ortools-clone/ortools/sat/cp_model_search_test.cc

// Copyright 2010-2025 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include <algorithm>
#include <limits>
#include <random>
#include <string>
#include <tuple>
#include <vector>

#include "absl/container/flat_hash_map.h"
#include "absl/log/log.h"
#include "absl/strings/str_join.h"
#include "gtest/gtest.h"
#include "ortools/base/gmock.h"
#include "ortools/base/parse_test_proto.h"
#include "ortools/sat/cp_model.pb.h"
#include "ortools/sat/cp_model_solver.h"
#include "ortools/sat/model.h"
#include "ortools/sat/sat_parameters.pb.h"
#include "ortools/util/stats.h"

namespace operations_research {
namespace sat {
namespace {

using ::google::protobuf::contrib::parse_proto::ParseTestProto;

CpModelProto CreateExactlyOneTrueBooleanCpModel(int size) {
  CpModelProto model_proto;
  auto* exactly_one_constraint =
      model_proto.add_constraints()->mutable_exactly_one();
  DecisionStrategyProto* const search_strategy =
      model_proto.add_search_strategy();

  for (int i = 0; i < size; ++i) {
    IntegerVariableProto* const var = model_proto.add_variables();
    var->add_domain(0);
    var->add_domain(1);
    exactly_one_constraint->add_literals(i);
    search_strategy->add_variables(i);
  }
  return model_proto;
}

TEST(RandomSearchTest, CheckDistribution) {
  const int kSize = 50;
  std::vector<int> winners(kSize, 0);
  const int kLoops = 100;
  for (int l = 0; l < kLoops; ++l) {
    const CpModelProto model_proto = CreateExactlyOneTrueBooleanCpModel(kSize);
    Model model;
    SatParameters parameters;
    parameters.set_search_random_variable_pool_size(10);
    parameters.set_cp_model_presolve(false);
    parameters.set_search_branching(SatParameters::FIXED_SEARCH);
    parameters.set_random_seed(l);
    parameters.set_num_workers(1);
    model.Add(NewSatParameters(parameters));
    const CpSolverResponse response = SolveCpModel(model_proto, &model);
    for (int i = 0; i < kSize; ++i) {
      if (response.solution(i)) {
        winners[i]++;
      }
    }
  }
  for (int i = 0; i < kSize; ++i) {
    EXPECT_LE(winners[i], kLoops / 10);
  }
}

TEST(RandomSearchTest, CheckSeed) {
  const int kSeeds = 10;
  for (int seed = 0; seed < kSeeds; ++seed) {
    const int kSize = 20;
    std::vector<int> winners(kSize, 0);
    const int kLoops = 50;
    for (int l = 0; l < kLoops; ++l) {
      const CpModelProto model_proto =
          CreateExactlyOneTrueBooleanCpModel(kSize);

      SatParameters params;
      params.set_randomize_search(true);
      params.set_cp_model_presolve(false);
      params.set_search_branching(SatParameters::FIXED_SEARCH);
      params.set_use_absl_random(false);  // Otherwise, each solve changes.
      params.set_random_seed(0);
      params.set_num_workers(1);
      const CpSolverResponse response =
          SolveWithParameters(model_proto, params);
      for (int i = 0; i < kSize; ++i) {
        if (response.solution(i)) {
          winners[i]++;
        }
      }
    }
    for (int i = 0; i < kSize; ++i) {
      EXPECT_TRUE(winners[i] == 0 || winners[i] == kLoops) << winners[i];
    }
  }
}

TEST(BasicFixedSearchBehaviorTest, Default) {
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 4, 50 ] }
    variables { domain: [ 3, 7 ] }
    variables { domain: [ 0, 7 ] }
    variables { domain: [ 4, 5 ] }
    variables { domain: [ 3, 9 ] }
    constraints {
      all_diff {
        exprs { vars: 0 coeffs: 1 }
        exprs { vars: 1 coeffs: 1 }
        exprs { vars: 2 coeffs: 1 }
        exprs { vars: 3 coeffs: 1 }
        exprs { vars: 4 coeffs: 1 }
      }
    }
  )pb");
  Model model;
  model.Add(NewSatParameters(
      "cp_model_presolve:false,search_branching:FIXED_SEARCH,num_workers:1"));
  const CpSolverResponse response = SolveCpModel(model_proto, &model);
  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(4, 3, 0, 5, 6));
}

