id = "l00416" name = "l00416" > < / a > < span class = "lineno" > 416< / span > < span class = "keywordflow" > if< / span > (< a class = "code hl_variable" href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > < result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08" > objective_value< / a > ()) {< / div >
< div class = "line" > < a id = "l00417" name = "l00417" > < / a > < span class = "lineno" > 417< / span > < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > = result.< a class = "code hl_function" href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08" > objective_value< / a > ();< / div >
< div class = "line" > < a id = "l00418" name = "l00418" > < / a > < span class = "lineno" > 418< / span > }< / div >
< div class = "line" > < a id = "l00419" name = "l00419" > < / a > < span class = "lineno" > 419< / span > < / div >
< div class = "line" > < a id = "l00420" name = "l00420" > < / a > < span class = "lineno" > 420< / span > < span class = "keywordflow" > if< / span > (lagrangian_output) {< / div >
< div class = "line" > < a id = "l00421" name = "l00421" > < / a > < span class = "lineno" > 421< / span > std::cout < < absl::StrFormat(< span class = "stringliteral" > " %4d %6.3f %6.3f %9.3f" < / span > , iterations,< / div >
< div class = "line" > < a id = "l00422" name = "l00422" > < / a > < span class = "lineno" > 422< / span > < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > , < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > , step_size_t)< / div >
< div class = "line" > < a id = "l00423" name = "l00423" > < / a > < span class = "lineno" > 423< / span > < < < span class = "stringliteral" > " " < / span > < < < a class = "code hl_function" href = "namespacegtl.html#a252ef610941828aa417152c3230ca670" > gtl::LogContainer< / a > (mu) < < < span class = "stringliteral" > " " < / span > < / div >
< div class = "line" > < a id = "l00424" name = "l00424" > < / a > < span class = "lineno" > 424< / span > < < < a class = "code hl_function" href = "namespacegtl.html#a252ef610941828aa417152c3230ca670" > gtl::LogContainer< / a > (grad_mu_vals) < < std::endl;< / div >
< div class = "line" > < a id = "l00425" name = "l00425" > < / a > < span class = "lineno" > 425< / span > }< / div >
< div class = "line" > < a id = "l00426" name = "l00426" > < / a > < span class = "lineno" > 426< / span > < / div >
< div class = "line" > < a id = "l00427" name = "l00427" > < / a > < span class = "lineno" > 427< / span > < span class = "comment" > // Termination criteria< / span > < / div >
< div class = "line" > < a id = "l00428" name = "l00428" > < / a > < span class = "lineno" > 428< / span > < span class = "keywordtype" > double< / span > norm = 0;< / div >
< div class = "line" > < a id = "l00429" name = "l00429" > < / a > < span class = "lineno" > 429< / span > < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > double< / span > < a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > : grad_mu_vals) {< / div >
< div class = "line" > < a id = "l00430" name = "l00430" > < / a > < span class = "lineno" > 430< / span > norm += (< a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > * < a class = "code hl_variable" href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > );< / div >
< div class = "line" > < a id = "l00431" name = "l00431" > < / a > < span class = "lineno" > 431< / span > }< / div >
< div class = "line" > < a id = "l00432" name = "l00432" > < / a > < span class = "lineno" > 432< / span > norm = sqrt(norm);< / div >
< div class = "line" > < a id = "l00433" name = "l00433" > < / a > < span class = "lineno" > 433< / span > < span class = "keywordflow" > if< / span > (iterations == max_iterations || < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > == < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > ||< / div >
< div class = "line" > < a id = "l00434" name = "l00434" > < / a > < span class = "lineno" > 434< / span > step_size_t * norm < < a class = "code hl_variable" href = "lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41" > kZeroTol< / a > ) {< / div >
< div class = "line" > < a id = "l00435" name = "l00435" > < / a > < span class = "lineno" > 435< / span > termination = < span class = "keyword" > true< / span > ;< / div >
< div class = "line" > < a id = "l00436" name = "l00436" > < / a > < span class = "lineno" > 436< / span > }< / div >
