branch_and_bound_test.cc

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
#include <memory>
#include <stdexcept>
#include <string>
 
#include <gtest/gtest.h>
 
#include <Knapsack.H>
#include <State_Search.H>
 
using namespace Aleph;
 
namespace
{
 
struct ArtificialState
{
  size_t depth = 0;
  int code = 1;
  int value = 0;
};
 
struct ArtificialMove
{
  int target_code = 1;
  int delta = 0;
  char label = 'L';
};
 
struct ArtificialMaxDomain
{
  using State = ArtificialState;
  using Move = ArtificialMove;
  using Objective = int;
 
  bool is_complete(const State &state) const
  {
    return state.depth == 2;
  }
 
  Objective objective_value(const State &state) const
  {
    return state.value;
  }
 
  Objective bound(const State &state) const
  {
    switch (state.code)
      {
      case 1: return 9;
      case 2: return 9;
      case 3: return 5;
      default: return state.value;
      }
  }
 
  void apply(State &state, const Move &move) const
  {
    state.code = move.target_code;
    state.value += move.delta;
    ++state.depth;
  }
 
  void undo(State &state, const Move &move) const
  {
    --state.depth;
    state.value -= move.delta;
    state.code /= 2;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.depth >= 2)
      return true;
 
    switch (state.code)
      {
      case 1:
        if (not visit(Move{2, 0, 'L'}))
          return false;
        return visit(Move{3, 0, 'R'});
 
      case 2:
        if (not visit(Move{4, 7, 'L'}))
          return false;
        return visit(Move{5, 9, 'R'});
 
      case 3:
        if (not visit(Move{6, 5, 'L'}))
          return false;
        return visit(Move{7, 4, 'R'});
 
      default:
        return true;
      }
  }
};
 
struct ArtificialMaxBadOrderDomain
{
  using State = ArtificialState;
  using Move = ArtificialMove;
  using Objective = int;
 
  bool is_complete(const State &state) const
  {
    return state.depth == 2;
  }
 
  Objective objective_value(const State &state) const
  {
    return state.value;
  }
 
  Objective bound(const State &state) const
  {
    switch (state.code)
      {
      case 1: return 9;
      case 2: return 9;
      case 3: return 5;
      default: return state.value;
      }
  }
 
  void apply(State &state, const Move &move) const
  {
    state.code = move.target_code;
    state.value += move.delta;
    ++state.depth;
  }
 
  void undo(State &state, const Move &move) const
  {
    --state.depth;
    state.value -= move.delta;
    state.code /= 2;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.depth >= 2)
      return true;
 
    switch (state.code)
      {
      case 1:
        if (not visit(Move{3, 0, 'R'}))
          return false;
        return visit(Move{2, 0, 'L'});
 
      case 2:
        if (not visit(Move{4, 7, 'L'}))
          return false;
        return visit(Move{5, 9, 'R'});
 
      case 3:
        if (not visit(Move{6, 5, 'L'}))
          return false;
        return visit(Move{7, 4, 'R'});
 
      default:
        return true;
      }
  }
};
 
struct ArtificialMaxVisitedDomain : ArtificialMaxDomain
{
  using State_Key = int;
 
  [[nodiscard]] State_Key state_key(const State &state) const noexcept
  {
    return state.code;
  }
};
 
struct ArtificialMinDomain
{
  using State = ArtificialState;
  using Move = ArtificialMove;
  using Objective = int;
 
  bool is_complete(const State &state) const
  {
    return state.depth == 2;
  }
 
  Objective objective_value(const State &state) const
  {
    return state.value;
  }
 
