1565 lines
57 KiB
Python
1565 lines
57 KiB
Python
# Copyright 2010-2018 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.
|
|
"""Propose a natural language on top of cp_model_pb2 python proto.
|
|
|
|
This file implements a easy-to-use API on top of the cp_model_pb2 protobuf
|
|
defined in ../ .
|
|
"""
|
|
|
|
from __future__ import absolute_import
|
|
from __future__ import division
|
|
from __future__ import print_function
|
|
|
|
import collections
|
|
import numbers
|
|
import time
|
|
from six import iteritems
|
|
|
|
from ortools.sat import cp_model_pb2
|
|
from ortools.sat import sat_parameters_pb2
|
|
from ortools.sat.python import cp_model_helper
|
|
from ortools.sat import pywrapsat
|
|
|
|
# The classes below allow linear expressions to be expressed naturally with the
|
|
# usual arithmetic operators +-*/ and with constant numbers, which makes the
|
|
# python API very intuitive. See ../samples/*.py for examples.
|
|
|
|
INT_MIN = -9223372036854775808 # hardcoded to be platform independent.
|
|
INT_MAX = 9223372036854775807
|
|
INT32_MAX = 2147483647
|
|
INT32_MIN = -2147483648
|
|
|
|
# Cp Solver status (exported to avoid importing cp_model_cp2).
|
|
UNKNOWN = cp_model_pb2.UNKNOWN
|
|
MODEL_INVALID = cp_model_pb2.MODEL_INVALID
|
|
FEASIBLE = cp_model_pb2.FEASIBLE
|
|
INFEASIBLE = cp_model_pb2.INFEASIBLE
|
|
OPTIMAL = cp_model_pb2.OPTIMAL
|
|
|
|
# Variable selection strategy
|
|
CHOOSE_FIRST = cp_model_pb2.DecisionStrategyProto.CHOOSE_FIRST
|
|
CHOOSE_LOWEST_MIN = cp_model_pb2.DecisionStrategyProto.CHOOSE_LOWEST_MIN
|
|
CHOOSE_HIGHEST_MAX = cp_model_pb2.DecisionStrategyProto.CHOOSE_HIGHEST_MAX
|
|
CHOOSE_MIN_DOMAIN_SIZE = (
|
|
cp_model_pb2.DecisionStrategyProto.CHOOSE_MIN_DOMAIN_SIZE)
|
|
CHOOSE_MAX_DOMAIN_SIZE = (
|
|
cp_model_pb2.DecisionStrategyProto.CHOOSE_MAX_DOMAIN_SIZE)
|
|
|
|
# Domain reduction strategy
|
|
SELECT_MIN_VALUE = cp_model_pb2.DecisionStrategyProto.SELECT_MIN_VALUE
|
|
SELECT_MAX_VALUE = cp_model_pb2.DecisionStrategyProto.SELECT_MAX_VALUE
|
|
SELECT_LOWER_HALF = cp_model_pb2.DecisionStrategyProto.SELECT_LOWER_HALF
|
|
SELECT_UPPER_HALF = cp_model_pb2.DecisionStrategyProto.SELECT_UPPER_HALF
|
|
|
|
# Search branching
|
|
AUTOMATIC_SEARCH = sat_parameters_pb2.SatParameters.AUTOMATIC_SEARCH
|
|
FIXED_SEARCH = sat_parameters_pb2.SatParameters.FIXED_SEARCH
|
|
PORTFOLIO_SEARCH = sat_parameters_pb2.SatParameters.PORTFOLIO_SEARCH
|
|
LP_SEARCH = sat_parameters_pb2.SatParameters.LP_SEARCH
|
|
|
|
|
|
def DisplayBounds(bounds):
|
|
"""Displays a flattened list of intervals."""
|
|
out = ''
|
|
for i in range(0, len(bounds), 2):
|
|
if i != 0:
|
|
out += ', '
|
|
if bounds[i] == bounds[i + 1]:
|
|
out += str(bounds[i])
|
|
else:
|
|
out += str(bounds[i]) + '..' + str(bounds[i + 1])
|
|
return out
|
|
|
|
|
|
def ShortName(model, i):
|
|
"""Returns a short name of an integer variable, or its negation."""
|
|
if i < 0:
|
|
return 'Not(%s)' % ShortName(model, -i - 1)
|
|
v = model.variables[i]
|
|
if v.name:
|
|
return v.name
|
|
elif len(v.domain) == 2 and v.domain[0] == v.domain[1]:
|
|
return str(v.domain[0])
|
|
else:
|
|
return '[%s]' % DisplayBounds(v.domain)
|
|
|
|
|
|
class LinearExpression(object):
|
|
"""Holds an integer linear expression.
|
|
|
|
An linear expression is built from integer constants and variables.
|
|
|
|
x + 2 * (y - z + 1) is one such linear expression, and can be written that
|
|
way directly in Python, provided x, y, and z are integer variables.
|
|
|
|
Linear expressions are used in two places in the cp_model.
|
|
When used with equality and inequality operators, they create linear
|
|
inequalities that can be added to the model as in:
|
|
|
|
model.Add(x + 2 * y <= 5)
|
|
model.Add(sum(array_of_vars) == 5)
|
|
|
|
Linear expressions can also be used to specify the objective of the model.
|
|
|
|
model.Minimize(x + 2 * y + z)
|
|
"""
|
|
|
|
def GetVarValueMap(self):
|
|
"""Scan the expression, and return a list of (var_coef_map, constant)."""
|
|
coeffs = collections.defaultdict(int)
|
|
constant = 0
|
|
to_process = [(self, 1)]
|
|
while to_process: # Flatten to avoid recursion.
