436 lines
17 KiB
Python
436 lines
17 KiB
Python
# Copyright 2010-2024 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.
|
||
|
||
"""The solution to an optimization problem defined by Model in model.py."""
|
||
import dataclasses
|
||
import enum
|
||
from typing import Dict, Optional, TypeVar
|
||
|
||
from ortools.math_opt import solution_pb2
|
||
from ortools.math_opt.python import model
|
||
from ortools.math_opt.python import sparse_containers
|
||
|
||
|
||
@enum.unique
|
||
class BasisStatus(enum.Enum):
|
||
"""Status of a variable/constraint in a LP basis.
|
||
|
||
Attributes:
|
||
FREE: The variable/constraint is free (it has no finite bounds).
|
||
AT_LOWER_BOUND: The variable/constraint is at its lower bound (which must be
|
||
finite).
|
||
AT_UPPER_BOUND: The variable/constraint is at its upper bound (which must be
|
||
finite).
|
||
FIXED_VALUE: The variable/constraint has identical finite lower and upper
|
||
bounds.
|
||
BASIC: The variable/constraint is basic.
|
||
"""
|
||
|
||
FREE = solution_pb2.BASIS_STATUS_FREE
|
||
AT_LOWER_BOUND = solution_pb2.BASIS_STATUS_AT_LOWER_BOUND
|
||
AT_UPPER_BOUND = solution_pb2.BASIS_STATUS_AT_UPPER_BOUND
|
||
FIXED_VALUE = solution_pb2.BASIS_STATUS_FIXED_VALUE
|
||
BASIC = solution_pb2.BASIS_STATUS_BASIC
|
||
|
||
|
||
@enum.unique
|
||
class SolutionStatus(enum.Enum):
|
||
"""Feasibility of a primal or dual solution as claimed by the solver.
|
||
|
||
Attributes:
|
||
UNDETERMINED: Solver does not claim a feasibility status.
|
||
FEASIBLE: Solver claims the solution is feasible.
|
||
INFEASIBLE: Solver claims the solution is infeasible.
|
||
"""
|
||
|
||
UNDETERMINED = solution_pb2.SOLUTION_STATUS_UNDETERMINED
|
||
FEASIBLE = solution_pb2.SOLUTION_STATUS_FEASIBLE
|
||
INFEASIBLE = solution_pb2.SOLUTION_STATUS_INFEASIBLE
|
||
|
||
|
||
def parse_optional_solution_status(
|
||
proto: solution_pb2.SolutionStatusProto,
|
||
) -> Optional[SolutionStatus]:
|
||
"""Converts a proto SolutionStatus to an optional Python SolutionStatus."""
|
||
return (
|
||
None
|
||
if proto == solution_pb2.SOLUTION_STATUS_UNSPECIFIED
|
||
else SolutionStatus(proto)
|
||
)
|
||
|
||
|
||
def optional_solution_status_to_proto(
|
||
status: Optional[SolutionStatus],
|
||
) -> solution_pb2.SolutionStatusProto:
|
||
"""Converts an optional Python SolutionStatus to a proto SolutionStatus."""
|
||
return solution_pb2.SOLUTION_STATUS_UNSPECIFIED if status is None else status.value
|
||
|
||
|
||
@dataclasses.dataclass
|
||
class PrimalSolution:
|
||
"""A solution to the optimization problem in a Model.
|
||
|
||
E.g. consider a simple linear program:
|
||
min c * x
|
||
s.t. A * x >= b
|
||
x >= 0.
|
||
A primal solution is assignment values to x. It is feasible if it satisfies
|
||
A * x >= b and x >= 0 from above. In the class PrimalSolution variable_values
|
||
is x and objective_value is c * x.
|
||
|
||
For the general case of a MathOpt optimization model, see go/mathopt-solutions
|
||
for details.
|
||
|
||
Attributes:
|
||
variable_values: The value assigned for each Variable in the model.
|
||
objective_value: The value of the objective value at this solution. This
|
||
value may not be always populated.
|
||
feasibility_status: The feasibility of the solution as claimed by the
|
||
solver.
|
||
"""
|
||
|
||
variable_values: Dict[model.Variable, float] = dataclasses.field(
|
||
default_factory=dict
|
||
)
|
||
objective_value: float = 0.0
|
||
feasibility_status: SolutionStatus = SolutionStatus.UNDETERMINED
|
||
|
||
def to_proto(self) -> solution_pb2.PrimalSolutionProto:
|
||
"""Returns an equivalent proto for a primal solution."""
|
||
return solution_pb2.PrimalSolutionProto(
|
||
variable_values=sparse_containers.to_sparse_double_vector_proto(
|
||
self.variable_values
|
||
),
|
||
objective_value=self.objective_value,
|
||
feasibility_status=self.feasibility_status.value,
|
||
)
|
||
|
||
|
||
def parse_primal_solution(
|
||
proto: solution_pb2.PrimalSolutionProto, mod: model.Model
|
||
) -> PrimalSolution:
|
||
"""Returns an equivalent PrimalSolution from the input proto."""
