solve_result.h

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// Copyright 2010-2021 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.
 
#ifndef OR_TOOLS_MATH_OPT_CPP_SOLVE_RESULT_H_
#define OR_TOOLS_MATH_OPT_CPP_SOLVE_RESULT_H_
 
#include <optional>
#include <string>
#include <vector>
 
#include "ortools/base/logging.h"
#include "absl/status/statusor.h"
#include "absl/time/time.h"
#include "absl/types/span.h"
#include "ortools/math_opt/core/model_storage.h"
#include "ortools/math_opt/cpp/enums.h"  // IWYU pragma: export
#include "ortools/math_opt/cpp/linear_constraint.h"
#include "ortools/math_opt/cpp/solution.h"  // IWYU pragma: export
#include "ortools/math_opt/cpp/variable_and_expressions.h"
#include "ortools/math_opt/result.pb.h"  // IWYU pragma: export
#include "ortools/base/protoutil.h"
 
namespace operations_research {
namespace math_opt {
 
// Problem feasibility status as claimed by the solver (solver is not required
// to return a certificate for the claim).
enum class FeasibilityStatus {
  // Solver does not claim a status.
  kUndetermined = FEASIBILITY_STATUS_UNDETERMINED,
 
  // Solver claims the problem is feasible.
  kFeasible = FEASIBILITY_STATUS_FEASIBLE,
 
  // Solver claims the problem is infeasible.
  kInfeasible = FEASIBILITY_STATUS_INFEASIBLE,
};
 
MATH_OPT_DEFINE_ENUM(FeasibilityStatus, FEASIBILITY_STATUS_UNSPECIFIED);
 
// Feasibility status of the primal problem and its dual (or the dual of a
// continuous relaxation) as claimed by the solver. The solver is not required
// to return a certificate for the claim (e.g. the solver may claim primal
// feasibility without returning a primal feasible solutuion). This combined
// status gives a comprehensive description of a solver's claims about
// feasibility and unboundedness of the solved problem. For instance,
//   * a feasible status for primal and dual problems indicates the primal is
//     feasible and bounded and likely has an optimal solution (guaranteed for
//     problems without non-linear constraints).
//   * a primal feasible and a dual infeasible status indicates the primal
//     problem is unbounded (i.e. has arbitrarily good solutions).
// Note that a dual infeasible status by itself (i.e. accompanied by an
// undetermined primal status) does not imply the primal problem is unbounded as
// we could have both problems be infeasible. Also, while a primal and dual
// feasible status may imply the existence of an optimal solution, it does not
// guarantee the solver has actually found such optimal solution.
struct ProblemStatus {
  // Status for the primal problem.
  FeasibilityStatus primal_status = FeasibilityStatus::kUndetermined;
 
  // Status for the dual problem (or for the dual of a continuous relaxation).
  FeasibilityStatus dual_status = FeasibilityStatus::kUndetermined;
 
  // If true, the solver claims the primal or dual problem is infeasible, but
  // it does not know which (or if both are infeasible). Can be true only when
  // primal_problem_status = dual_problem_status = kUndetermined. This extra
  // information is often needed when preprocessing determines there is no
  // optimal solution to the problem (but can't determine if it is due to
  // infeasibility, unboundedness, or both).
  bool primal_or_dual_infeasible = false;
 
  static ProblemStatus FromProto(
      const ProblemStatusProto& problem_status_proto);
 
  ProblemStatusProto ToProto() const;
  std::string ToString() const;
};
 
std::ostream& operator<<(std::ostream& ostr, const ProblemStatus& status);
 
struct SolveStats {
  // Elapsed wall clock time as measured by math_opt, roughly the time inside
  // Solver::Solve(). Note: this does not include work done building the model.
  absl::Duration solve_time = absl::ZeroDuration();
 
  // TODO(b/195295177): Update to add clearer contracts once PDLP's bounds
  // contract is clarified.
 