|
|
expr, coef = to_process.pop()
|
|
if isinstance(expr, _ProductCst):
|
|
to_process.append((expr.Expression(),
|
|
coef * expr.Coefficient()))
|
|
elif isinstance(expr, _SumArray):
|
|
for e in expr.Array():
|
|
to_process.append((e, coef))
|
|
constant += expr.Constant() * coef
|
|
elif isinstance(expr, IntVar):
|
|
coeffs[expr] += coef
|
|
elif isinstance(expr, _NotBooleanVariable):
|
|
constant += coef
|
|
coeffs[expr.Not()] -= coef
|
|
else:
|
|
raise TypeError('Unrecognized linear expression: ' + str(expr))
|
|
|
|
return coeffs, constant
|
|
|
|
def __hash__(self):
|
|
return object.__hash__(self)
|
|
|
|
def __add__(self, expr):
|
|
return _SumArray([self, expr])
|
|
|
|
def __radd__(self, arg):
|
|
return _SumArray([self, arg])
|
|
|
|
def __sub__(self, expr):
|
|
return _SumArray([self, -expr])
|
|
|
|
def __rsub__(self, arg):
|
|
return _SumArray([-self, arg])
|
|
|
|
def __mul__(self, arg):
|
|
if isinstance(arg, numbers.Integral):
|
|
if arg == 1:
|
|
return self
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
return _ProductCst(self, arg)
|
|
else:
|
|
raise TypeError('Not an integer linear expression: ' + str(arg))
|
|
|
|
def __rmul__(self, arg):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
if arg == 1:
|
|
return self
|
|
return _ProductCst(self, arg)
|
|
|
|
def __div__(self, _):
|
|
raise NotImplementedError('LinearExpression.__div__')
|
|
|
|
def __truediv__(self, _):
|
|
raise NotImplementedError('LinearExpression.__truediv__')
|
|
|
|
def __mod__(self, _):
|
|
raise NotImplementedError('LinearExpression.__mod__')
|
|
|
|
def __neg__(self):
|
|
return _ProductCst(self, -1)
|
|
|
|
def __eq__(self, arg):
|
|
if arg is None:
|
|
return False
|
|
if isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
return LinearInequality(self, [arg, arg])
|
|
else:
|
|
return LinearInequality(self - arg, [0, 0])
|
|
|
|
def __ge__(self, arg):
|
|
if isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
return LinearInequality(self, [arg, INT_MAX])
|
|
else:
|
|
return LinearInequality(self - arg, [0, INT_MAX])
|
|
|
|
def __le__(self, arg):
|
|
if isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
return LinearInequality(self, [INT_MIN, arg])
|
|
else:
|
|
return LinearInequality(self - arg, [INT_MIN, 0])
|
|
|
|
def __lt__(self, arg):
|
|
if isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
if arg == INT_MIN:
|
|
raise ArithmeticError('< INT_MIN is not supported')
|
|
return LinearInequality(
|
|
self, [INT_MIN, cp_model_helper.CapInt64(arg - 1)])
|
|
else:
|
|
return LinearInequality(self - arg, [INT_MIN, -1])
|
|
|
|
def __gt__(self, arg):
|
|
if isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
if arg == INT_MAX:
|
|
raise ArithmeticError('> INT_MAX is not supported')
|
|
return LinearInequality(
|
|
self, [cp_model_helper.CapInt64(arg + 1), INT_MAX])
|
|
else:
|
|
return LinearInequality(self - arg, [1, INT_MAX])
|
|
|
|
def __ne__(self, arg):
|
|
if arg is None:
|
|
return True
|
|
if isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
if arg == INT_MAX:
|
|
return LinearInequality(self, [INT_MIN, INT_MAX - 1])
|
|
elif arg == INT_MIN:
|
|
return LinearInequality(self, [INT_MIN + 1, INT_MAX])
|
|
else:
|
|
return LinearInequality(self, [
|
|
INT_MIN,
|
|
cp_model_helper.CapInt64(arg - 1),
|
|
cp_model_helper.CapInt64(arg + 1), INT_MAX
|
|
])
|
|
else:
|
|
return LinearInequality(self - arg, [INT_MIN, -1, 1, INT_MAX])
|
|
|
|
|
|
class _ProductCst(LinearExpression):
|
|
"""Represents the product of a LinearExpression by a constant."""
|
|
|
|
def __init__(self, expr, coef):
|
|
cp_model_helper.AssertIsInt64(coef)
|
|
if isinstance(expr, _ProductCst):
|
|
self.__expr = expr.Expression()
|
|
self.__coef = expr.Coefficient() * coef
|
|
else:
|
|
self.__expr = expr
|
|
self.__coef = coef
|
|
|
|
def __str__(self):
|
|
if self.__coef == -1:
|
|
return '-' + str(self.__expr)
|
|
else:
|
|
return '(' + str(self.__coef) + ' * ' + str(self.__expr) + ')'
|
|
|
|
def __repr__(self):
|
|
return 'ProductCst(' + repr(self.__expr) + ', ' + repr(
|
|
self.__coef) + ')'
|
|
|
|
def Coefficient(self):
|
|
return self.__coef
|
|
|
|
def Expression(self):
|
|
return self.__expr
|
|
|
|
|
|
class _SumArray(LinearExpression):
|
|
"""Represents the sum of a list of LinearExpression and a constant."""
|
|
|
|
def __init__(self, array):
|
|
self.__array = []
|
|
self.__constant = 0
|
|
for x in array:
|
|
if isinstance(x, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(x)
|
|
self.__constant += x
|
|
elif isinstance(x, LinearExpression):
|
|
self.__array.append(x)
|
|
else:
|
|
raise TypeError('Not an linear expression: ' + str(x))
|
|
|
|
def __str__(self):
|
|
if self.__constant == 0:
|
|
return '({})'.format(' + '.join(map(str, self.__array)))
|
|
else:
|
|
return '({} + {})'.format(' + '.join(map(str, self.__array)),
|
|
self.__constant)
|
|
|
|
def __repr__(self):
|
|
return 'SumArray({}, {})'.format(', '.join(map(repr, self.__array)),
|
|
self.__constant)
|
|
|
|
def Array(self):
|
|
return self.__array
|
|
|
|
def Constant(self):
|
|
return self.__constant
|
|
|
|
|
|
class IntVar(LinearExpression):
|
|
"""An integer variable.
|
|
|
|
An IntVar is an object that can take on any integer value within defined
|
|
ranges. Variables appears in constraint like:
|
|
|
|
x + y >= 5
|
|
AllDifferent([x, y, z])
|
|
|
|
Solving a model is equivalent to finding, for each variable, a single value
|
|
from the set of initial values (called the initial domain), such that the
|
|
model is feasible, or optimal if you provided an objective function.
|
|
"""
|
|
|
|
def __init__(self, model, bounds, name):
|
|
"""See CpModel.NewIntVar below."""
|
|
self.__model = model
|
|
self.__index = len(model.variables)
|
|
self.__var = model.variables.add()
|
|
self.__var.domain.extend(bounds)
|
|
self.__var.name = name
|
|
self.__negation = None
|
|
|
|
def Index(self):
|
|
return self.__index
|
|
|
|
def __str__(self):
|
|
return self.__var.name
|
|
|
|
def __repr__(self):
|
|
return '%s(%s)' % (self.__var.name, DisplayBounds(self.__var.domain))
|
|
|
|
def Name(self):
|
|
return self.__var.name
|
|
|
|
def Not(self):
|
|
"""Returns the negation of a Boolean variable.
|
|
|
|
This method implements the logical negation of a Boolean variable.
|
|
It is only valid of the variable has a Boolean domain (0 or 1).
|
|
|
|
Note that this method is nilpotent: x.Not().Not() == x.