|
||
result = PrimalSolution()
|
||
result.objective_value = proto.objective_value
|
||
result.variable_values = sparse_containers.parse_variable_map(
|
||
proto.variable_values, mod
|
||
)
|
||
status_proto = proto.feasibility_status
|
||
if status_proto == solution_pb2.SOLUTION_STATUS_UNSPECIFIED:
|
||
raise ValueError("Primal solution feasibility status should not be UNSPECIFIED")
|
||
result.feasibility_status = SolutionStatus(status_proto)
|
||
return result
|
||
|
||
|
||
@dataclasses.dataclass
|
||
class PrimalRay:
|
||
"""A direction of unbounded objective improvement in an optimization Model.
|
||
|
||
Equivalently, a certificate of infeasibility for the dual of the optimization
|
||
problem.
|
||
|
||
E.g. consider a simple linear program:
|
||
min c * x
|
||
s.t. A * x >= b
|
||
x >= 0.
|
||
A primal ray is an x that satisfies:
|
||
c * x < 0
|
||
A * x >= 0
|
||
x >= 0.
|
||
Observe that given a feasible solution, any positive multiple of the primal
|
||
ray plus that solution is still feasible, and gives a better objective
|
||
value. A primal ray also proves the dual optimization problem infeasible.
|
||
|
||
In the class PrimalRay, variable_values is this x.
|
||
|
||
For the general case of a MathOpt optimization model, see
|
||
go/mathopt-solutions for details.
|
||
|
||
Attributes:
|
||
variable_values: The value assigned for each Variable in the model.
|
||
"""
|
||
|
||
variable_values: Dict[model.Variable, float] = dataclasses.field(
|
||
default_factory=dict
|
||
)
|
||
|
||
|
||
def parse_primal_ray(proto: solution_pb2.PrimalRayProto, mod: model.Model) -> PrimalRay:
|
||
"""Returns an equivalent PrimalRay from the input proto."""
|
||
result = PrimalRay()
|
||
result.variable_values = sparse_containers.parse_variable_map(
|
||
proto.variable_values, mod
|
||
)
|
||
return result
|
||
|
||
|
||
@dataclasses.dataclass
|
||
class DualSolution:
|
||
"""A solution to the dual of the optimization problem given by a Model.
|
||
|
||
E.g. consider the primal dual pair linear program pair:
|
||
(Primal) (Dual)
|
||
min c * x max b * y
|
||
s.t. A * x >= b s.t. y * A + r = c
|
||
x >= 0 y, r >= 0.
|
||
The dual solution is the pair (y, r). It is feasible if it satisfies the
|
||
constraints from (Dual) above.
|
||
|
||
Below, y is dual_values, r is reduced_costs, and b * y is objective_value.
|
||
|
||
For the general case, see go/mathopt-solutions and go/mathopt-dual (and note
|
||
that the dual objective depends on r in the general case).
|
||
|
||
Attributes:
|
||
dual_values: The value assigned for each LinearConstraint in the model.
|
||
reduced_costs: The value assigned for each Variable in the model.
|
||
objective_value: The value of the dual objective value at this solution.
|
||
This value may not be always populated.
|
||
feasibility_status: The feasibility of the solution as claimed by the
|
||
solver.
|
||
"""
|
||
|
||
dual_values: Dict[model.LinearConstraint, float] = dataclasses.field(
|
||
default_factory=dict
|
||
)
|
||
reduced_costs: Dict[model.Variable, float] = dataclasses.field(default_factory=dict)
|
||
objective_value: Optional[float] = None
|
||
feasibility_status: SolutionStatus = SolutionStatus.UNDETERMINED
|
||
|
||
def to_proto(self) -> solution_pb2.DualSolutionProto:
|
||
"""Returns an equivalent proto for a dual solution."""
|
||
return solution_pb2.DualSolutionProto(
|
||
dual_values=sparse_containers.to_sparse_double_vector_proto(
|
||
self.dual_values
|
||
),
|
||
reduced_costs=sparse_containers.to_sparse_double_vector_proto(
|
||
self.reduced_costs
|
||
),
|
||
objective_value=self.objective_value,
|
||
feasibility_status=self.feasibility_status.value,
|
||
)
|
||
|
||
|
||
def parse_dual_solution(
|
||
proto: solution_pb2.DualSolutionProto, mod: model.Model
|
||
) -> DualSolution:
|
||
"""Returns an equivalent DualSolution from the input proto."""