  Objective bound(const State &state) const
  {
    switch (state.code)
      {
      case 1: return 6;
      case 2: return 6;
      case 3: return 7;
      default: return state.value;
      }
  }
 
  void apply(State &state, const Move &move) const
  {
    state.code = move.target_code;
    state.value += move.delta;
    ++state.depth;
  }
 
  void undo(State &state, const Move &move) const
  {
    --state.depth;
    state.value -= move.delta;
    state.code /= 2;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.depth >= 2)
      return true;
 
    switch (state.code)
      {
      case 1:
        if (not visit(Move{2, 0, 'L'}))
          return false;
        return visit(Move{3, 0, 'R'});
 
      case 2:
        if (not visit(Move{4, 8, 'L'}))
          return false;
        return visit(Move{5, 6, 'R'});
 
      case 3:
        if (not visit(Move{6, 7, 'L'}))
          return false;
        return visit(Move{7, 9, 'R'});
 
      default:
        return true;
      }
  }
};
 
struct KnapsackState
{
  size_t index = 0;
  int weight = 0;
  double value = 0;
  Array<unsigned char> chosen;
 
  explicit KnapsackState(const size_t n = 0)
    : index(0), weight(0), value(0), chosen(n, 0)
  {
    // empty
  }
};
 
class KnapsackBBDomain
{
public:
  using State = KnapsackState;
 
  struct Move
  {
    bool take = false;
  };
 
  using Objective = double;
 
  KnapsackBBDomain(const Array<Knapsack_Item<int, double>> &items,
                   const int capacity,
                   const bool fractional_bound)
    : items_(items),
      suffix_values_(items.size() + 1, 0.0),
      capacity_(capacity),
      use_fractional_bound_(fractional_bound)
  {
    for (size_t i = items_.size(); i > 0; --i)
      suffix_values_[i - 1] = suffix_values_[i] + items_[i - 1].value;
  }
 
  bool is_complete(const State &state) const
  {
    return state.index == items_.size();
  }
 
  Objective objective_value(const State &state) const
  {
    return state.value;
  }
 
  Objective bound(const State &state) const
  {
    if (not use_fractional_bound_)
      return state.value + suffix_values_[state.index];
 
    Objective optimistic = state.value;
    int remaining = capacity_ - state.weight;
 
    for (size_t i = state.index; i < items_.size() and remaining > 0; ++i)
      if (items_[i].weight <= remaining)
        {
          optimistic += items_[i].value;
          remaining -= items_[i].weight;
        }
      else
        {
          optimistic += items_[i].value * (static_cast<Objective>(remaining)/
                                           static_cast<Objective>(items_[i].weight));
          break;
        }
 
    return optimistic;
  }
 
  void apply(State &state, const Move &move) const
  {
    if (move.take)
      {
        state.weight += items_[state.index].weight;
        state.value += items_[state.index].value;
        state.chosen[state.index] = 1;
      }
    else
      state.chosen[state.index] = 0;
 
    ++state.index;
  }
 
  void undo(State &state, const Move &move) const
  {
    --state.index;
    if (move.take)
      {
        state.weight -= items_[state.index].weight;
        state.value -= items_[state.index].value;
      }
 
    state.chosen[state.index] = 0;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.index >= items_.size())
      return true;
 
    if (state.weight + items_[state.index].weight <= capacity_)
      if (not visit(Move{true}))
        return false;
 
    return visit(Move{false});
  }
 
private:
  Array<Knapsack_Item<int, double>> items_;
  Array<double> suffix_values_;
  int capacity_ = 0;
  bool use_fractional_bound_ = true;
};
 
struct AssignmentState
{
  size_t row = 0;
  int total_cost = 0;
  Array<unsigned char> used_columns;
  Array<int> assigned_column;
 
  explicit AssignmentState(const size_t n = 0)
    : row(0), total_cost(0), used_columns(n, 0), assigned_column(n, -1)
  {
    // empty
  }
};
 
class AssignmentBBDomain
{
public:
  struct Move
  {
    size_t col = 0;
  };
 
  using State = AssignmentState;
  using Objective = int;
 
  explicit AssignmentBBDomain(const Array<Array<int>> &costs)
    : costs_(costs)
  {
    // empty
  }
 
  bool is_complete(const State &state) const
  {
    return state.row == costs_.size();
  }
 