< div class = "line" > < a id = "l00437" name = "l00437" > < / a > < span class = "lineno" > 437< / span > iterations++;< / div >
< div class = "line" > < a id = "l00438" name = "l00438" > < / a > < span class = "lineno" > 438< / span > }< / div >
< div class = "line" > < a id = "l00439" name = "l00439" > < / a > < span class = "lineno" > 439< / span > < / div >
< div class = "line" > < a id = "l00440" name = "l00440" > < / a > < span class = "lineno" > 440< / span > std::cout < < < span class = "stringliteral" > " Lagrangian relaxation with 2 side constraints" < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00441" name = "l00441" > < / a > < span class = "lineno" > 441< / span > std::cout < < < span class = "stringliteral" > " Constraint for resource 1 dualized: " < / span > < / div >
< div class = "line" > < a id = "l00442" name = "l00442" > < / a > < span class = "lineno" > 442< / span > < < (dualized_resource_1 ? < span class = "stringliteral" > " true" < / span > : < span class = "stringliteral" > " false" < / span > ) < < std::endl;< / div >
< div class = "line" > < a id = "l00443" name = "l00443" > < / a > < span class = "lineno" > 443< / span > std::cout < < < span class = "stringliteral" > " Constraint for resource 2 dualized: " < / span > < / div >
< div class = "line" > < a id = "l00444" name = "l00444" > < / a > < span class = "lineno" > 444< / span > < < (dualized_resource_2 ? < span class = "stringliteral" > " true" < / span > : < span class = "stringliteral" > " false" < / span > ) < < std::endl;< / div >
< div class = "line" > < a id = "l00445" name = "l00445" > < / a > < span class = "lineno" > 445< / span > std::cout < < absl::StrFormat(< span class = "stringliteral" > " Lower bound: %6.3f" < / span > , < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > ) < < std::endl;< / div >
< div class = "line" > < a id = "l00446" name = "l00446" > < / a > < span class = "lineno" > 446< / span > std::cout < < absl::StrFormat(< span class = "stringliteral" > " Upper bound: %6.3f (Integer solution)" < / span > ,< / div >
< div class = "line" > < a id = "l00447" name = "l00447" > < / a > < span class = "lineno" > 447< / span > < a class = "code hl_variable" href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > )< / div >
< div class = "line" > < a id = "l00448" name = "l00448" > < / a > < span class = "lineno" > 448< / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00449" name = "l00449" > < / a > < span class = "lineno" > 449< / span > std::cout < < < span class = "stringliteral" > " ========================================" < / span > < < std::endl;< / div >
< div class = "line" > < a id = "l00450" name = "l00450" > < / a > < span class = "lineno" > 450< / span > < span class = "keywordflow" > return< / span > absl::OkStatus();< / div >
< div class = "line" > < a id = "l00451" name = "l00451" > < / a > < span class = "lineno" > 451< / span > }< / div >
< div class = "line" > < a id = "l00452" name = "l00452" > < / a > < span class = "lineno" > 452< / span > < / div >
< div class = "line" > < a id = "l00453" name = "l00453" > < / a > < span class = "lineno" > 453< / span > < span class = "keywordtype" > void< / span > RelaxModel(FlowModel& flow_model) {< / div >
< div class = "line" > < a id = "l00454" name = "l00454" > < / a > < span class = "lineno" > 454< / span > < span class = "keywordflow" > for< / span > (< a class = "code hl_class" href = "classoperations__research_1_1math__opt_1_1_variable.html" > math_opt::Variable< / a > & < a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > : flow_model.flow_vars) {< / div >
< div class = "line" > < a id = "l00455" name = "l00455" > < / a > < span class = "lineno" > 455< / span > flow_model.model-> set_continuous(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > );< / div >
< div class = "line" > < a id = "l00456" name = "l00456" > < / a > < span class = "lineno" > 456< / span > flow_model.model-> set_lower_bound(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > , 0.0);< / div >
< div class = "line" > < a id = "l00457" name = "l00457" > < / a > < span class = "lineno" > 457< / span > flow_model.model-> set_upper_bound(< a class = "code hl_variable" href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > , 1.0);< / div >
< div class = "line" > < a id = "l00458" name = "l00458" > < / a > < span class = "lineno" > 458< / span > }< / div >
< div class = "line" > < a id = "l00459" name = "l00459" > < / a > < span class = "lineno" > 459< / span > }< / div >