  // Solver claims the optimal value is equal or better (smaller for
  // minimization and larger for maximization) than best_primal_bound:
  //   * best_primal_bound is trivial (+inf for minimization and -inf
  //     maximization) when the solver does not claim to have such bound. This
  //     may happen for some solvers (e.g., PDLP, typically continuous solvers)
  //     even when returning optimal (solver could terminate with slightly
  //     infeasible primal solutions).
  //   * best_primal_bound can be closer to the optimal value than the objective
  //     of the best primal feasible solution. In particular, best_primal_bound
  //     may be non-trivial even when no primal feasible solutions are returned.
  //   * best_dual_bound is always better (smaller for minimization and larger
  //     for maximization) than best_primal_bound.
 
  double best_primal_bound = 0.0;
 
  // Solver claims the optimal value is equal or worse (larger for
  // minimization and smaller for maximization) than best_dual_bound:
  //   * best_dual_bound is always better (smaller for minimization and larger
  //     for maximization) than best_primal_bound.
  //   * best_dual_bound is trivial (-inf for minimization and +inf
  //     maximization) when the solver does not claim to have such bound.
  //     Similarly to best_primal_bound, this may happen for some solvers even
  //     when returning optimal. MIP solvers will typically report a bound even
  //     if it is imprecise.
  //   * for continuous problems best_dual_bound can be closer to the optimal
  //     value than the objective of the best dual feasible solution. For MIP
  //     one of the first non-trivial values for best_dual_bound is often the
  //     optimal value of the LP relaxation of the MIP.
  double best_dual_bound = 0.0;
 
  // Feasibility statuses for primal and dual problems.
  ProblemStatus problem_status;
 
  int simplex_iterations = 0;
 
  int barrier_iterations = 0;
 
  int node_count = 0;
 
  // Will CHECK fail on invalid input, if problem_status is invalid.
  static SolveStats FromProto(const SolveStatsProto& solve_stats_proto);
 
  SolveStatsProto ToProto() const;
  std::string ToString() const;
};
 
std::ostream& operator<<(std::ostream& ostr, const SolveStats& stats);
 
// The reason a call to Solve() terminates.
enum class TerminationReason {
  // A provably optimal solution (up to numerical tolerances) has been found.
  kOptimal = TERMINATION_REASON_OPTIMAL,
 
  // The primal problem has no feasible solutions.
  kInfeasible = TERMINATION_REASON_INFEASIBLE,
 
  // The primal problem is feasible and arbitrarily good solutions can be
  // found along a primal ray.
  kUnbounded = TERMINATION_REASON_UNBOUNDED,
 
  // The primal problem is either infeasible or unbounded. More details on the
  // problem status may be available in solve_stats.problem_status. Note that
  // Gurobi's unbounded status may be mapped here as explained in
  // go/mathopt-solver-specific#gurobi-inf-or-unb.
  kInfeasibleOrUnbounded = TERMINATION_REASON_INFEASIBLE_OR_UNBOUNDED,
 
  // The problem was solved to one of the criteria above (Optimal, Infeasible,
  // Unbounded, or InfeasibleOrUnbounded), but one or more tolerances was not
  // met. Some primal/dual solutions/rays be present, but either they will be
  // slightly infeasible, or (if the problem was nearly optimal) their may be
  // a gap between the best solution objective and best objective bound.
  //
  // Users can still query primal/dual solutions/rays and solution stats, but
  // they are responsible for dealing with the numerical imprecision.
  kImprecise = TERMINATION_REASON_IMPRECISE,
 
  // The optimizer reached some kind of limit and a primal feasible solution
  // is returned. See SolveResultProto.limit_detail for detailed description of
  // the kind of limit that was reached.
  kFeasible = TERMINATION_REASON_FEASIBLE,
 
  // The optimizer reached some kind of limit and it did not find a primal
  // feasible solution. See SolveResultProto.limit_detail for detailed
  // description of the kind of limit that was reached.
  kNoSolutionFound = TERMINATION_REASON_NO_SOLUTION_FOUND,
 
  // The algorithm stopped because it encountered unrecoverable numerical
  // error. No solution information is available.
  kNumericalError = TERMINATION_REASON_NUMERICAL_ERROR,
 
  // The algorithm stopped because of an error not covered by one of the
  // statuses defined above. No solution information is available.
  kOtherError = TERMINATION_REASON_OTHER_ERROR
};
 
MATH_OPT_DEFINE_ENUM(TerminationReason, TERMINATION_REASON_UNSPECIFIED);
 