  Objective objective_value(const State &state) const
  {
    return state.total_cost;
  }
 
  Objective bound(const State &state) const
  {
    Objective optimistic = state.total_cost;
 
    for (size_t row = state.row; row < costs_.size(); ++row)
      {
        int best = -1;
        for (size_t col = 0; col < costs_[row].size(); ++col)
          if (not state.used_columns[col] and (best < 0 or costs_[row][col] < best))
            best = costs_[row][col];
 
        optimistic += best;
      }
 
    return optimistic;
  }
 
  void apply(State &state, const Move &move) const
  {
    state.total_cost += costs_[state.row][move.col];
    state.used_columns[move.col] = 1;
    state.assigned_column[state.row] = static_cast<int>(move.col);
    ++state.row;
  }
 
  void undo(State &state, const Move &move) const
  {
    --state.row;
    state.total_cost -= costs_[state.row][move.col];
    state.used_columns[move.col] = 0;
    state.assigned_column[state.row] = -1;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.row >= costs_.size())
      return true;
 
    for (size_t col = 0; col < costs_[state.row].size(); ++col)
      if (not state.used_columns[col] and not visit(Move{col}))
        return false;
 
    return true;
  }
 
private:
  Array<Array<int>> costs_;
};
 
struct ThrowingApplyState
{
  std::shared_ptr<bool> undo_called;
  size_t node = 0;
};
 
struct ThrowingApplyMove
{
  bool throws = true;
};
 
struct ThrowingApplyBBDomain
{
  using State = ThrowingApplyState;
  using Move = ThrowingApplyMove;
  using Objective = int;
 
  bool is_complete(const State &state) const
  {
    return state.node == 1;
  }
 
  Objective objective_value(const State &) const
  {
    return 0;
  }
 
  Objective bound(const State &) const
  {
    return 1;
  }
 
  void apply(State &state, const Move &move) const
  {
    if (move.throws)
      ah_runtime_error() << "apply failed";
 
    state.node = 1;
  }
 
  void undo(State &state, const Move &) const
  {
    *state.undo_called = true;
    state.node = 0;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.node != 0)
      return true;
 
    return visit(Move{true});
  }
};
 
struct ThrowingApplyVisitedBBDomain : ThrowingApplyBBDomain
{
  using State_Key = size_t;
 
  [[nodiscard]] State_Key state_key(const State &state) const noexcept
  {
    return state.node;
  }
};
 
static_assert(BranchAndBoundDomain<ArtificialMaxDomain>);
static_assert(SearchStateKeyProvider<ArtificialMaxVisitedDomain>);
static_assert(BranchAndBoundDomain<ArtificialMinDomain>);
static_assert(BranchAndBoundDomain<KnapsackBBDomain>);
static_assert(BranchAndBoundDomain<AssignmentBBDomain>);
static_assert(BranchAndBoundDomain<ThrowingApplyBBDomain>);
static_assert(SearchStateKeyProvider<ThrowingApplyVisitedBBDomain>);
static_assert(BranchAndBoundObjectivePolicy<Maximize_Objective<int>, int>);
static_assert(BranchAndBoundObjectivePolicy<Minimize_Objective<int>, int>);
 
std::string artificial_signature(const SearchPath<ArtificialMove> &path)
{
  std::string out;
  for (const auto &move : path)
    out.push_back(move.label);
  return out;
}
 
int brute_assignment_cost(const Array<Array<int>> &costs,
                          const size_t row,
                          Array<unsigned char> &used)
{
  if (row == costs.size())
    return 0;
 
  int best = -1;
  for (size_t col = 0; col < costs[row].size(); ++col)
    if (not used[col])
      {
        used[col] = 1;
        const int candidate = costs[row][col] + brute_assignment_cost(costs, row + 1, used);
        used[col] = 0;
        if (best < 0 or candidate < best)
          best = candidate;
      }
 
