308 lines
11 KiB
C++
308 lines
11 KiB
C++
// Copyright 2010-2025 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "ortools/sat/linear_programming_constraint.h"
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#include <stdint.h>
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#include <cstdlib>
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#include <string>
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#include <utility>
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#include <vector>
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#include "absl/log/check.h"
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#include "absl/types/span.h"
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#include "gtest/gtest.h"
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#include "ortools/lp_data/lp_types.h"
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#include "ortools/sat/cp_model_solver.h"
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#include "ortools/sat/integer.h"
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#include "ortools/sat/integer_base.h"
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#include "ortools/sat/integer_search.h"
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#include "ortools/sat/linear_constraint.h"
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#include "ortools/sat/linear_constraint_manager.h"
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#include "ortools/sat/model.h"
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#include "ortools/sat/sat_parameters.pb.h"
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#include "ortools/sat/sat_solver.h"
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#include "ortools/util/strong_integers.h"
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namespace operations_research {
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namespace sat {
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namespace {
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TEST(ScatteredIntegerVectorTest, BasicDenseBehavior) {
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ScatteredIntegerVector v;
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v.ClearAndResize(10);
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v.AddLinearExpressionMultiple(IntegerValue(4), {glop::ColIndex(2)},
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{IntegerValue(3)}, IntegerValue(3));
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v.AddLinearExpressionMultiple(IntegerValue(3), {glop::ColIndex(1)},
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{IntegerValue(3)}, IntegerValue(3));
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v.AddLinearExpressionMultiple(IntegerValue(5), {glop::ColIndex(2)},
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{IntegerValue(3)}, IntegerValue(3));
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const std::vector<std::pair<glop::ColIndex, IntegerValue>> expected{
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{glop::ColIndex(1), IntegerValue(3 * 3)},
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{glop::ColIndex(2), IntegerValue(3 * 4 + 5 * 3)}};
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EXPECT_FALSE(v.IsSparse());
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EXPECT_EQ(v.GetTerms(), expected);
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}
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TEST(ScatteredIntegerVectorTest, BasicSparseBehavior) {
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ScatteredIntegerVector v;
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v.ClearAndResize(100000);
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v.AddLinearExpressionMultiple(IntegerValue(4), {glop::ColIndex(2)},
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{IntegerValue(3)}, IntegerValue(3));
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v.AddLinearExpressionMultiple(IntegerValue(3), {glop::ColIndex(1)},
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{IntegerValue(3)}, IntegerValue(3));
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v.AddLinearExpressionMultiple(IntegerValue(5), {glop::ColIndex(2)},
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{IntegerValue(3)}, IntegerValue(3));
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const std::vector<std::pair<glop::ColIndex, IntegerValue>> expected{
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{glop::ColIndex(1), IntegerValue(3 * 3)},
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{glop::ColIndex(2), IntegerValue(3 * 4 + 5 * 3)}};
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EXPECT_EQ(v.GetTerms(), expected);
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EXPECT_TRUE(v.IsSparse());
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}
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// TODO(user): Check that SAT solutions respect linear equations.
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struct LPProblem {
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const std::vector<IntegerValue> integer_lb;
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const std::vector<IntegerValue> integer_ub;
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const std::vector<IntegerValue> constraint_lb;
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const std::vector<IntegerValue> constraint_ub;
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const std::vector<std::vector<int>> constraint_integer_indices;
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const std::vector<std::vector<IntegerValue>> constraint_integer_coefs;
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const std::vector<int> objective_indices;
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int num_integer_vars() const { return integer_lb.size(); }
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int num_constraints() const { return constraint_lb.size(); }
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int num_objectives() const { return objective_indices.size(); }
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};
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// Generates a problem that encodes a permutation as a bipartite matching
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// from size 'left' nodes to size 'right' nodes.
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// Decision variables are edges linking left nodes to right nodes.
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// For a given node, only one adjacent edge can be present,
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// which is encoded by one constraint per node.
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LPProblem GeneratePermutationProblem(int size) {
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const std::vector<IntegerValue> edge_lb(size * size, IntegerValue(0));
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const std::vector<IntegerValue> edge_ub(size * size, IntegerValue(1));
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const std::vector<IntegerValue> node_lb(2 * size, IntegerValue(1));
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const std::vector<IntegerValue> node_ub(2 * size, IntegerValue(1));
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std::vector<std::vector<int>> node_constraint_indices;
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std::vector<std::vector<IntegerValue>> node_constraint_coefs;
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// Left and right nodes are indexed by [0, size).