|
||
result = DualSolution()
|
||
result.objective_value = (
|
||
proto.objective_value if proto.HasField("objective_value") else None
|
||
)
|
||
result.dual_values = sparse_containers.parse_linear_constraint_map(
|
||
proto.dual_values, mod
|
||
)
|
||
result.reduced_costs = sparse_containers.parse_variable_map(
|
||
proto.reduced_costs, mod
|
||
)
|
||
status_proto = proto.feasibility_status
|
||
if status_proto == solution_pb2.SOLUTION_STATUS_UNSPECIFIED:
|
||
raise ValueError("Dual solution feasibility status should not be UNSPECIFIED")
|
||
result.feasibility_status = SolutionStatus(status_proto)
|
||
return result
|
||
|
||
|
||
@dataclasses.dataclass
|
||
class DualRay:
|
||
"""A direction of unbounded objective improvement in an optimization Model.
|
||
|
||
A direction of unbounded improvement to the dual of an optimization,
|
||
problem; equivalently, a certificate of primal infeasibility.
|
||
|
||
E.g. consider the primal dual pair linear program pair:
|
||
(Primal) (Dual)
|
||
min c * x max b * y
|
||
s.t. A * x >= b s.t. y * A + r = c
|
||
x >= 0 y, r >= 0.
|
||
|
||
The dual ray is the pair (y, r) satisfying:
|
||
b * y > 0
|
||
y * A + r = 0
|
||
y, r >= 0.
|
||
Observe that adding a positive multiple of (y, r) to dual feasible solution
|
||
maintains dual feasibility and improves the objective (proving the dual is
|
||
unbounded). The dual ray also proves the primal problem is infeasible.
|
||
|
||
In the class DualRay below, y is dual_values and r is reduced_costs.
|
||
|
||
For the general case, see go/mathopt-solutions and go/mathopt-dual (and note
|
||
that the dual objective depends on r in the general case).
|
||
|
||
Attributes:
|
||
dual_values: The value assigned for each LinearConstraint in the model.
|
||
reduced_costs: The value assigned for each Variable in the model.
|
||
"""
|
||
|
||
dual_values: Dict[model.LinearConstraint, float] = dataclasses.field(
|
||
default_factory=dict
|
||
)
|
||
reduced_costs: Dict[model.Variable, float] = dataclasses.field(default_factory=dict)
|
||
|
||
|
||
def parse_dual_ray(proto: solution_pb2.DualRayProto, mod: model.Model) -> DualRay:
|
||
"""Returns an equivalent DualRay from the input proto."""
|
||
result = DualRay()
|
||
result.dual_values = sparse_containers.parse_linear_constraint_map(
|
||
proto.dual_values, mod
|
||
)
|
||
result.reduced_costs = sparse_containers.parse_variable_map(
|
||
proto.reduced_costs, mod
|
||
)
|
||
return result
|
||
|
||
|
||
@dataclasses.dataclass
|
||
class Basis:
|
||
"""A combinatorial characterization for a solution to a linear program.
|
||
|
||
The simplex method for solving linear programs always returns a "basic
|
||
feasible solution" which can be described combinatorially as a Basis. A basis
|
||
assigns a BasisStatus for every variable and linear constraint.
|
||
|
||
E.g. consider a standard form LP:
|
||
min c * x
|
||
s.t. A * x = b
|
||
x >= 0
|
||
that has more variables than constraints and with full row rank A.
|
||
|
||
Let n be the number of variables and m the number of linear constraints. A
|
||
valid basis for this problem can be constructed as follows:
|
||
* All constraints will have basis status FIXED.
|
||
* Pick m variables such that the columns of A are linearly independent and
|
||
assign the status BASIC.
|
||
* Assign the status AT_LOWER for the remaining n - m variables.
|
||
|
||
The basic solution for this basis is the unique solution of A * x = b that has
|
||
all variables with status AT_LOWER fixed to their lower bounds (all zero). The
|
||
resulting solution is called a basic feasible solution if it also satisfies
|
||
x >= 0.
|
||
|
||
See go/mathopt-basis for treatment of the general case and an explanation of
|
||
how a dual solution is determined for a basis.
|
||
|
||
Attributes:
|
||
variable_status: The basis status for each variable in the model.
|
||
constraint_status: The basis status for each linear constraint in the model.
|
||
basic_dual_feasibility: This is an advanced feature used by MathOpt to
|
||
characterize feasibility of suboptimal LP solutions (optimal solutions
|
||
will always have status SolutionStatus.FEASIBLE). For single-sided LPs it
|
||
should be equal to the feasibility status of the associated dual solution.