  return best;
}
 
// ---------------------------------------------------------------------------
// Domain with IncrementalBoundProvider (bound_after) to exercise the fast
// path in Branch_And_Bound::collect_ordered_moves.
// Same tree shape as ArtificialMaxDomain.
// ---------------------------------------------------------------------------
struct IncrementalBoundDomain
{
  using State = ArtificialState;
  using Move = ArtificialMove;
  using Objective = int;
 
  mutable size_t bound_after_calls = 0;
  mutable size_t apply_calls = 0;
 
  bool is_complete(const State &state) const
  {
    return state.depth == 2;
  }
 
  Objective objective_value(const State &state) const
  {
    return state.value;
  }
 
  Objective bound(const State &state) const
  {
    switch (state.code)
      {
      case 1: return 9;
      case 2: return 9;
      case 3: return 5;
      default: return state.value;
      }
  }
 
  Objective bound_after(const State &, const Move &move) const
  {
    ++bound_after_calls;
    // Return the bound of the child state without mutating.
    switch (move.target_code)
      {
      case 2: return 9;
      case 3: return 5;
      default: return move.delta;
      }
  }
 
  void apply(State &state, const Move &move) const
  {
    ++apply_calls;
    state.code = move.target_code;
    state.value += move.delta;
    ++state.depth;
  }
 
  void undo(State &state, const Move &move) const
  {
    --state.depth;
    state.value -= move.delta;
    state.code /= 2;
  }
 
  template <typename Visitor>
  bool for_each_successor(const State &state, Visitor visit) const
  {
    if (state.depth >= 2)
      return true;
 
    switch (state.code)
      {
      case 1:
        if (not visit(Move{2, 0, 'L'}))
          return false;
        return visit(Move{3, 0, 'R'});
 
      case 2:
        if (not visit(Move{4, 7, 'L'}))
          return false;
        return visit(Move{5, 9, 'R'});
 
      case 3:
        if (not visit(Move{6, 5, 'L'}))
          return false;
        return visit(Move{7, 4, 'R'});
 
      default:
        return true;
      }
  }
};
 
} // end namespace
 
TEST(BranchAndBoundFramework, ObjectivePoliciesAndIncumbentConstruct)
{
  using Sol = OptimizationSolution<int, int, int>;
 
  ObjectiveIncumbent<Sol, Maximize_Objective<int>> incumbent(Maximize_Objective<int>{});
  EXPECT_FALSE(incumbent.has_value());
  EXPECT_TRUE(incumbent.can_improve(10));
 
  Sol first;
  first.objective_value = 5;
  EXPECT_TRUE(incumbent.consider(first));
  EXPECT_TRUE(incumbent.has_value());
  EXPECT_EQ(incumbent.best_value(), 5);
  EXPECT_FALSE(incumbent.can_improve(5));
  EXPECT_TRUE(incumbent.can_improve(6));
}
 
TEST(BranchAndBoundFramework, ArtificialMaximizationPrunesByBound)
{
  ArtificialMaxDomain domain;
  SearchSolutionCollector<Branch_And_Bound<ArtificialMaxDomain>::Solution> collector;
 
  auto result = branch_and_bound_search(domain, ArtificialState{}, collector);
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_TRUE(result.exhausted());
  EXPECT_EQ(result.incumbent.best_value(), 9);
  EXPECT_EQ(artificial_signature(result.incumbent.get().path), "LR");
  EXPECT_EQ(result.stats.solutions_found, 2u);
  EXPECT_EQ(result.stats.pruned_by_bound, 1u);
  EXPECT_EQ(result.stats.incumbent_updates, 2u);
  EXPECT_EQ(collector.size(), 2u);
}
 
TEST(BranchAndBoundFramework, VisitedMapSearchKeepsRecordedBoundsOnSuccess)
{
  ArtificialMaxVisitedDomain domain;
  Branch_And_Bound<ArtificialMaxVisitedDomain> engine(domain);
  SearchStorageMap<int, int> visited;
 
  auto result = engine.search(ArtificialState{}, visited);
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_NE(visited.search(1), nullptr);
  EXPECT_NE(visited.search(2), nullptr);
}
 