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// The edge (left, right) has number left * size + right.
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const std::vector<IntegerValue> ones(size, IntegerValue(1));
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for (int left = 0; left < size; left++) {
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std::vector<int> indices;
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for (int right = 0; right < size; right++) {
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indices.push_back(left * size + right);
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}
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node_constraint_indices.push_back(indices);
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node_constraint_coefs.push_back(ones);
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}
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for (int right = 0; right < size; right++) {
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std::vector<int> indices;
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for (int left = 0; left < size; left++) {
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indices.push_back(left * size + right);
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}
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node_constraint_indices.push_back(indices);
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node_constraint_coefs.push_back(ones);
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}
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return LPProblem{edge_lb,
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edge_ub,
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node_lb,
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node_ub,
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node_constraint_indices,
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node_constraint_coefs,
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{}};
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}
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int CountSolutionsOfLPProblemUsingSAT(const LPProblem& problem) {
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Model model;
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model.GetOrCreate<SatParameters>()->set_add_lp_constraints_lazily(false);
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std::vector<IntegerVariable> cp_variables;
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const int num_cp_vars = problem.num_integer_vars();
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for (int i = 0; i < num_cp_vars; i++) {
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IntegerVariable var = model.Add(NewIntegerVariable(
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problem.integer_lb[i].value(), problem.integer_ub[i].value()));
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cp_variables.push_back(var);
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}
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LinearProgrammingConstraint* lp =
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new LinearProgrammingConstraint(&model, cp_variables);
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model.TakeOwnership(lp);
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const int num_constraints = problem.num_constraints();
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for (int c = 0; c < num_constraints; c++) {
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LinearConstraint ct(problem.constraint_lb[c], problem.constraint_ub[c]);
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const int num_integer = problem.constraint_integer_indices[c].size();
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ct.resize(num_integer);
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for (int j = 0; j < num_integer; j++) {
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ct.vars[j] = cp_variables[problem.constraint_integer_indices[c][j]];
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ct.coeffs[j] = problem.constraint_integer_coefs[c][j];
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}
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lp->AddLinearConstraint(std::move(ct));
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}
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lp->RegisterWith(&model);
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int num_solutions = 0;
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while (SolveIntegerProblemWithLazyEncoding(&model) ==
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SatSolver::Status::FEASIBLE) {
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model.Add(ExcludeCurrentSolutionAndBacktrack());
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num_solutions++;
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}
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return num_solutions;
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}
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TEST(LinearProgrammingConstraintTest, CountPermutations) {
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int factorial_of_size = 1;
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for (int size = 2; size < 6; size++) {
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factorial_of_size *= size;
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LPProblem problem = GeneratePermutationProblem(size);
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ASSERT_EQ(CountSolutionsOfLPProblemUsingSAT(problem), factorial_of_size);
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}
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}
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TEST(LinearProgrammingConstraintTest, SimpleInfeasibility) {
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// The following flow is infeasible, LP should detect it.
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//
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// source
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// = 2/2 0/2
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// ---------> ---------> A
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// | |
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// | |
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// 0/2 | | 0/2
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// | |
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// V V
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// B -------> ------->
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// 0/2 [3,4] = sink
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Model model;
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// We need this parameter at false to detect it on the first propagation.
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model.Add(NewSatParameters("add_lp_constraints_lazily:false"));
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// Variables for the source and sink demands, and flow amounts.
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const IntegerVariable source = model.Add(NewIntegerVariable(2, 2));
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const IntegerVariable source_a = model.Add(NewIntegerVariable(0, 2));
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const IntegerVariable source_b = model.Add(NewIntegerVariable(0, 2));
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const IntegerVariable a_sink = model.Add(NewIntegerVariable(0, 2));
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const IntegerVariable b_sink = model.Add(NewIntegerVariable(0, 2));
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const IntegerVariable sink = model.Add(NewIntegerVariable(3, 4));
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// LP Constraint and flow conservation equalities.