TEST(BasicFixedSearchBehaviorTest, ReverseOrder) {
  // Note that SELECT_LOWER_HALF or SELECT_MIN_VALUE result in the same
  // solution.
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 4, 50 ] }
    variables { domain: [ 3, 7 ] }
    variables { domain: [ 0, 7 ] }
    variables { domain: [ 4, 5 ] }
    variables { domain: [ 3, 9 ] }
    constraints {
      all_diff {
        exprs { vars: 0 coeffs: 1 }
        exprs { vars: 1 coeffs: 1 }
        exprs { vars: 2 coeffs: 1 }
        exprs { vars: 3 coeffs: 1 }
        exprs { vars: 4 coeffs: 1 }
      }
    }
    search_strategy {
      variables: [ 4, 3, 2, 1, 0 ]
      variable_selection_strategy: CHOOSE_FIRST
      domain_reduction_strategy: SELECT_LOWER_HALF
    }
  )pb");
  Model model;
  model.Add(NewSatParameters(
      "cp_model_presolve:false,search_branching:FIXED_SEARCH,num_workers:1"));
  const CpSolverResponse response = SolveCpModel(model_proto, &model);
  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(6, 5, 0, 4, 3));
}

// The strategies that sort variables according to their domain do not have
// a fixed solution depending on the propagation strength...
TEST(BasicFixedSearchBehaviorTest, MinDomainSize) {
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 4, 10 ] }
    variables { domain: [ 3, 7 ] }
    variables { domain: [ 0, 7 ] }
    variables { domain: [ 4, 5 ] }
    variables { domain: [ 3, 9 ] }
    constraints {
      all_diff {
        exprs { vars: 0 coeffs: 1 }
        exprs { vars: 1 coeffs: 1 }
        exprs { vars: 2 coeffs: 1 }
        exprs { vars: 3 coeffs: 1 }
        exprs { vars: 4 coeffs: 1 }
      }
    }
    search_strategy {
      variables: [ 0, 1, 2, 3, 4 ]
      variable_selection_strategy: CHOOSE_MIN_DOMAIN_SIZE
      domain_reduction_strategy: SELECT_MAX_VALUE
    }
  )pb");
  Model model;
  model.Add(NewSatParameters(
      "cp_model_presolve:false,search_branching:FIXED_SEARCH,num_workers:1"));
  const CpSolverResponse response = SolveCpModel(model_proto, &model);
  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(10, 7, 6, 5, 9));
}

TEST(BasicFixedSearchBehaviorTest, WithTransformation1) {
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 3, 10 ] }
    variables { domain: [ 3, 7 ] }
    constraints {
      all_diff {
        exprs { vars: 0 coeffs: 1 }
        exprs { vars: 1 coeffs: 1 }
      }
    }
    search_strategy {
      exprs { vars: 0 coeffs: 1 offset: 4 }
      exprs { vars: 1 coeffs: 4 }
      variable_selection_strategy: CHOOSE_LOWEST_MIN
      domain_reduction_strategy: SELECT_MIN_VALUE
    }
  )pb");
  Model model;
  model.Add(NewSatParameters(
      "cp_model_presolve:false,search_branching:FIXED_SEARCH,num_workers:1"));
  const CpSolverResponse response = SolveCpModel(model_proto, &model);
  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(3, 4));
}

TEST(BasicFixedSearchBehaviorTest, WithTransformation2) {
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 3, 7 ] }
    variables { domain: [ 3, 7 ] }
    constraints {
      all_diff {
        exprs { vars: 0 coeffs: 1 }
        exprs { vars: 1 coeffs: 1 }
      }
    }
    search_strategy {
      exprs { vars: 0 coeffs: -1 offset: 4 }
      exprs { vars: 1 coeffs: -4 }
      variable_selection_strategy: CHOOSE_LOWEST_MIN
      domain_reduction_strategy: SELECT_MIN_VALUE
    }
  )pb");
  Model model;
  model.Add(NewSatParameters(
      "cp_model_presolve:false,search_branching:FIXED_SEARCH,num_workers:1"));
  const CpSolverResponse response = SolveCpModel(model_proto, &model);
  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(6, 7));
}

TEST(BasicFixedSearchBehaviorTest, MedianTest) {
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 0, 8 ] }
    variables { domain: [ 0, 8 ] }
    constraints {
      linear {
        vars: [ 0, 1 ]
        coeffs: [ 1, 1 ]
        domain: [ 8, 100 ]
      }
    }
    search_strategy {
      variables: [ 0, 1 ]
      variable_selection_strategy: CHOOSE_FIRST
      domain_reduction_strategy: SELECT_MEDIAN_VALUE
    }
  )pb");
  SatParameters params;
  params.set_keep_all_feasible_solutions_in_presolve(true);
  params.set_search_branching(SatParameters::FIXED_SEARCH);
  params.set_num_workers(1);
  const CpSolverResponse response = SolveWithParameters(model_proto, params);
  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(4, 6));
}