|
|
"""
|
|
|
|
for bound in self.__var.domain:
|
|
if bound < 0 or bound > 1:
|
|
raise TypeError(
|
|
'Cannot call Not on a non boolean variable: %s' % self)
|
|
if not self.__negation:
|
|
self.__negation = _NotBooleanVariable(self)
|
|
return self.__negation
|
|
|
|
|
|
class _NotBooleanVariable(LinearExpression):
|
|
"""Negation of a boolean variable."""
|
|
|
|
def __init__(self, boolvar):
|
|
self.__boolvar = boolvar
|
|
|
|
def Index(self):
|
|
return -self.__boolvar.Index() - 1
|
|
|
|
def Not(self):
|
|
return self.__boolvar
|
|
|
|
def __str__(self):
|
|
return 'not(%s)' % str(self.__boolvar)
|
|
|
|
|
|
class LinearInequality(object):
|
|
"""Represents a linear constraint: lb <= expression <= ub.
|
|
|
|
The only use of this class is to be added to the CpModel through
|
|
CpModel.Add(expression), as in:
|
|
|
|
model.Add(x + 2 * y -1 >= z)
|
|
"""
|
|
|
|
def __init__(self, expr, bounds):
|
|
self.__expr = expr
|
|
self.__bounds = bounds
|
|
|
|
def __str__(self):
|
|
if len(self.__bounds) == 2:
|
|
lb = self.__bounds[0]
|
|
ub = self.__bounds[1]
|
|
if lb > INT_MIN and ub < INT_MAX:
|
|
if lb == ub:
|
|
return str(self.__expr) + ' == ' + str(lb)
|
|
else:
|
|
return str(lb) + ' <= ' + str(
|
|
self.__expr) + ' <= ' + str(ub)
|
|
elif lb > INT_MIN:
|
|
return str(self.__expr) + ' >= ' + str(lb)
|
|
elif ub < INT_MAX:
|
|
return str(self.__expr) + ' <= ' + str(ub)
|
|
else:
|
|
return 'True (unbounded expr ' + str(self.__expr) + ')'
|
|
else:
|
|
return str(self.__expr) + ' in [' + DisplayBounds(
|
|
self.__bounds) + ']'
|
|
|
|
def Expression(self):
|
|
return self.__expr
|
|
|
|
def Bounds(self):
|
|
return self.__bounds
|
|
|
|
|
|
class Constraint(object):
|
|
"""Base class for constraints.
|
|
|
|
Constraints are built by the CpModel through the Add<XXX> methods.
|
|
Once created by the CpModel class, they are automatically added to the model.
|
|
The purpose of this class is to allow specification of enforcement literals
|
|
for this constraint.
|
|
|
|
b = model.BoolVar('b')
|
|
x = model.IntVar(0, 10, 'x')
|
|
y = model.IntVar(0, 10, 'y')
|
|
|
|
model.Add(x + 2 * y == 5).OnlyEnforceIf(b.Not())
|
|
"""
|
|
|
|
def __init__(self, constraints):
|
|
self.__index = len(constraints)
|
|
self.__constraint = constraints.add()
|
|
|
|
def OnlyEnforceIf(self, boolvar):
|
|
"""Adds an enforcement literal to the constraint.
|
|
|
|
Args:
|
|
boolvar: A boolean literal or a list of boolean literals.
|
|
|
|
Returns:
|
|
self.
|
|
|
|
This method adds one or more literals (that is a boolean variable or its
|
|
negation) as enforcement literals. The conjunction of all these literals
|
|
decides whether the constraint is active or not. It acts as an
|
|
implication, so if the conjunction is true, it implies that the constraint
|
|
must be enforced. If it is false, then the constraint is ignored.
|
|
|
|
The following constraints support enforcement literals:
|
|
bool or, bool and, and any linear constraints support any number of
|
|
enforcement literals.
|
|
"""
|
|
|
|
if isinstance(boolvar, numbers.Integral) and boolvar == 1:
|
|
# Always true. Do nothing.
|
|
pass
|
|
elif isinstance(boolvar, list):
|
|
for b in boolvar:
|
|
if isinstance(b, numbers.Integral) and b == 1:
|
|
pass
|
|
else:
|
|
self.__constraint.enforcement_literal.append(b.Index())
|
|
else:
|
|
self.__constraint.enforcement_literal.append(boolvar.Index())
|
|
return self
|
|
|
|
def Index(self):
|
|
return self.__index
|
|
|
|
def ConstraintProto(self):
|
|
return self.__constraint
|
|
|
|
|
|
class IntervalVar(object):
|
|
"""Represents a Interval variable.
|
|
|
|
An interval variable is both a constraint and a variable. It is defined by
|
|
three integer variables: start, size, and end.
|
|
|
|
It is a constraint because, internally, it enforces that start + size == end.
|
|
|
|
It is also a variable as it can appear in specific scheduling constraints:
|
|
NoOverlap, NoOverlap2D, Cumulative.
|
|
|
|
Optionally, an enforcement literal can be added to this
|
|
constraint. This enforcement literal is understood by the same constraints.
|
|
These constraints ignore interval variables with enforcement literals assigned
|
|
to false. Conversely, these constraints will also set these enforcement
|
|
literals to false if they cannot fit these intervals into the schedule.
|
|
"""
|
|
|
|
def __init__(self, model, start_index, size_index, end_index,
|
|
is_present_index, name):
|
|
self.__model = model
|
|
self.__index = len(model.constraints)
|
|
self.__ct = self.__model.constraints.add()
|
|
self.__ct.interval.start = start_index
|
|
self.__ct.interval.size = size_index
|
|
self.__ct.interval.end = end_index
|
|
if is_present_index is not None:
|
|
self.__ct.enforcement_literal.append(is_present_index)
|
|
if name:
|
|
self.__ct.name = name
|
|
|
|
def Index(self):
|
|
return self.__index
|
|
|
|
def __str__(self):
|
|
return self.__ct.name
|
|
|
|
def __repr__(self):
|
|
interval = self.__ct.interval
|
|
if self.__ct.enforcement_literal:
|
|
return '%s(start = %s, size = %s, end = %s, is_present = %s)' % (
|
|
self.__ct.name, ShortName(self.__model, interval.start),
|
|
ShortName(self.__model, interval.size),
|
|
ShortName(self.__model, interval.end),
|
|
ShortName(self.__model, self.__ct.enforcement_literal[0]))
|
|
else:
|
|
return '%s(start = %s, size = %s, end = %s)' % (
|
|
self.__ct.name, ShortName(self.__model, interval.start),
|
|
ShortName(self.__model, interval.size),
|
|
ShortName(self.__model, interval.end))
|
|
|
|
def Name(self):
|
|
return self.__ct.name
|
|
|
|
|
|
class CpModel(object):
|
|
"""Wrapper class around the cp_model proto.