TEST(BranchAndBoundFramework, ArtificialMinimizationWorksWithBestFirst)
{
  ArtificialMinDomain domain;
  ExplorationPolicy policy = Branch_And_Bound<ArtificialMinDomain,
                                              Minimize_Objective<int>>::default_policy();
  policy.strategy = ExplorationPolicy::Strategy::Best_First;
 
  Branch_And_Bound<ArtificialMinDomain, Minimize_Objective<int>> engine(domain, policy);
  auto result = engine.search(ArtificialState{});
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_TRUE(result.exhausted());
  EXPECT_EQ(result.incumbent.best_value(), 6);
  EXPECT_EQ(artificial_signature(result.incumbent.get().path), "LR");
  EXPECT_GT(result.stats.pruned_by_bound, 0u);
}
 
TEST(BranchAndBoundFramework, BoundOrderedDepthFirstAndBestFirstBeatPlainBadOrder)
{
  ArtificialMaxBadOrderDomain domain;
 
  auto plain_result = branch_and_bound_search(domain, ArtificialState{});
 
  ExplorationPolicy ordered_policy = Branch_And_Bound<ArtificialMaxBadOrderDomain>::default_policy();
  ordered_policy.move_ordering = MoveOrderingMode::Estimated_Bound;
  auto ordered_result = branch_and_bound_search(domain, ArtificialState{}, ordered_policy);
 
  ExplorationPolicy best_policy = Branch_And_Bound<ArtificialMaxBadOrderDomain>::default_policy();
  best_policy.strategy = ExplorationPolicy::Strategy::Best_First;
  auto best_result = branch_and_bound_search(domain, ArtificialState{}, best_policy);
 
  ASSERT_TRUE(plain_result.found_solution());
  ASSERT_TRUE(ordered_result.found_solution());
  ASSERT_TRUE(best_result.found_solution());
  EXPECT_EQ(plain_result.incumbent.best_value(), 9);
  EXPECT_EQ(ordered_result.incumbent.best_value(), plain_result.incumbent.best_value());
  EXPECT_EQ(best_result.incumbent.best_value(), plain_result.incumbent.best_value());
  EXPECT_EQ(artificial_signature(ordered_result.incumbent.get().path), "LR");
  EXPECT_LT(ordered_result.stats.visited_states, plain_result.stats.visited_states);
  EXPECT_GT(ordered_result.stats.move_ordering.ordered_batches, 0u);
  EXPECT_GT(ordered_result.stats.move_ordering.priority_estimates, 0u);
  EXPECT_LT(best_result.stats.visited_states, plain_result.stats.visited_states);
}
 
TEST(BranchAndBoundFramework, ApplyExceptionDuringMoveOrderingDoesNotCallUndo)
{
  auto undo_called = std::make_shared<bool>(false);
  ThrowingApplyBBDomain domain;
  ExplorationPolicy policy = Branch_And_Bound<ThrowingApplyBBDomain>::default_policy();
  policy.move_ordering = MoveOrderingMode::Estimated_Bound;
 
  Branch_And_Bound<ThrowingApplyBBDomain> engine(domain, policy);
 
  EXPECT_THROW((void) engine.search(ThrowingApplyState{undo_called, 0}), std::runtime_error);
  EXPECT_FALSE(*undo_called);
}
 
TEST(BranchAndBoundFramework, ApplyExceptionDuringDepthFirstExpansionDoesNotCallUndo)
{
  auto undo_called = std::make_shared<bool>(false);
  ThrowingApplyBBDomain domain;
  Branch_And_Bound<ThrowingApplyBBDomain> engine(domain);
 
  EXPECT_THROW((void) engine.search(ThrowingApplyState{undo_called, 0}), std::runtime_error);
  EXPECT_FALSE(*undo_called);
}
 