< div class = "line" > < a id = "l00460" name = "l00460" > < / a > < span class = "lineno" > 460< / span > < / div >
< div class = "line" > < a id = "l00461" name = "l00461" > < / a > < span class = "lineno" > 461< / span > absl::Status SolveFullModel(< span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > & graph, < span class = "keywordtype" > double< / span > max_resource_1,< / div >
< div class = "line" > < a id = "l00462" name = "l00462" > < / a > < span class = "lineno" > 462< / span > < span class = "keywordtype" > double< / span > max_resource_2) {< / div >
< div class = "line" > < a id = "l00463" name = "l00463" > < / a > < span class = "lineno" > 463< / span > < a class = "code hl_define" href = "base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011" > ASSIGN_OR_RETURN< / a > (FlowModel flow_model,< / div >
< div class = "line" > < a id = "l00464" name = "l00464" > < / a > < span class = "lineno" > 464< / span > SolveMip(graph, max_resource_1, max_resource_2));< / div >
< div class = "line" > < a id = "l00465" name = "l00465" > < / a > < span class = "lineno" > 465< / span > RelaxModel(flow_model);< / div >
< div class = "line" > < a id = "l00466" name = "l00466" > < / a > < span class = "lineno" > 466< / span > < span class = "keywordflow" > return< / span > SolveLinearRelaxation(flow_model, graph, max_resource_1,< / div >
< div class = "line" > < a id = "l00467" name = "l00467" > < / a > < span class = "lineno" > 467< / span > max_resource_2);< / div >
< div class = "line" > < a id = "l00468" name = "l00468" > < / a > < span class = "lineno" > 468< / span > }< / div >
< div class = "line" > < a id = "l00469" name = "l00469" > < / a > < span class = "lineno" > 469< / span > < / div >
< div class = "line" > < a id = "l00470" name = "l00470" > < / a > < span class = "lineno" > 470< / span > absl::Status Main() {< / div >
< div class = "line" > < a id = "l00471" name = "l00471" > < / a > < span class = "lineno" > 471< / span > < span class = "comment" > // Problem data< / span > < / div >
< div class = "line" > < a id = "l00472" name = "l00472" > < / a > < span class = "lineno" > 472< / span > < span class = "keyword" > const< / span > < a class = "code hl_typedef" href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > Graph< / a > graph = CreateSampleNetwork();< / div >
< div class = "line" > < a id = "l00473" name = "l00473" > < / a > < span class = "lineno" > 473< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_1 = 10;< / div >
< div class = "line" > < a id = "l00474" name = "l00474" > < / a > < span class = "lineno" > 474< / span > < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > max_resource_2 = 4;< / div >
< div class = "line" > < a id = "l00475" name = "l00475" > < / a > < span class = "lineno" > 475< / span > < / div >
< div class = "line" > < a id = "l00476" name = "l00476" > < / a > < span class = "lineno" > 476< / span > < a class = "code hl_define" href = "base_2status__macros_8h.html#acdc223d8c59d5c591dc6b4e88257627b" > RETURN_IF_ERROR< / a > (SolveFullModel(graph, max_resource_1, max_resource_2))< / div >
< div class = "line" > < a id = "l00477" name = "l00477" > < / a > < span class = "lineno" > 477< / span > < < < span class = "stringliteral" > " full solve failed" < / span > ;< / div >
< div class = "line" > < a id = "l00478" name = "l00478" > < / a > < span class = "lineno" > 478< / span > < a class = "code hl_define" href = "base_2status__macros_8h.html#acdc223d8c59d5c591dc6b4e88257627b" > RETURN_IF_ERROR< / a > (< / div >
< div class = "line" > < a id = "l00479" name = "l00479" > < / a > < span class = "lineno" > 479< / span > SolveLagrangianRelaxation(graph, max_resource_1, max_resource_2))< / div >
< div class = "line" > < a id = "l00480" name = "l00480" > < / a > < span class = "lineno" > 480< / span > < < < span class = "stringliteral" > " lagrangian solve failed" < / span > ;< / div >
< div class = "line" > < a id = "l00481" name = "l00481" > < / a > < span class = "lineno" > 481< / span > < span class = "keywordflow" > return< / span > absl::OkStatus();< / div >
< div class = "line" > < a id = "l00482" name = "l00482" > < / a > < span class = "lineno" > 482< / span > }< / div >
< div class = "line" > < a id = "l00483" name = "l00483" > < / a > < span class = "lineno" > 483< / span > } < span class = "comment" > // namespace< / span > < / div >