|
|
|
|
This class provides two types of methods:
|
|
- NewXXX to create integer, boolean, or interval variables.
|
|
- AddXXX to create new constraints and add them to the model.
|
|
"""
|
|
|
|
def __init__(self):
|
|
self.__model = cp_model_pb2.CpModelProto()
|
|
self.__constant_map = {}
|
|
self.__optional_constant_map = {}
|
|
|
|
# Integer variable.
|
|
|
|
def NewIntVar(self, lb, ub, name):
|
|
"""Creates an integer variable with domain [lb, ub]."""
|
|
return IntVar(self.__model, [lb, ub], name)
|
|
|
|
def NewEnumeratedIntVar(self, bounds, name):
|
|
"""Creates an integer variable with an enumerated domain.
|
|
|
|
Args:
|
|
bounds: A flattened list of disjoint intervals.
|
|
name: The name of the variable.
|
|
|
|
Returns:
|
|
a variable whose domain is union[bounds[2*i]..bounds[2*i + 1]].
|
|
|
|
To create a variable with domain [1, 2, 3, 5, 7, 8], pass in the
|
|
array [1, 3, 5, 5, 7, 8].
|
|
"""
|
|
return IntVar(self.__model, bounds, name)
|
|
|
|
def NewBoolVar(self, name):
|
|
"""Creates a 0-1 variable with the given name."""
|
|
return IntVar(self.__model, [0, 1], name)
|
|
|
|
# Integer constraints.
|
|
|
|
def AddLinearConstraint(self, terms, lb, ub):
|
|
"""Adds the constraints lb <= sum(terms) <= ub, where term = (var, coef)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
for t in terms:
|
|
if not isinstance(t[0], IntVar):
|
|
raise TypeError('Wrong argument' + str(t))
|
|
cp_model_helper.AssertIsInt64(t[1])
|
|
model_ct.linear.vars.append(t[0].Index())
|
|
model_ct.linear.coeffs.append(t[1])
|
|
model_ct.linear.domain.extend([lb, ub])
|
|
return ct
|
|
|
|
def AddSumConstraint(self, variables, lb, ub):
|
|
"""Adds the constraints lb <= sum(variables) <= ub."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
for v in variables:
|
|
model_ct.linear.vars.append(v.Index())
|
|
model_ct.linear.coeffs.append(1)
|
|
model_ct.linear.domain.extend([lb, ub])
|
|
return ct
|
|
|
|
def AddLinearConstraintWithBounds(self, terms, bounds):
|
|
"""Adds the constraints sum(terms) in bounds, where term = (var, coef)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
for t in terms:
|
|
if not isinstance(t[0], IntVar):
|
|
raise TypeError('Wrong argument' + str(t))
|
|
cp_model_helper.AssertIsInt64(t[1])
|
|
model_ct.linear.vars.append(t[0].Index())
|
|
model_ct.linear.coeffs.append(t[1])
|
|
model_ct.linear.domain.extend(bounds)
|
|
return ct
|
|
|
|
def Add(self, ct):
|
|
"""Adds a LinearInequality to the model."""
|
|
if isinstance(ct, LinearInequality):
|
|
coeffs_map, constant = ct.Expression().GetVarValueMap()
|
|
bounds = [cp_model_helper.CapSub(x, constant) for x in ct.Bounds()]
|
|
return self.AddLinearConstraintWithBounds(
|
|
iteritems(coeffs_map), bounds)
|
|
elif ct and isinstance(ct, bool):
|
|
pass # Nothing to do, was already evaluated to true.
|
|
elif not ct and isinstance(ct, bool):
|
|
return self.AddBoolOr([]) # Evaluate to false.
|
|
else:
|
|
raise TypeError('Not supported: CpModel.Add(' + str(ct) + ')')
|
|
|
|
def AddAllDifferent(self, variables):
|
|
"""Adds AllDifferent(variables).
|
|
|
|
This constraint forces all variables to have different values.
|
|
|
|
Args:
|
|
variables: a list of integer variables.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.all_diff.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
return ct
|
|
|
|
def AddElement(self, index, variables, target):
|
|
"""Adds the element constraint: variables[index] == target."""
|
|
|
|
if not variables:
|
|
raise ValueError('AddElement expects a non empty variables array')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.element.index = self.GetOrMakeIndex(index)
|
|
model_ct.element.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.element.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddCircuit(self, arcs):
|
|
"""Adds Circuit(arcs).
|
|
|
|
Adds a circuit constraint from a sparse list of arcs that encode the graph.
|
|
|
|
A circuit is a unique Hamiltonian path in a subgraph of the total
|
|
graph. In case a node 'i' is not in the path, then there must be a
|
|
loop arc 'i -> i' associated with a true literal. Otherwise
|
|
this constraint will fail.
|
|
|
|
Args:
|
|
arcs: a list of arcs. An arc is a tuple (source_node, destination_node,
|
|
literal). The arc is selected in the circuit if the literal is true.
|
|
Both source_node and destination_node must be integer value between 0
|
|
and the number of nodes - 1.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
ValueError: If the list of arc is empty.
|
|
"""
|
|
if not arcs:
|
|
raise ValueError('AddCircuit expects a non empty array of arcs')
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
for arc in arcs:
|
|
cp_model_helper.AssertIsInt32(arc[0])
|
|
cp_model_helper.AssertIsInt32(arc[1])
|
|
lit = self.GetOrMakeBooleanIndex(arc[2])
|
|
model_ct.circuit.tails.append(arc[0])
|
|
model_ct.circuit.heads.append(arc[1])
|
|
model_ct.circuit.literals.append(lit)
|
|
return ct
|
|
|
|
def AddAllowedAssignments(self, variables, tuples_list):
|
|
"""Adds AllowedAssignments(variables, tuples_list).
|
|
|
|
An AllowedAssignments constraint is a constraint on an array of variables
|
|
that forces, when all variables are fixed to a single value, that the
|
|
corresponding list of values is equal to one of the tuple of the
|
|
tuple_list.
|
|
|
|
Args:
|
|
variables: A list of variables.
|
|
tuples_list: A list of admissible tuples. Each tuple must have the same
|
|
length as the variables, and the ith value of a tuple corresponds to the
|
|
ith variable.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
TypeError: If a tuple does not have the same size as the list of
|
|
variables.
|
|
ValueError: If the array of variables is empty.