TEST(BranchAndBoundFramework, ApplyExceptionDuringVisitedDepthFirstDoesNotCallUndo)
{
  auto undo_called = std::make_shared<bool>(false);
  ThrowingApplyVisitedBBDomain domain;
  Branch_And_Bound<ThrowingApplyVisitedBBDomain> engine(domain);
  SearchStorageMap<size_t, int> visited;
 
  EXPECT_THROW((void) engine.search(ThrowingApplyState{undo_called, 0}, visited),
               std::runtime_error);
  EXPECT_FALSE(*undo_called);
}
 
struct ThrowingPostApplyDomain : ThrowingApplyBBDomain
{
  bool is_complete(const State &) const
  {
    return false;
  }
 
  void apply(State &state, const Move &move) const
  {
    (void) move;
    state.node = 1; // succeed
  }
 
  Objective bound(const State &state) const
  {
    if (state.node == 1)
      ah_runtime_error() << "post-apply bound failed";
    return 1;
  }
};
 
TEST(BranchAndBoundFramework, PostApplyExceptionCallsUndo)
{
  auto undo_called = std::make_shared<bool>(false);
  ThrowingPostApplyDomain domain;
  Branch_And_Bound<ThrowingPostApplyDomain> engine(domain);
 
  EXPECT_THROW((void) engine.search(ThrowingApplyState{undo_called, 0}), std::runtime_error);
  EXPECT_TRUE(*undo_called);
}
 
struct ThrowingPostApplyVisitedDomain : ThrowingPostApplyDomain
{
  using State_Key = size_t;
  [[nodiscard]] State_Key state_key(const State &state) const noexcept
  {
    return state.node;
  }
};
 
TEST(BranchAndBoundFramework, PostApplyExceptionDuringVisitedDepthFirstCallsUndo)
{
  auto undo_called = std::make_shared<bool>(false);
  ThrowingPostApplyVisitedDomain domain;
  Branch_And_Bound<ThrowingPostApplyVisitedDomain> engine(domain);
  SearchStorageMap<size_t, int> visited;
 
  // First call should throw and rollback.
  EXPECT_THROW((void) engine.search(ThrowingApplyState{undo_called, 0}, visited), std::runtime_error);
  EXPECT_TRUE(*undo_called);
  EXPECT_FALSE(visited.contains(0)); // Root key 0 should have been rolled back.
 
  // Retry with same visited map to ensure it's clean.
  *undo_called = false;
  EXPECT_THROW((void) engine.search(ThrowingApplyState{undo_called, 0}, visited), std::runtime_error);
  EXPECT_TRUE(*undo_called);
  EXPECT_FALSE(visited.contains(0));
}
 
TEST(BranchAndBoundFramework, StopAtFirstSolutionUsesCommonExplorationPolicy)
{
  ArtificialMaxDomain domain;
  ExplorationPolicy policy = Branch_And_Bound<ArtificialMaxDomain>::default_policy();
  policy.stop_at_first_solution = true;
 
  auto result = branch_and_bound_search(domain, ArtificialState{}, policy);
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_TRUE(result.stopped_on_solution());
  EXPECT_EQ(result.stats.solutions_found, 1u);
  EXPECT_EQ(result.incumbent.best_value(), 7);
  EXPECT_EQ(artificial_signature(result.incumbent.get().path), "LL");
}
 
TEST(BranchAndBoundFramework, KnapsackFractionalBoundFindsOptimal)
{
  const Array<Knapsack_Item<int, double>> items = {
    {2, 40.0}, {5, 30.0}, {10, 50.0}, {5, 10.0}
  };
  constexpr int capacity = 16;
 
  KnapsackBBDomain domain(items, capacity, true);
  auto result = branch_and_bound_search(domain, KnapsackState(items.size()));
  const double optimum = knapsack_01_value<double, int>(items, capacity);
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_DOUBLE_EQ(result.incumbent.best_value(), 90.0);
  EXPECT_DOUBLE_EQ(result.incumbent.best_value(), optimum);
}
 