< div class = "line" > < a id = "l00484" name = "l00484" > < / a > < span class = "lineno" > 484< / span > < / div >
< div class = "line" > < a id = "l00485" name = "l00485" > < / a > < span class = "lineno" > < a class = "line" href = "lagrangian__relaxation_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627" > 485< / a > < / span > < span class = "keywordtype" > int< / span > < a class = "code hl_function" href = "lagrangian__relaxation_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627" > main< / a > (< span class = "keywordtype" > int< / span > argc, < span class = "keywordtype" > char< / span > ** argv) {< / div >
< div class = "line" > < a id = "l00486" name = "l00486" > < / a > < span class = "lineno" > 486< / span > < a class = "code hl_function" href = "init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb" > InitGoogle< / a > (argv[0], & argc, & argv, < span class = "keyword" > true< / span > );< / div >
< div class = "line" > < a id = "l00487" name = "l00487" > < / a > < span class = "lineno" > 487< / span > < span class = "keyword" > const< / span > absl::Status < a class = "code hl_variable" href = "g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d" > status< / a > = Main();< / div >
< div class = "line" > < a id = "l00488" name = "l00488" > < / a > < span class = "lineno" > 488< / span > < span class = "keywordflow" > if< / span > (!< a class = "code hl_variable" href = "g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d" > status< / a > .ok()) {< / div >
< div class = "line" > < a id = "l00489" name = "l00489" > < / a > < span class = "lineno" > 489< / span > < a class = "code hl_define" href = "base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae" > LOG< / a > (QFATAL) < < < a class = "code hl_variable" href = "g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d" > status< / a > ;< / div >
< div class = "line" > < a id = "l00490" name = "l00490" > < / a > < span class = "lineno" > 490< / span > }< / div >
< div class = "line" > < a id = "l00491" name = "l00491" > < / a > < span class = "lineno" > 491< / span > < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < a id = "l00492" name = "l00492" > < / a > < span class = "lineno" > 492< / span > }< / div >
2022-01-17 21:42:14 +01:00
< div class = "ttc" id = "aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045" > < div class = "ttname" > < a href = "alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045" > min< / a > < / div > < div class = "ttdeci" > int64_t min< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "alldiff__cst_8cc_source.html#l00139" > alldiff_cst.cc:139< / a > < / div > < / div >
< div class = "ttc" id = "abase_2logging_8h_html" > < div class = "ttname" > < a href = "base_2logging_8h.html" > logging.h< / a > < / div > < / div >
< div class = "ttc" id = "abase_2logging_8h_html_a3e1cfef60e774a81f30eaddf26a3a274" > < div class = "ttname" > < a href = "base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274" > CHECK< / a > < / div > < div class = "ttdeci" > #define CHECK(condition)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00495" > base/logging.h:495< / a > < / div > < / div >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "abase_2logging_8h_html_a4bd2e815ca2f702a4b6aa744b1ff3b82" > < div class = "ttname" > < a href = "base_2logging_8h.html#a4bd2e815ca2f702a4b6aa744b1ff3b82" > CHECK_LT< / a > < / div > < div class = "ttdeci" > #define CHECK_LT(val1, val2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00706" > base/logging.h:706< / a > < / div > < / div >
< div class = "ttc" id = "abase_2logging_8h_html_a7e03ec13560fa94a8fea569960d7efc6" > < div class = "ttname" > < a href = "base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6" > CHECK_GT< / a > < / div > < div class = "ttdeci" > #define CHECK_GT(val1, val2)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2logging_8h_source.html#l00708" > base/logging.h:708< / a > < / div > < / div >
< 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#l00420" > base/logging.h:420< / a > < / div > < / div >
< div class = "ttc" id = "abase_2status__macros_8h_html" > < div class = "ttname" > < a href = "base_2status__macros_8h.html" > status_macros.h< / a > < / div > < / div >