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LinearProgrammingConstraint* lp = new LinearProgrammingConstraint(
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&model, {source, source_a, source_b, a_sink, b_sink, sink});
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model.TakeOwnership(lp);
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LinearConstraintBuilder ct_source(IntegerValue(0), IntegerValue(0));
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ct_source.AddTerm(source, IntegerValue(1));
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ct_source.AddTerm(source_a, IntegerValue(-1));
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ct_source.AddTerm(source_b, IntegerValue(-1));
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lp->AddLinearConstraint(ct_source.Build());
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LinearConstraintBuilder ct_a(IntegerValue(0), IntegerValue(0));
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ct_a.AddTerm(source_a, IntegerValue(1));
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ct_a.AddTerm(a_sink, IntegerValue(-1));
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lp->AddLinearConstraint(ct_a.Build());
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LinearConstraintBuilder ct_b(IntegerValue(0), IntegerValue(0));
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ct_b.AddTerm(source_b, IntegerValue(1));
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ct_b.AddTerm(b_sink, IntegerValue(-1));
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lp->AddLinearConstraint(ct_b.Build());
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LinearConstraintBuilder ct_sink(IntegerValue(0), IntegerValue(0));
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ct_sink.AddTerm(a_sink, IntegerValue(1));
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ct_sink.AddTerm(b_sink, IntegerValue(1));
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ct_sink.AddTerm(sink, IntegerValue(-1));
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lp->AddLinearConstraint(ct_sink.Build());
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lp->RegisterWith(&model);
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ASSERT_FALSE(model.GetOrCreate<SatSolver>()->Propagate());
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}
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TEST(LinearProgrammingConstraintTest, EmptyLP) {
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Model model;
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model.Add(NewSatParameters("linearization_level:2"));
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LinearProgrammingConstraint* lp = new LinearProgrammingConstraint(&model, {});
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model.TakeOwnership(lp);
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lp->RegisterWith(&model);
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ASSERT_TRUE(model.GetOrCreate<SatSolver>()->Propagate());
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}
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// This tests that the scaling of reduced costs is done correctly,
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// using the problem
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// min 64 x s.t. 0 <= 27x <= 81, x in [0, 50]
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// The reduced cost of x should be 64.
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// This will be wrong if the reduced cost ignores the objective scaling.
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TEST(LinearProgrammingConstraintTest, ReducedCostScalingObjective) {
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Model m;
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IntegerVariable x = m.Add(NewIntegerVariable(0, 50));
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LinearProgrammingConstraint* lp = new LinearProgrammingConstraint(&m, {x});
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m.TakeOwnership(lp);
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LinearConstraintBuilder ct(IntegerValue(0), IntegerValue(81));
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ct.AddTerm(x, IntegerValue(27));
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lp->AddLinearConstraint(ct.Build());
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IntegerVariable obj = m.Add(NewIntegerVariable(0, 64 * 50));
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lp->SetObjectiveCoefficient(x, IntegerValue(64));
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lp->SetMainObjectiveVariable(obj);
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lp->RegisterWith(&m);
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lp->Propagate();
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const auto& reduced_costs = *m.GetOrCreate<ModelReducedCosts>();
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CHECK_LE(std::abs(reduced_costs[x] - 64), 1e-6);
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}
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// This tests that the scaling of reduced costs is done correctly,
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// using the problem
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// min 64 x + 32 y s.t. 0 <= 27x + 9y <= 81, x in [0, 50], y in [0, 20]
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// The reduced cost of x should be 64, y should be 20.
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// This will be wrong if the reduced cost ignores the column scaling.
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TEST(LinearProgrammingConstraintTest, ReducedCostScalingColumns) {
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Model m;
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IntegerVariable x = m.Add(NewIntegerVariable(0, 50));
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IntegerVariable y = m.Add(NewIntegerVariable(0, 20));
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LinearProgrammingConstraint* lp = new LinearProgrammingConstraint(&m, {x, y});
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m.TakeOwnership(lp);
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LinearConstraintBuilder ct(IntegerValue(0), IntegerValue(81));
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ct.AddTerm(x, IntegerValue(27));
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ct.AddTerm(y, IntegerValue(9));
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lp->AddLinearConstraint(ct.Build());
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IntegerVariable obj = m.Add(NewIntegerVariable(0, 64 * 50 + 32 * 20));
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lp->SetObjectiveCoefficient(x, IntegerValue(64));
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lp->SetObjectiveCoefficient(y, IntegerValue(32));
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lp->SetMainObjectiveVariable(obj);
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lp->RegisterWith(&m);
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lp->Propagate();
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const auto& reduced_costs = *m.GetOrCreate<ModelReducedCosts>();
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CHECK_LE(std::abs(reduced_costs[x] - 64), 1e-6);
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CHECK_LE(std::abs(reduced_costs[y] - 32), 1e-6);
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}
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} // namespace
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} // namespace sat
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} // namespace operations_research
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