TEST(BranchAndBoundFramework, KnapsackBestFirstMatchesDepthFirst)
{
  const Array<Knapsack_Item<int, double>> items = {
    {2, 40.0}, {5, 30.0}, {10, 50.0}, {5, 10.0}
  };
  constexpr int capacity = 16;
 
  KnapsackBBDomain domain(items, capacity, true);
  auto depth_result = branch_and_bound_search(domain, KnapsackState(items.size()));
 
  ExplorationPolicy policy = Branch_And_Bound<KnapsackBBDomain>::default_policy();
  policy.strategy = ExplorationPolicy::Strategy::Best_First;
  Branch_And_Bound<KnapsackBBDomain> best_first(domain, policy);
  auto best_result = best_first.search(KnapsackState(items.size()));
 
  EXPECT_DOUBLE_EQ(depth_result.incumbent.best_value(), best_result.incumbent.best_value());
  EXPECT_GT(best_result.stats.pruned_by_bound, 0u);
}
 
TEST(BranchAndBoundFramework, KnapsackFractionalBoundPrunesMoreThanWeakBound)
{
  const Array<Knapsack_Item<int, double>> items = {
    {10, 100.0}, {9, 80.0}, {9, 80.0}, {9, 80.0}
  };
  constexpr int capacity = 10;
 
  auto tight_result = branch_and_bound_search(KnapsackBBDomain(items, capacity, true),
                                              KnapsackState(items.size()));
  auto weak_result = branch_and_bound_search(KnapsackBBDomain(items, capacity, false),
                                             KnapsackState(items.size()));
 
  EXPECT_DOUBLE_EQ(tight_result.incumbent.best_value(), weak_result.incumbent.best_value());
  EXPECT_GT(tight_result.stats.pruned_by_bound, 0u);
  EXPECT_LT(tight_result.stats.visited_states, weak_result.stats.visited_states);
  EXPECT_LT(tight_result.stats.expanded_states, weak_result.stats.expanded_states);
}
 
TEST(BranchAndBoundFramework, AssignmentMinimizationFindsExpectedOptimum)
{
  const Array<Array<int>> costs = {
    Array<int>{9, 2, 7, 8},
    Array<int>{6, 4, 3, 7},
    Array<int>{5, 8, 1, 8},
    Array<int>{7, 6, 9, 4}
  };
 
  AssignmentBBDomain domain(costs);
  Branch_And_Bound<AssignmentBBDomain, Minimize_Objective<int>> engine(
    domain,
    Branch_And_Bound<AssignmentBBDomain, Minimize_Objective<int>>::default_policy(),
    {},
    Minimize_Objective<int>{});
 
  auto result = engine.search(AssignmentState(costs.size()));
 
  Array<unsigned char> used(costs.size(), 0);
  const int brute = brute_assignment_cost(costs, 0, used);
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_EQ(result.incumbent.best_value(), brute);
  EXPECT_EQ(result.incumbent.best_value(), 13);
}
 
TEST(BranchAndBoundFramework, AssignmentBestFirstMatchesDepthFirst)
{
  const Array<Array<int>> costs = {
    Array<int>{9, 2, 7, 8},
    Array<int>{6, 4, 3, 7},
    Array<int>{5, 8, 1, 8},
    Array<int>{7, 6, 9, 4}
  };
 
  AssignmentBBDomain domain(costs);
  Branch_And_Bound<AssignmentBBDomain, Minimize_Objective<int>> depth_engine(
    domain,
    Branch_And_Bound<AssignmentBBDomain, Minimize_Objective<int>>::default_policy(),
    {},
    Minimize_Objective<int>{});
  auto depth_result = depth_engine.search(AssignmentState(costs.size()));
 