|
|
"""
|
|
|
|
if not variables:
|
|
raise ValueError(
|
|
'AddAllowedAssignments expects a non empty variables '
|
|
'array')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.table.vars.extend([self.GetOrMakeIndex(x) for x in variables])
|
|
arity = len(variables)
|
|
for t in tuples_list:
|
|
if len(t) != arity:
|
|
raise TypeError('Tuple ' + str(t) + ' has the wrong arity')
|
|
for v in t:
|
|
cp_model_helper.AssertIsInt64(v)
|
|
model_ct.table.values.extend(t)
|
|
return ct
|
|
|
|
def AddForbiddenAssignments(self, variables, tuples_list):
|
|
"""Adds AddForbiddenAssignments(variables, [tuples_list]).
|
|
|
|
A ForbiddenAssignments constraint is a constraint on an array of variables
|
|
where the list of impossible combinations is provided in the tuples list.
|
|
|
|
Args:
|
|
variables: A list of variables.
|
|
tuples_list: A list of forbidden tuples. Each tuple must have the same
|
|
length as the variables, and the ith value of a tuple corresponds to the
|
|
ith variable.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
TypeError: If a tuple does not have the same size as the list of
|
|
variables.
|
|
ValueError: If the array of variables is empty.
|
|
"""
|
|
|
|
if not variables:
|
|
raise ValueError(
|
|
'AddForbiddenAssignments expects a non empty variables '
|
|
'array')
|
|
|
|
index = len(self.__model.constraints)
|
|
ct = self.AddAllowedAssignments(variables, tuples_list)
|
|
self.__model.constraints[index].table.negated = True
|
|
return ct
|
|
|
|
def AddAutomaton(self, transition_variables, starting_state, final_states,
|
|
transition_triples):
|
|
"""Adds an automaton constraint.
|
|
|
|
An automaton constraint takes a list of variables (of size n), an initial
|
|
state, a set of final states, and a set of transitions. A transition is a
|
|
triplet ('tail', 'transition', 'head'), where 'tail' and 'head' are states,
|
|
and 'transition' is the label of an arc from 'head' to 'tail',
|
|
corresponding to the value of one variable in the list of variables.
|
|
|
|
This automaton will be unrolled into a flow with n + 1 phases. Each phase
|
|
contains the possible states of the automaton. The first state contains the
|
|
initial state. The last phase contains the final states.
|
|
|
|
Between two consecutive phases i and i + 1, the automaton creates a set of
|
|
arcs. For each transition (tail, transition, head), it will add an arc from
|
|
the state 'tail' of phase i and the state 'head' of phase i + 1. This arc
|
|
labeled by the value 'transition' of the variables 'variables[i]'. That is,
|
|
this arc can only be selected if 'variables[i]' is assigned the value
|
|
'transition'.
|
|
|
|
A feasible solution of this constraint is an assignment of variables such
|
|
that, starting from the initial state in phase 0, there is a path labeled by
|
|
the values of the variables that ends in one of the final states in the
|
|
final phase.
|
|
|
|
Args:
|
|
transition_variables: A non empty list of variables whose values
|
|
correspond to the labels of the arcs traversed by the automaton.
|
|
starting_state: The initial state of the automaton.
|
|
final_states: A non empty list of admissible final states.
|
|
transition_triples: A list of transition for the automaton, in the
|
|
following format (current_state, variable_value, next_state).
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
ValueError: if transition_variables, final_states, or transition_triples
|
|
are empty.
|
|
"""
|
|
|
|
if not transition_variables:
|
|
raise ValueError(
|
|
'AddAutomaton expects a non empty transition_variables '
|
|
'array')
|
|
if not final_states:
|
|
raise ValueError('AddAutomaton expects some final states')
|
|
|
|
if not transition_triples:
|
|
raise ValueError('AddAutomaton expects some transtion triples')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.automaton.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in transition_variables])
|
|
cp_model_helper.AssertIsInt64(starting_state)
|
|
model_ct.automaton.starting_state = starting_state
|
|
for v in final_states:
|
|
cp_model_helper.AssertIsInt64(v)
|
|
model_ct.automaton.final_states.append(v)
|
|
for t in transition_triples:
|
|
if len(t) != 3:
|
|
raise TypeError('Tuple ' + str(t) +
|
|
' has the wrong arity (!= 3)')
|
|
cp_model_helper.AssertIsInt64(t[0])
|
|
cp_model_helper.AssertIsInt64(t[1])
|
|
cp_model_helper.AssertIsInt64(t[2])
|
|
model_ct.automaton.transition_tail.append(t[0])
|
|
model_ct.automaton.transition_label.append(t[1])
|
|
model_ct.automaton.transition_head.append(t[2])
|
|
return ct
|
|
|
|
def AddInverse(self, variables, inverse_variables):
|
|
"""Adds Inverse(variables, inverse_variables).
|
|
|
|
An inverse constraint enforces that if 'variables[i]' is assigned a value
|
|
'j', then inverse_variables[j] is assigned a value 'i'. And vice versa.
|
|
|
|
Args:
|
|
variables: An array of integer variables.
|
|
inverse_variables: An array of integer variables.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
TypeError: if variables and inverse_variables have different length, or
|
|
if they are empty.
|
|
"""
|
|
|
|
if not variables or not inverse_variables:
|
|
raise TypeError(
|
|
'The Inverse constraint does not accept empty arrays')
|
|
if len(variables) != len(inverse_variables):
|
|
raise TypeError(
|
|
'In the inverse constraint, the two array variables and'
|
|
' inverse_variables must have the same length.')
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.inverse.f_direct.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.inverse.f_inverse.extend(
|
|
[self.GetOrMakeIndex(x) for x in inverse_variables])
|
|
return ct
|
|
|
|
def AddReservoirConstraint(self, times, demands, min_level, max_level):
|
|
"""Adds Reservoir(times, demands, min_level, max_level).
|
|
|
|
Maintains a reservoir level within bounds. The water level starts at 0, and
|
|
at any time >= 0, it must be between min_level and max_level. Furthermore,
|
|
this constraints expect all times variables to be >= 0.
|
|
If the variable times[i] is assigned a value t, then the current level
|
|
changes by demands[i] (which is constant) at the time t.
|
|
|
|
Note that level min can be > 0, or level max can be < 0. It just forces
|
|
some demands to be executed at time 0 to make sure that we are within those
|
|
bounds with the executed demands. Therefore, at any time t >= 0:
|
|
sum(demands[i] if times[i] <= t) in [min_level, max_level]
|
|
|
|
Args:
|
|
times: A list of positive integer variables which specify the time of the
|
|
filling or emptying the reservoir.
|
|
demands: A list of integer values that specifies the amount of the
|
|
emptying or feeling.
|
|
min_level: At any time >= 0, the level of the reservoir must be greater of
|
|
equal than the min level.
|
|
max_level: At any time >= 0, the level of the reservoir must be less or
|
|
equal than the max level.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
ValueError: if max_level < min_level.