TEST(BasicFixedSearchBehaviorTest, MedianTest2) {
  const CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 0, 20 ] }
    variables { domain: [ 6, 12 ] }
    constraints {
      all_diff {
        exprs { vars: 0 coeffs: 1 }
        exprs { vars: 1 coeffs: 1 }
      }
    }
    search_strategy {
      variables: [ 0, 1 ]
      variable_selection_strategy: CHOOSE_MAX_DOMAIN_SIZE
      domain_reduction_strategy: SELECT_MEDIAN_VALUE
    }
  )pb");
  SatParameters params;
  params.set_keep_all_feasible_solutions_in_presolve(true);
  params.set_search_branching(SatParameters::FIXED_SEARCH);
  params.set_num_workers(1);
  const CpSolverResponse response = SolveWithParameters(model_proto, params);

  EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
  EXPECT_THAT(response.solution(), testing::ElementsAre(10, 8));
}

TEST(BasicFixedSearchBehaviorTest, RandomHalfTest) {
  CpModelProto model_proto = ParseTestProto(R"pb(
    variables { domain: [ 0, 1 ] }
    variables { domain: [ 0, 10 ] }
    variables { domain: [ 0, 10 ] }
    variables { domain: [ 0, 10 ] }
    constraints {
      linear {
        vars: [ 0, 1, 2, 3 ]
        coeffs: [ 1, 1, 1, 1 ]
        domain: [ 10, 10 ]
      }
    }
    search_strategy {
      variables: [ 0, 1, 2, 3 ]
      variable_selection_strategy: CHOOSE_FIRST
      domain_reduction_strategy: SELECT_RANDOM_HALF
    }
  )pb");

  absl::flat_hash_map<std::tuple<int, int, int, int>, int> count_by_solution;
  {
    SatParameters params;
    params.set_enumerate_all_solutions(true);
    params.set_num_workers(1);
    Model model;
    model.Add(NewSatParameters(params));
    model.Add(NewFeasibleSolutionObserver(
        [&count_by_solution](const CpSolverResponse& response) {
          count_by_solution[std::make_tuple(
              response.solution(0), response.solution(1), response.solution(2),
              response.solution(3))] = 0;
        }));
    EXPECT_EQ(SolveCpModel(model_proto, &model).status(),
              CpSolverStatus::OPTIMAL);
  }
  constexpr int kNumExpectedSolutions = 121;
  EXPECT_EQ(count_by_solution.size(), kNumExpectedSolutions);

  // Repeatedly solve the model with a different seed and count the number of
  // times each solution occurs. If each solution is found with equal
  // probability, each solution should be found "near" kExpectedMean times.
  constexpr int kExpectedMean = 100;
  std::mt19937_64 random(12345);
  for (int i = 0; i < kNumExpectedSolutions * kExpectedMean; ++i) {
    SatParameters params;
    params.set_cp_model_presolve(false);
    params.set_search_branching(SatParameters::FIXED_SEARCH);
    params.set_random_seed(i);
    params.set_num_workers(1);
    auto search_order =
        model_proto.mutable_search_strategy(0)->mutable_variables();
    std::shuffle(search_order->begin(), search_order->end(), random);
    const CpSolverResponse response = SolveWithParameters(model_proto, params);
    EXPECT_EQ(response.status(), CpSolverStatus::OPTIMAL);
    count_by_solution[std::make_tuple(
        response.solution(0), response.solution(1), response.solution(2),
        response.solution(3))]++;
  }
  EXPECT_EQ(count_by_solution.size(), kNumExpectedSolutions);
  DoubleDistribution counts;
  int min_count = std::numeric_limits<int>::max();
  std::tuple<int, int, int, int> min_count_solution;
  int max_count = 0;
  std::tuple<int, int, int, int> max_count_solution;
  for (const auto& [solution, count] : count_by_solution) {
    if (count < min_count) {
      min_count = count;
      min_count_solution = solution;
    }
    if (count > max_count) {
      max_count = count;
      max_count_solution = solution;
    }
    counts.Add(count);
  }
  const double std_dev = counts.StdDeviation();
  LOG(INFO) << "min_count = " << min_count << " for "
            << absl::StrJoin(min_count_solution, ",");
  LOG(INFO) << "max_count = " << max_count << " for "
            << absl::StrJoin(max_count_solution, ",");
  LOG(INFO) << "std_dev / mean = " << std_dev / kExpectedMean;
  EXPECT_GE(min_count, kExpectedMean / 10);
  // If each solution was really found with equal probability, the coefficient
  // of variation would be much lower (about 0.1 for kExpectedMean = 100).
  EXPECT_LE(std_dev / kExpectedMean, 0.5);
}

}  // namespace
}  // namespace sat
}  // namespace operations_research