< div class = "ttc" id = "abase_2status__macros_8h_html_a600de4b8f65fe0a4b1898041634f9011" > < div class = "ttname" > < a href = "base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011" > ASSIGN_OR_RETURN< / a > < / div > < div class = "ttdeci" > #define ASSIGN_OR_RETURN(lhs, rexpr)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2status__macros_8h_source.html#l00046" > base/status_macros.h:46< / a > < / div > < / div >
< div class = "ttc" id = "abase_2status__macros_8h_html_acdc223d8c59d5c591dc6b4e88257627b" > < div class = "ttname" > < a href = "base_2status__macros_8h.html#acdc223d8c59d5c591dc6b4e88257627b" > RETURN_IF_ERROR< / a > < / div > < div class = "ttdeci" > #define RETURN_IF_ERROR(expr)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "base_2status__macros_8h_source.html#l00027" > base/status_macros.h:27< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1math__opt_1_1_id_map_html" > < div class = "ttname" > < a href = "classoperations__research_1_1math__opt_1_1_id_map.html" > operations_research::math_opt::IdMap< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "id__map_8h_source.html#l00053" > id_map.h:53< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1math__opt_1_1_linear_expression_html" > < div class = "ttname" > < a href = "classoperations__research_1_1math__opt_1_1_linear_expression.html" > operations_research::math_opt::LinearExpression< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "variable__and__expressions_8h_source.html#l00193" > variable_and_expressions.h:193< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1math__opt_1_1_linear_expression_html_a22c903e7b46f35670371e44edd8dc6b1" > < div class = "ttname" > < a href = "classoperations__research_1_1math__opt_1_1_linear_expression.html#a22c903e7b46f35670371e44edd8dc6b1" > operations_research::math_opt::LinearExpression::Evaluate< / a > < / div > < div class = "ttdeci" > double Evaluate(const VariableMap< double > & variable_values) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "variable__and__expressions_8cc_source.html#l00068" > variable_and_expressions.cc:68< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1math__opt_1_1_model_html" > < div class = "ttname" > < a href = "classoperations__research_1_1math__opt_1_1_model.html" > operations_research::math_opt::Model< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "math__opt_2cpp_2model_8h_source.html#l00091" > math_opt/cpp/model.h:91< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1math__opt_1_1_variable_html" > < div class = "ttname" > < a href = "classoperations__research_1_1math__opt_1_1_variable.html" > operations_research::math_opt::Variable< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "variable__and__expressions_8h_source.html#l00115" > variable_and_expressions.h:115< / a > < / div > < / div >
2022-01-17 21:42:14 +01:00
< div class = "ttc" id = "acontainer__logging_8h_html" > < div class = "ttname" > < a href = "container__logging_8h.html" > container_logging.h< / a > < / div > < / div >
< div class = "ttc" id = "ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514" > < div class = "ttname" > < a href = "demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514" > value< / a > < / div > < div class = "ttdeci" > int64_t value< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "demon__profiler_8cc_source.html#l00044" > demon_profiler.cc:44< / a > < / div > < / div >
< div class = "ttc" id = "aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465" > < div class = "ttname" > < a href = "expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465" > var< / a > < / div > < div class = "ttdeci" > IntVar * var< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "expr__array_8cc_source.html#l01874" > expr_array.cc:1874< / a > < / div > < / div >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "ag__gurobi_8cc_html_a2237393c7ae7ad7344c9885066d5ab6d" > < div class = "ttname" > < a href = "g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d" > status< / a > < / div > < div class = "ttdeci" > absl::Status status< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "g__gurobi_8cc_source.html#l00035" > g_gurobi.cc:35< / a > < / div > < / div >
2022-01-17 21:42:14 +01:00
< div class = "ttc" id = "agscip__solver_8cc_html_a1ba5ca0f61f2fa13bd23bf0f89004f35" > < div class = "ttname" > < a href = "gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35" > upper_bound< / a > < / div > < div class = "ttdeci" > double upper_bound< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "gscip__solver_8cc_source.html#l00137" > gscip_solver.cc:137< / a > < / div > < / div >