|
|
"""
|
|
|
|
if max_level < min_level:
|
|
return ValueError(
|
|
'Reservoir constraint must have a max_level >= min_level')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.reservoir.times.extend([self.GetOrMakeIndex(x) for x in times])
|
|
model_ct.reservoir.demands.extend(demands)
|
|
model_ct.reservoir.min_level = min_level
|
|
model_ct.reservoir.max_level = max_level
|
|
return ct
|
|
|
|
def AddReservoirConstraintWithActive(self, times, demands, actives,
|
|
min_level, max_level):
|
|
"""Adds Reservoir(times, demands, actives, min_level, max_level).
|
|
|
|
Maintain a reservoir level within bounds. The water level starts at 0, and
|
|
at
|
|
any time >= 0, it must be within min_level, and max_level. Furthermore, this
|
|
constraints expect all times variables to be >= 0.
|
|
If actives[i] is true, and if times[i] is assigned a value t, then the
|
|
level of the reservoir changes by demands[i] (which is constant) at time t.
|
|
|
|
Note that level_min can be > 0, or level_max can be < 0. It just forces
|
|
some demands to be executed at time 0 to make sure that we are within those
|
|
bounds with the executed demands. Therefore, at any time t >= 0:
|
|
sum(demands[i] * actives[i] if times[i] <= t) in [min_level, max_level]
|
|
The array of boolean variables 'actives', if defined, indicates which
|
|
actions are actually performed.
|
|
|
|
Args:
|
|
times: A list of positive integer variables which specify the time of the
|
|
filling or emptying the reservoir.
|
|
demands: A list of integer values that specifies the amount of the
|
|
emptying or feeling.
|
|
actives: a list of boolean variables. They indicates if the
|
|
emptying/refilling events actually take place.
|
|
min_level: At any time >= 0, the level of the reservoir must be greater of
|
|
equal than the min level.
|
|
max_level: At any time >= 0, the level of the reservoir must be less or
|
|
equal than the max level.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
|
|
Raises:
|
|
ValueError: if max_level < min_level.
|
|
"""
|
|
|
|
if max_level < min_level:
|
|
return ValueError(
|
|
'Reservoir constraint must have a max_level >= min_level')
|
|
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.reservoir.times.extend([self.GetOrMakeIndex(x) for x in times])
|
|
model_ct.reservoir.demands.extend(demands)
|
|
model_ct.reservoir.actives.extend([self.GetOrMakeIndex(x) for x in actives])
|
|
model_ct.reservoir.min_level = min_level
|
|
model_ct.reservoir.max_level = max_level
|
|
return ct
|
|
|
|
def AddMapDomain(self, var, bool_var_array, offset=0):
|
|
"""Adds var == i + offset <=> bool_var_array[i] == true for all i."""
|
|
|
|
for i, bool_var in enumerate(bool_var_array):
|
|
b_index = bool_var.Index()
|
|
var_index = var.Index()
|
|
model_ct = self.__model.constraints.add()
|
|
model_ct.linear.vars.append(var_index)
|
|
model_ct.linear.coeffs.append(1)
|
|
model_ct.linear.domain.extend([offset + i, offset + i])
|
|
model_ct.enforcement_literal.append(b_index)
|
|
|
|
model_ct = self.__model.constraints.add()
|
|
model_ct.linear.vars.append(var_index)
|
|
model_ct.linear.coeffs.append(1)
|
|
model_ct.enforcement_literal.append(-b_index - 1)
|
|
if offset + i - 1 >= INT_MIN:
|
|
model_ct.linear.domain.extend([INT_MIN, offset + i - 1])
|
|
if offset + i + 1 <= INT_MAX:
|
|
model_ct.linear.domain.extend([offset + i + 1, INT_MAX])
|
|
|
|
def AddImplication(self, a, b):
|
|
"""Adds a => b."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_or.literals.append(self.GetOrMakeBooleanIndex(b))
|
|
model_ct.enforcement_literal.append(self.GetOrMakeBooleanIndex(a))
|
|
return ct
|
|
|
|
def AddBoolOr(self, literals):
|
|
"""Adds Or(literals) == true."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_or.literals.extend(
|
|
[self.GetOrMakeBooleanIndex(x) for x in literals])
|
|
return ct
|
|
|
|
def AddBoolAnd(self, literals):
|
|
"""Adds And(literals) == true."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_and.literals.extend(
|
|
[self.GetOrMakeBooleanIndex(x) for x in literals])
|
|
return ct
|
|
|
|
def AddBoolXOr(self, literals):
|
|
"""Adds XOr(literals) == true."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.bool_xor.literals.extend(
|
|
[self.GetOrMakeBooleanIndex(x) for x in literals])
|
|
return ct
|
|
|
|
def AddMinEquality(self, target, variables):
|
|
"""Adds target == Min(variables)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_min.vars.extend(
|
|
[self.GetOrMakeIndex(x) for x in variables])
|
|
model_ct.int_min.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddMaxEquality(self, target, args):
|
|
"""Adds target == Max(variables)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_max.vars.extend([self.GetOrMakeIndex(x) for x in args])
|
|
model_ct.int_max.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddDivisionEquality(self, target, num, denom):
|
|
"""Adds target == num // denom."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_div.vars.extend(
|
|
[self.GetOrMakeIndex(num),
|
|
self.GetOrMakeIndex(denom)])
|
|
model_ct.int_div.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddAbsEquality(self, target, var):
|
|
"""Adds target == Abs(var)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
index = self.GetOrMakeIndex(var)
|
|
model_ct.int_max.vars.extend([index, -index - 1])
|
|
model_ct.int_max.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddModuloEquality(self, target, var, mod):
|
|
"""Adds target = var % mod."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_mod.vars.extend(
|
|
[self.GetOrMakeIndex(var),
|
|
self.GetOrMakeIndex(mod)])
|
|
model_ct.int_mod.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
def AddProdEquality(self, target, args):
|
|
"""Adds target == PROD(args)."""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.int_prod.vars.extend([self.GetOrMakeIndex(x) for x in args])
|
|
model_ct.int_prod.target = self.GetOrMakeIndex(target)
|
|
return ct
|
|
|
|
# Scheduling support
|
|
|
|
def NewIntervalVar(self, start, size, end, name):
|
|
"""Creates an interval variable from start, size, and end.
|
|
|
|
An interval variable is a constraint, that is itself used in other
|
|
constraints like NoOverlap.
|
|
|
|
Internally, it ensures that start + size == end.
|
|
|
|
Args:
|
|
start: The start of the interval. It can be an integer value, or an
|
|
integer variable.
|
|
size: The size of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
end: The end of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
name: The name of the interval variable.
|
|
|
|
Returns:
|
|
An IntervalVar object.