// When a Solve() stops early with TerminationReason kFeasible or
// kNoSolutionFound, the specific limit that was hit.
enum class Limit {
  // Used if the underlying solver cannot determine which limit was reached, or
  // as a null value when we terminated not from a limit (e.g. kOptimal).
  kUndetermined = LIMIT_UNDETERMINED,
 
  // An iterative algorithm stopped after conducting the maximum number of
  // iterations (e.g. simplex or barrier iterations).
  kIteration = LIMIT_ITERATION,
 
  // The algorithm stopped after a user-specified computation time.
  kTime = LIMIT_TIME,
 
  // A branch-and-bound algorithm stopped because it explored a maximum number
  // of nodes in the branch-and-bound tree.
  kNode = LIMIT_NODE,
 
  // The algorithm stopped because it found the required number of solutions.
  // This is often used in MIPs to get the solver to return the first feasible
  // solution it encounters.
  kSolution = LIMIT_SOLUTION,
 
  // The algorithm stopped because it ran out of memory.
  kMemory = LIMIT_MEMORY,
 
  // The solver was run with a cutoff (e.g. SolveParameters.cutoff_limit was
  // set) on the objective, indicating that the user did not want any solution
  // worse than the cutoff, and the solver concluded there were no solutions at
  // least as good as the cutoff. Typically no further solution information is
  // provided.
  kCutoff = LIMIT_CUTOFF,
 
  // The algorithm stopped because it found a solution better than a minimum
  // limit set by the user.
  kObjective = LIMIT_OBJECTIVE,
 
  // The algorithm stopped because the norm of an iterate became too large.
  kNorm = LIMIT_NORM,
 
  // The algorithm stopped because of an interrupt signal or a user interrupt
  // request.
  kInterrupted = LIMIT_INTERRUPTED,
 
  // The algorithm stopped because it was unable to continue making progress
  // towards the solution.
  kSlowProgress = LIMIT_SLOW_PROGRESS,
 
  // The algorithm stopped due to a limit not covered by one of the above. Note
  // that kUndetermined is used when the reason cannot be determined, and kOther
  // is used when the reason is known but does not fit into any of the above
  // alternatives.
  kOther = LIMIT_OTHER
};
 
MATH_OPT_DEFINE_ENUM(Limit, LIMIT_UNSPECIFIED);
 
// All information regarding why a call to Solve() terminated.
struct Termination {
  // When the reason is kFeasible or kNoSolutionFound, please use the static
  // functions Feasible and NoSolutionFound.
  explicit Termination(TerminationReason reason, std::string detail = {});
 
  TerminationReason reason;
 
  // Is set iff reason is kFeasible or kNoSolutionFound.
  std::optional<Limit> limit;
 
  // Additional typically solver specific information about termination.
  // Not all solvers can always determine the limit which caused termination,
  // Limit::kUndetermined is used when the cause cannot be determined.
  std::string detail;
 
  // Returns true if a limit was reached (i.e. if reason is kFeasible or
  // kNoSolutionFound, and limit is not empty).
  bool limit_reached() const;
 
  // Will CHECK fail on invalid input, if reason is unspecified, if limit is
  // set when reason is not TERMINATION_REASON_FEASIBLE or
  // TERMINATION_REASON_NO_SOLUTION_FOUND, or if limit is unspecified when
  // reason is TERMINATION_REASON_FEASIBLE or
  // TERMINATION_REASON_NO_SOLUTION_FOUND (see solution_validator.h).
  static Termination FromProto(const TerminationProto& termination_proto);
 
  // Sets the reason to kFeasible
  static Termination Feasible(Limit limit, std::string detail = {});
 
  // Sets the reason to kNoSolutionFound
  static Termination NoSolutionFound(Limit limit, std::string detail = {});
 
  TerminationProto ToProto() const;
  std::string ToString() const;
};
 
std::ostream& operator<<(std::ostream& ostr, const Termination& termination);
 
// The result of solving an optimization problem with Solve().
struct SolveResult {
  explicit SolveResult(Termination termination)
      : termination(std::move(termination)) {}
 
  // Non-fatal errors, e.g. an unsupported parameter that was skipped.
  std::vector<std::string> warnings;
 
  // The reason the solver stopped.
  Termination termination;
 
  // Statistics on the solve process, e.g. running time, iterations.
  SolveStats solve_stats;
 
  //  Basic solutions use, as of Nov 2021:
  //    * All convex optimization solvers (LP, convex QP) return only one
  //      solution as a primal dual pair.
  //    * Only MI(Q)P solvers return more than one solution. MIP solvers do not
  //      return any dual information, or primal infeasible solutions. Solutions
  //      are returned in order of best primal objective first. Gurobi solves
  //      nonconvex QP (integer or continuous) as MIQP.
 