< div class = "ttc" id = "agscip__solver_8cc_html_a1e2f9a2352c1d9a6cada9544898fceec" > < div class = "ttname" > < a href = "gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec" > lower_bound< / a > < / div > < div class = "ttdeci" > double lower_bound< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "gscip__solver_8cc_source.html#l00136" > gscip_solver.cc:136< / a > < / div > < / div >
< div class = "ttc" id = "agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf" > < div class = "ttname" > < a href = "gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf" > model< / a > < / div > < div class = "ttdeci" > GRBmodel * model< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "gurobi__interface_8cc_source.html#l00274" > gurobi_interface.cc:274< / a > < / div > < / div >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "ainit__google_8h_html" > < div class = "ttname" > < a href = "init__google_8h.html" > init_google.h< / a > < / div > < / div >
< div class = "ttc" id = "ainit__google_8h_html_a16af2bccb0196e1a9bb628559c95b7cb" > < div class = "ttname" > < a href = "init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb" > InitGoogle< / a > < / div > < div class = "ttdeci" > void InitGoogle(const char *usage, int *argc, char ***argv, bool deprecated)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "init__google_8h_source.html#l00032" > init_google.h:32< / a > < / div > < / div >
< div class = "ttc" id = "alagrangian__relaxation_8cc_html_a3c04138a5bfe5d72780bb7e82a18e627" > < div class = "ttname" > < a href = "lagrangian__relaxation_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627" > main< / a > < / div > < div class = "ttdeci" > int main(int argc, char **argv)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lagrangian__relaxation_8cc_source.html#l00485" > lagrangian_relaxation.cc:485< / a > < / div > < / div >
2022-01-17 21:42:14 +01:00
< div class = "ttc" id = "alagrangian__relaxation_8cc_html_a3dd301d5a8f137443e3619bd9882b23a" > < div class = "ttname" > < a href = "lagrangian__relaxation_8cc.html#a3dd301d5a8f137443e3619bd9882b23a" > ABSL_FLAG< / a > < / div > < div class = "ttdeci" > ABSL_FLAG(double, step_size, 0.95, " Stepsize for gradient ascent, determined as step_size^t." )< / div > < / div >
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< div class = "ttc" id = "alagrangian__relaxation_8cc_html_a6ffb9a02546adae760787b2366ae6e41" > < div class = "ttname" > < a href = "lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41" > kZeroTol< / a > < / div > < div class = "ttdeci" > constexpr double kZeroTol< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lagrangian__relaxation_8cc_source.html#l00115" > lagrangian_relaxation.cc:115< / a > < / div > < / div >
< div class = "ttc" id = "alocal__search_8cc_html_a30b5726116ac85ea64777e5d6e333894" > < div class = "ttname" > < a href = "local__search_8cc.html#a30b5726116ac85ea64777e5d6e333894" > arc< / a > < / div > < div class = "ttdeci" > int arc< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "local__search_8cc_source.html#l02751" > local_search.cc:2751< / a > < / div > < / div >
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< div class = "ttc" id = "amath__opt_8h_html" > < div class = "ttname" > < a href = "math__opt_8h.html" > math_opt.h< / a > < / div > < / div >
< div class = "ttc" id = "amathutil_8h_html" > < div class = "ttname" > < a href = "mathutil_8h.html" > mathutil.h< / a > < / div > < / div >
< div class = "ttc" id = "anamespacegtl_html_a252ef610941828aa417152c3230ca670" > < div class = "ttname" > < a href = "namespacegtl.html#a252ef610941828aa417152c3230ca670" > gtl::LogContainer< / a > < / div > < div class = "ttdeci" > auto LogContainer(const ContainerT & container, const PolicyT & policy) -> decltype(gtl::LogRange(container.begin(), container.end(), policy))< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "container__logging_8h_source.html#l00275" > container_logging.h:275< / a > < / div > < / div >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "anamespaceoperations__research_1_1math__opt_html" > < div class = "ttname" > < a href = "namespaceoperations__research_1_1math__opt.html" > operations_research::math_opt< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "arrow__operator__proxy_8h_source.html#l00020" > arrow_operator_proxy.h:20< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_1_1math__opt_html_a5767ee23f380e72488d3c7ebf2d742b1" > < div class = "ttname" > < a href = "namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1" > operations_research::math_opt::Solve< / a > < / div > < div class = "ttdeci" > absl::StatusOr< SolveResult > Solve(const Model & model, const SolverType solver_type, const SolveArguments & solve_args, const SolverInitArguments & init_args)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "solve_8cc_source.html#l00094" > solve.cc:94< / a > < / div > < / div >