|
|
"""
|
|
|
|
start_index = self.GetOrMakeIndex(start)
|
|
size_index = self.GetOrMakeIndex(size)
|
|
end_index = self.GetOrMakeIndex(end)
|
|
return IntervalVar(self.__model, start_index, size_index, end_index,
|
|
None, name)
|
|
|
|
def NewOptionalIntervalVar(self, start, size, end, is_present, name):
|
|
"""Creates an optional interval var from start, size, end and is_present.
|
|
|
|
An optional interval variable is a constraint, that is itself used in other
|
|
constraints like NoOverlap. This constraint is protected by an is_present
|
|
literal that indicates if it is active or not.
|
|
|
|
Internally, it ensures that is_present implies start + size == end.
|
|
|
|
Args:
|
|
start: The start of the interval. It can be an integer value, or an
|
|
integer variable.
|
|
size: The size of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
end: The end of the interval. It can be an integer value, or an integer
|
|
variable.
|
|
is_present: A literal that indicates if the interval is active or not. A
|
|
inactive interval is simply ignored by all constraints.
|
|
name: The name of the interval variable.
|
|
|
|
Returns:
|
|
An IntervalVar object.
|
|
"""
|
|
is_present_index = self.GetOrMakeBooleanIndex(is_present)
|
|
start_index = self.GetOrMakeIndex(start)
|
|
size_index = self.GetOrMakeIndex(size)
|
|
end_index = self.GetOrMakeIndex(end)
|
|
return IntervalVar(self.__model, start_index, size_index, end_index,
|
|
is_present_index, name)
|
|
|
|
def AddNoOverlap(self, interval_vars):
|
|
"""Adds NoOverlap(interval_vars).
|
|
|
|
A NoOverlap constraint ensures that all present intervals do not overlap
|
|
in time.
|
|
|
|
Args:
|
|
interval_vars: The list of interval variables to constrain.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.no_overlap.intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in interval_vars])
|
|
return ct
|
|
|
|
def AddNoOverlap2D(self, x_intervals, y_intervals):
|
|
"""Adds NoOverlap2D(x_intervals, y_intervals).
|
|
|
|
A NoOverlap2D constraint ensures that all present rectangles do not overlap
|
|
on a plan. Each rectangle is aligned with the X and Y axis, and is defined
|
|
by two intervals which represent its projection onto the X and Y axis.
|
|
|
|
Args:
|
|
x_intervals: The X coordinates of the rectangles.
|
|
y_intervals: The Y coordinates of the rectangles.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.no_overlap_2d.x_intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in x_intervals])
|
|
model_ct.no_overlap_2d.y_intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in y_intervals])
|
|
return ct
|
|
|
|
def AddCumulative(self, intervals, demands, capacity):
|
|
"""Adds Cumulative(intervals, demands, capacity).
|
|
|
|
This constraint enforces that:
|
|
for all t:
|
|
sum(demands[i]
|
|
if (start(intervals[t]) <= t < end(intervals[t])) and
|
|
(t is present)) <= capacity
|
|
|
|
Args:
|
|
intervals: The list of intervals.
|
|
demands: The list of demands for each interval. Each demand must be >= 0.
|
|
Each demand can be an integer value, or an integer variable.
|
|
capacity: The maximum capacity of the cumulative constraint. It must be a
|
|
positive integer value or variable.
|
|
|
|
Returns:
|
|
An instance of the Constraint class.
|
|
"""
|
|
ct = Constraint(self.__model.constraints)
|
|
model_ct = self.__model.constraints[ct.Index()]
|
|
model_ct.cumulative.intervals.extend(
|
|
[self.GetIntervalIndex(x) for x in intervals])
|
|
model_ct.cumulative.demands.extend(
|
|
[self.GetOrMakeIndex(x) for x in demands])
|
|
model_ct.cumulative.capacity = self.GetOrMakeIndex(capacity)
|
|
return ct
|
|
|
|
# Helpers.
|
|
|
|
def __str__(self):
|
|
return str(self.__model)
|
|
|
|
def ModelProto(self):
|
|
return self.__model
|
|
|
|
def Negated(self, index):
|
|
return -index - 1
|
|
|
|
def GetOrMakeIndex(self, arg):
|
|
"""Returns the index of a variables, its negation, or a number."""
|
|
if isinstance(arg, IntVar):
|
|
return arg.Index()
|
|
elif (isinstance(arg, _ProductCst) and
|
|
isinstance(arg.Expression(), IntVar) and arg.Coefficient() == -1):
|
|
return -arg.Expression().Index() - 1
|
|
elif isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsInt64(arg)
|
|
return self.GetOrMakeIndexFromConstant(arg)
|
|
else:
|
|
raise TypeError('NotSupported: model.GetOrMakeIndex(' + str(arg) +
|
|
')')
|
|
|
|
def GetOrMakeBooleanIndex(self, arg):
|
|
"""Returns an index from a boolean expression."""
|
|
if isinstance(arg, IntVar):
|
|
self.AssertIsBooleanVariable(arg)
|
|
return arg.Index()
|
|
elif isinstance(arg, _NotBooleanVariable):
|
|
self.AssertIsBooleanVariable(arg.Not())
|
|
return arg.Index()
|
|
elif isinstance(arg, numbers.Integral):
|
|
cp_model_helper.AssertIsBoolean(arg)
|
|
return self.GetOrMakeIndexFromConstant(arg)
|
|
else:
|
|
raise TypeError('NotSupported: model.GetOrMakeBooleanIndex(' +
|
|
str(arg) + ')')
|
|
|
|
def GetIntervalIndex(self, arg):
|
|
if not isinstance(arg, IntervalVar):
|
|
raise TypeError('NotSupported: model.GetIntervalIndex(%s)' % arg)
|
|
return arg.Index()
|
|
|
|
def GetOrMakeIndexFromConstant(self, value):
|
|
if value in self.__constant_map:
|
|
return self.__constant_map[value]
|
|
index = len(self.__model.variables)
|
|
var = self.__model.variables.add()
|
|
var.domain.extend([value, value])
|
|
self.__constant_map[value] = index
|
|
return index
|
|
|
|
def VarIndexToVarProto(self, var_index):
|
|
if var_index > 0:
|
|
return self.__model.variables[var_index]
|
|
else:
|
|
return self.__model.variables[-var_index - 1]
|
|
|
|
def _SetObjective(self, obj, minimize):
|
|
"""Sets the objective of the model."""