|
||
For two-sided LPs it may be different in some edge cases (e.g. incomplete
|
||
solves with primal simplex). For more details see
|
||
go/mathopt-basis-advanced#dualfeasibility. If you are providing a starting
|
||
basis via ModelSolveParameters.initial_basis, this value is ignored and
|
||
can be None. It is only relevant for the basis returned by Solution.basis,
|
||
and it is never None when returned from solve(). This is an advanced
|
||
status. For single-sided LPs it should be equal to the feasibility status
|
||
of the associated dual solution. For two-sided LPs it may be different in
|
||
some edge cases (e.g. incomplete solves with primal simplex). For more
|
||
details see go/mathopt-basis-advanced#dualfeasibility.
|
||
"""
|
||
|
||
variable_status: Dict[model.Variable, BasisStatus] = dataclasses.field(
|
||
default_factory=dict
|
||
)
|
||
constraint_status: Dict[model.LinearConstraint, BasisStatus] = dataclasses.field(
|
||
default_factory=dict
|
||
)
|
||
basic_dual_feasibility: Optional[SolutionStatus] = None
|
||
|
||
def to_proto(self) -> solution_pb2.BasisProto:
|
||
"""Returns an equivalent proto for the basis."""
|
||
return solution_pb2.BasisProto(
|
||
variable_status=_to_sparse_basis_status_vector_proto(self.variable_status),
|
||
constraint_status=_to_sparse_basis_status_vector_proto(
|
||
self.constraint_status
|
||
),
|
||
basic_dual_feasibility=optional_solution_status_to_proto(
|
||
self.basic_dual_feasibility
|
||
),
|
||
)
|
||
|
||
|
||
def parse_basis(proto: solution_pb2.BasisProto, mod: model.Model) -> Basis:
|
||
"""Returns an equivalent Basis to the input proto."""
|
||
result = Basis()
|
||
for index, vid in enumerate(proto.variable_status.ids):
|
||
status_proto = proto.variable_status.values[index]
|
||
if status_proto == solution_pb2.BASIS_STATUS_UNSPECIFIED:
|
||
raise ValueError("Variable basis status should not be UNSPECIFIED")
|
||
result.variable_status[mod.get_variable(vid)] = BasisStatus(status_proto)
|
||
for index, cid in enumerate(proto.constraint_status.ids):
|
||
status_proto = proto.constraint_status.values[index]
|
||
if status_proto == solution_pb2.BASIS_STATUS_UNSPECIFIED:
|
||
raise ValueError("Constraint basis status should not be UNSPECIFIED")
|
||
result.constraint_status[mod.get_linear_constraint(cid)] = BasisStatus(
|
||
status_proto
|
||
)
|
||
result.basic_dual_feasibility = parse_optional_solution_status(
|
||
proto.basic_dual_feasibility
|
||
)
|
||
return result
|
||
|
||
|
||
T = TypeVar("T", model.Variable, model.LinearConstraint)
|
||
|
||
|
||
def _to_sparse_basis_status_vector_proto(
|
||
terms: Dict[T, BasisStatus]
|
||
) -> solution_pb2.SparseBasisStatusVector:
|
||
"""Converts a basis vector from a python Dict to a protocol buffer."""
|
||
result = solution_pb2.SparseBasisStatusVector()
|
||
if terms:
|
||
id_and_status = sorted(
|
||
(key.id, status.value) for (key, status) in terms.items()
|
||
)
|
||
ids, values = zip(*id_and_status)
|
||
result.ids[:] = ids
|
||
result.values[:] = values
|
||
return result
|
||
|
||
|
||
@dataclasses.dataclass
|
||
class Solution:
|
||
"""A solution to the optimization problem in a Model."""
|
||
|
||
primal_solution: Optional[PrimalSolution] = None
|
||
dual_solution: Optional[DualSolution] = None
|
||
basis: Optional[Basis] = None
|
||
|
||
def to_proto(self) -> solution_pb2.SolutionProto:
|
||
"""Returns an equivalent proto for a solution."""
|
||
return solution_pb2.SolutionProto(
|
||
primal_solution=(
|
||
self.primal_solution.to_proto()
|
||
if self.primal_solution is not None
|
||
else None
|
||
),
|
||
dual_solution=(
|
||
self.dual_solution.to_proto()
|
||
if self.dual_solution is not None
|
||
else None
|
||
),
|
||
basis=self.basis.to_proto() if self.basis is not None else None,
|
||
)
|
||
|
||
|
||
def parse_solution(proto: solution_pb2.SolutionProto, mod: model.Model) -> Solution:
|
||
"""Returns a Solution equivalent to the input proto."""
|
||
result = Solution()
|
||
if proto.HasField("primal_solution"):
|
||
result.primal_solution = parse_primal_solution(proto.primal_solution, mod)
|
||
if proto.HasField("dual_solution"):
|
||
result.dual_solution = parse_dual_solution(proto.dual_solution, mod)
|
||
result.basis = parse_basis(proto.basis, mod) if proto.HasField("basis") else None
|
||
return result
|