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< div class = "ttc" id = "anamespaceoperations__research_html_a7deeae530369e107f9d91c1a189f451f" > < div class = "ttname" > < a href = "namespaceoperations__research.html#a7deeae530369e107f9d91c1a189f451f" > operations_research::Arc< / a > < / div > < div class = "ttdeci" > std::pair< int64_t, int64_t > Arc< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "search_8cc_source.html#l03434" > search.cc:3434< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceutil_html_a2f76166dbe0c4055a1f256235ad00478" > < div class = "ttname" > < a href = "namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478" > util::Graph< / a > < / div > < div class = "ttdeci" > ListGraph Graph< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "graph_8h_source.html#l02362" > graph.h:2362< / a > < / div > < / div >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "anamespaceutil_html_a302ee4bfcb86ea9ed64a193ed0b14648" > < div class = "ttname" > < a href = "namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648" > util::InternalErrorBuilder< / a > < / div > < div class = "ttdeci" > StatusBuilder InternalErrorBuilder()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "status__builder_8h_source.html#l00084" > status_builder.h:84< / a > < / div > < / div >
2022-01-17 21:42:14 +01:00
< 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 >
2022-03-04 00:11:33 +01:00
< div class = "ttc" id = "astatus__builder_8h_html" > < div class = "ttname" > < a href = "status__builder_8h.html" > status_builder.h< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1math__opt_1_1_solve_result_html" > < div class = "ttname" > < a href = "structoperations__research_1_1math__opt_1_1_solve_result.html" > operations_research::math_opt::SolveResult< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "solve__result_8h_source.html#l00295" > solve_result.h:295< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1math__opt_1_1_solve_result_html_a77d1ea96211300e9417b965981953c81" > < div class = "ttname" > < a href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81" > operations_research::math_opt::SolveResult::termination< / a > < / div > < div class = "ttdeci" > Termination termination< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "solve__result_8h_source.html#l00300" > solve_result.h:300< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1math__opt_1_1_solve_result_html_a84f066c304d8bcbb9567be094feb9b08" > < div class = "ttname" > < a href = "structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08" > operations_research::math_opt::SolveResult::objective_value< / a > < / div > < div class = "ttdeci" > double objective_value() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "solve__result_8cc_source.html#l00358" > solve_result.cc:358< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1math__opt_1_1_solve_result_html_ac4a6e078f25aa73eec5271d449a12532" > < div class = "ttname" > < a href = "structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532" > operations_research::math_opt::SolveResult::variable_values< / a > < / div > < div class = "ttdeci" > const VariableMap< double > & variable_values() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "solve__result_8cc_source.html#l00369" > solve_result.cc:369< / a > < / div > < / div >
< div class = "ttc" id = "astructoperations__research_1_1math__opt_1_1_termination_html_a36d5365d462f57468ba3a9d8ae6bbec9" > < div class = "ttname" > < a href = "structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9" > operations_research::math_opt::Termination::reason< / a > < / div > < div class = "ttdeci" > TerminationReason reason< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "solve__result_8h_source.html#l00261" > solve_result.h:261< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
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