  // The general contract for the order of solutions that future solvers should
  // implement is to order by:
  //   1. The solutions with a primal feasible solution, ordered by best primal
  //      objective first.
  //   2. The solutions with a dual feasible solution, ordered by best dual
  //      objective (unknown dual objective is worst)
  //   3. All remaining solutions can be returned in any order.
  std::vector<Solution> solutions;
 
  // Directions of unbounded primal improvement, or equivalently, dual
  // infeasibility certificates. Typically provided for TerminationReasons
  // kUnbounded and kInfeasibleOrUnbounded.
  std::vector<PrimalRay> primal_rays;
 
  // Directions of unbounded dual improvement, or equivalently, primal
  // infeasibility certificates. Typically provided for TerminationReason
  // kInfeasible.
  std::vector<DualRay> dual_rays;
 
  static SolveResult FromProto(const ModelStorage* model,
                               const SolveResultProto& solve_result_proto);
 
  absl::Duration solve_time() const { return solve_stats.solve_time; }
 
  // Indicates if at least one primal feasible solution is available.
  //
  // When termination.reason is TerminationReason::kOptimal, this is guaranteed
  // to be true and need not be checked.
  bool has_primal_feasible_solution() const;
 
  // The objective value of the best primal feasible solution. Will CHECK fail
  // if there are no primal feasible solutions.
  double objective_value() const;
 
  // A bound on the best possible objective value.
  double best_objective_bound() const;
 
  // The variable values from the best primal feasible solution. Will CHECK fail
  // if there are no primal feasible solutions.
  const VariableMap<double>& variable_values() const;
 
  // Returns true only if the problem has been shown to be feasible and bounded.
  bool bounded() const;
 
  // Indicates if at least one primal ray is available.
  //
  // This is NOT guaranteed to be true when termination.reason is
  // TerminationReason::kUnbounded or TerminationReason::kInfeasibleOrUnbounded.
  bool has_ray() const { return !primal_rays.empty(); }
 
  // The variable values from the first primal ray. Will CHECK fail if there
  // are no primal rays.
  const VariableMap<double>& ray_variable_values() const;
 
  // Indicates if the best primal solution has an associated dual feasible
  // solution.
  //
  // This is NOT guaranteed to be true when termination.reason is
  // TerminationReason::kOptimal. It also may be true even when the best primal
  // solution is not feasible.
  bool has_dual_feasible_solution() const;
 
  // The dual values from the best dual solution. Will CHECK fail if there
  // are no dual solutions.
  const LinearConstraintMap<double>& dual_values() const;
 
  // The reduced from the best dual solution. Will CHECK fail if there
  // are no dual solutions.
  const VariableMap<double>& reduced_costs() const;
 
  // Indicates if at least one dual ray is available.
  //
  // This is NOT guaranteed to be true when termination.reason is
  // TerminationReason::kInfeasible.
  bool has_dual_ray() const { return !dual_rays.empty(); }
 
  // The dual values from the first dual ray. Will CHECK fail if there
  // are no dual rays.
  const LinearConstraintMap<double>& ray_dual_values() const;
 
  // The reduced from the first dual ray. Will CHECK fail if there
  // are no dual rays.
  const VariableMap<double>& ray_reduced_costs() const;
 
  // Indicates if at least one basis is available.
  bool has_basis() const;
 
  // The constraint basis status for the first primal/dual pair.
  const LinearConstraintMap<BasisStatus>& constraint_status() const;
 
  // The variable basis status for the first primal/dual pair.
  const VariableMap<BasisStatus>& variable_status() const;
};
 
}  // namespace math_opt
}  // namespace operations_research
 
#endif  // OR_TOOLS_MATH_OPT_CPP_SOLVE_RESULT_H_