  ExplorationPolicy policy = Branch_And_Bound<AssignmentBBDomain,
                                              Minimize_Objective<int>>::default_policy();
  policy.strategy = ExplorationPolicy::Strategy::Best_First;
  Branch_And_Bound<AssignmentBBDomain, Minimize_Objective<int>> best_engine(
    domain, policy, {}, Minimize_Objective<int>{});
  auto best_result = best_engine.search(AssignmentState(costs.size()));
 
  EXPECT_EQ(depth_result.incumbent.best_value(), best_result.incumbent.best_value());
  EXPECT_GE(best_result.stats.pruned_by_bound, 0u);
}
 
// ===========================================================================
// H3: B&B with max_depth limit, max_expansions limit, knapsack capacity=0
// ===========================================================================
 
// max_depth=1: root is expanded (depth 0→1), but children at depth 1 are
// pruned before expansion. Since leaves are at depth 2, no complete solution
// is recorded.
TEST(BranchAndBoundFramework, MaxDepthOnePreventsCompleteSolution)
{
  ArtificialMaxDomain domain;
  ExplorationPolicy policy = Branch_And_Bound<ArtificialMaxDomain>::default_policy();
  policy.stop_at_first_solution = false;
 
  SearchLimits limits;
  limits.max_depth = 1;
 
  Branch_And_Bound<ArtificialMaxDomain> engine(domain, policy, limits);
  auto result = engine.search(ArtificialState{});
 
  EXPECT_FALSE(result.found_solution());
  EXPECT_GT(result.stats.pruned_by_depth, 0u);
}
 
// max_expansions=1: only the root node is expanded. The two children are
// visited but not expanded, so no leaves are reached and no solution found.
TEST(BranchAndBoundFramework, MaxExpansionsOnePreventsCompleteSolution)
{
  ArtificialMaxDomain domain;
  ExplorationPolicy policy = Branch_And_Bound<ArtificialMaxDomain>::default_policy();
  policy.stop_at_first_solution = false;
 
  SearchLimits limits;
  limits.max_expansions = 1;
 
  Branch_And_Bound<ArtificialMaxDomain> engine(domain, policy, limits);
  auto result = engine.search(ArtificialState{});
 
  EXPECT_TRUE(result.limit_reached());
  EXPECT_EQ(result.stats.expanded_states, 1u);
  EXPECT_FALSE(result.found_solution());
}
 
// Knapsack with capacity=0: no item fits, so the only complete solution is
// the empty selection with value=0.
TEST(BranchAndBoundFramework, KnapsackCapacityZeroReturnsEmptySolution)
{
  const Array<Knapsack_Item<int, double>> items = {
    {2, 40.0}, {5, 30.0}, {10, 50.0}
  };
  constexpr int capacity = 0;
 
  KnapsackBBDomain domain(items, capacity, true);
  auto result = branch_and_bound_search(domain, KnapsackState(items.size()));
 
  ASSERT_TRUE(result.found_solution());
  EXPECT_DOUBLE_EQ(result.incumbent.best_value(), 0.0);
}
 
// ===========================================================================
// H4: IncrementalBoundProvider fast path in collect_ordered_moves
// ===========================================================================
 
TEST(BranchAndBoundFramework, IncrementalBoundProviderUsedForOrdering)
{
  IncrementalBoundDomain domain;
  ExplorationPolicy policy;
  policy.move_ordering = MoveOrderingMode::Estimated_Bound;
  policy.stop_at_first_solution = false;
 
  Branch_And_Bound<IncrementalBoundDomain> engine(domain, policy);
  auto result = engine.search(ArtificialState{});
 
  // Same tree as ArtificialMaxDomain: optimal = 9.
  ASSERT_TRUE(result.found_solution());
  EXPECT_EQ(result.incumbent.best_value(), 9);
 
  // bound_after must have been called (fast path taken).
  EXPECT_GT(engine.domain().bound_after_calls, 0u);
 
  // Move ordering stats must reflect priority estimates.
  EXPECT_GT(result.stats.move_ordering.priority_estimates, 0u);
}