|
|
if isinstance(obj, IntVar):
|
|
self.__model.ClearField('objective')
|
|
self.__model.objective.coeffs.append(1)
|
|
self.__model.objective.offset = 0
|
|
if minimize:
|
|
self.__model.objective.vars.append(obj.Index())
|
|
self.__model.objective.scaling_factor = 1
|
|
else:
|
|
self.__model.objective.vars.append(self.Negated(obj.Index()))
|
|
self.__model.objective.scaling_factor = -1
|
|
elif isinstance(obj, LinearExpression):
|
|
coeffs_map, constant = obj.GetVarValueMap()
|
|
self.__model.ClearField('objective')
|
|
if minimize:
|
|
self.__model.objective.scaling_factor = 1
|
|
self.__model.objective.offset = constant
|
|
else:
|
|
self.__model.objective.scaling_factor = -1
|
|
self.__model.objective.offset = -constant
|
|
for v, c, in iteritems(coeffs_map):
|
|
self.__model.objective.coeffs.append(c)
|
|
if minimize:
|
|
self.__model.objective.vars.append(v.Index())
|
|
else:
|
|
self.__model.objective.vars.append(self.Negated(v.Index()))
|
|
elif isinstance(obj, numbers.Integral):
|
|
self.__model.objective.offset = obj
|
|
self.__model.objective.scaling_factor = 1
|
|
else:
|
|
raise TypeError('TypeError: ' + str(obj) +
|
|
' is not a valid objective')
|
|
|
|
def Minimize(self, obj):
|
|
"""Sets the objective of the model to minimize(obj)."""
|
|
self._SetObjective(obj, minimize=True)
|
|
|
|
def Maximize(self, obj):
|
|
"""Sets the objective of the model to maximize(obj)."""
|
|
self._SetObjective(obj, minimize=False)
|
|
|
|
def HasObjective(self):
|
|
return self.__model.HasField('objective')
|
|
|
|
def AddDecisionStrategy(self, variables, var_strategy, domain_strategy):
|
|
"""Adds a search strategy to the model.
|
|
|
|
Args:
|
|
variables: a list of variables this strategy will assign.
|
|
var_strategy: heuristic to choose the next variable to assign.
|
|
domain_strategy: heuristic to reduce the domain of the selected variable.
|
|
Currently, this is advanced code, the union of all strategies added to
|
|
the model must be complete, i.e. instantiates all variables. Otherwise,
|
|
Solve() will fail.
|
|
"""
|
|
|
|
strategy = self.__model.search_strategy.add()
|
|
for v in variables:
|
|
strategy.variables.append(v.Index())
|
|
strategy.variable_selection_strategy = var_strategy
|
|
strategy.domain_reduction_strategy = domain_strategy
|
|
|
|
def ModelStats(self):
|
|
"""Returns some statistics on the model as a string."""
|
|
return pywrapsat.SatHelper.ModelStats(self.__model)
|
|
|
|
def Validate(self):
|
|
"""Returns a string explaining the issue is the model is not valid."""
|
|
return pywrapsat.SatHelper.ValidateModel(self.__model)
|
|
|
|
def AssertIsBooleanVariable(self, x):
|
|
if isinstance(x, IntVar):
|
|
var = self.__model.variables[x.Index()]
|
|
if len(var.domain) != 2 or var.domain[0] < 0 or var.domain[1] > 1:
|
|
raise TypeError('TypeError: ' + str(x) +
|
|
' is not a boolean variable')
|
|
elif not isinstance(x, _NotBooleanVariable):
|
|
raise TypeError('TypeError: ' + str(x) +
|
|
' is not a boolean variable')
|
|
|
|
|
|
def EvaluateLinearExpression(expression, solution):
|
|
"""Evaluate an linear expression against a solution."""
|
|
if isinstance(expression, numbers.Integral):
|
|
return expression
|
|
value = 0
|
|
to_process = [(expression, 1)]
|
|
while to_process:
|
|
expr, coef = to_process.pop()
|
|
if isinstance(expr, _ProductCst):
|
|
to_process.append((expr.Expression(), coef * expr.Coefficient()))
|
|
elif isinstance(expr, _SumArray):
|
|
for e in expr.Array():
|
|
to_process.append((e, coef))
|
|
value += expr.Constant() * coef
|
|
elif isinstance(expr, IntVar):
|
|
value += coef * solution.solution[expr.Index()]
|
|
elif isinstance(expr, _NotBooleanVariable):
|
|
value += coef * (1 - solution.solution[expr.Not().Index()])
|
|
return value
|
|
|
|
|
|
def EvaluateBooleanExpression(literal, solution):
|
|
"""Evaluate an boolean expression against a solution."""
|
|
if isinstance(literal, numbers.Integral):
|
|
return bool(literal)
|
|
elif isinstance(literal, IntVar) or isinstance(literal,
|
|
_NotBooleanVariable):
|
|
index = literal.Index()
|
|
if index >= 0:
|
|
return bool(solution.solution[index])
|
|
else:
|
|
return not solution.solution[-index - 1]
|
|
else:
|
|
raise TypeError(
|
|
'Cannot interpret %s as a boolean expression.' % literal)
|
|
|
|
|
|
class CpSolver(object):
|
|
"""Main solver class.
|
|
|
|
The purpose of this class is to search for a solution of a model given to the
|
|
Solve() method.
|
|
|
|
Once Solve() is called, this class allows inspecting the solution found
|
|
with the Value() and BooleanValue() methods, as well as general statistics
|
|
about the solve procedure.
|
|
"""
|
|
|
|
def __init__(self):
|
|
self.__model = None
|
|
self.__solution = None
|
|
self.parameters = sat_parameters_pb2.SatParameters()
|
|
|
|
def Solve(self, model):
|
|
"""Solves the given model and returns the solve status."""
|
|
self.__solution = pywrapsat.SatHelper.SolveWithParameters(
|
|
model.ModelProto(), self.parameters)
|
|
return self.__solution.status
|
|
|
|
def SolveWithSolutionCallback(self, model, callback):
|
|
"""Solves a problem and pass each solution found to the callback."""
|
|
self.__solution = (
|
|
pywrapsat.SatHelper.SolveWithParametersAndSolutionCallback(
|
|
model.ModelProto(), self.parameters, callback))
|
|
return self.__solution.status
|
|
|
|
def SearchForAllSolutions(self, model, callback):
|
|
"""Search for all solutions of a satisfiability problem.
|
|
|
|
This method searches for all feasible solution of a given model.
|
|
Then it feeds the solution to the callback.
|
|
|
|
Args:
|
|
model: The model to solve.
|
|
callback: The callback that will be called at each solution.
|
|
|
|
Returns:
|
|
The status of the solve (FEASIBLE, INFEASIBLE...).
|
|
"""
|
|
if model.HasObjective():
|
|
raise TypeError('Search for all solutions is only defined on '
|
|
'satisfiability problems')
|
|
# Store old values.
|
|
enumerate_all = self.parameters.enumerate_all_solutions
|
|
self.parameters.enumerate_all_solutions = True
|
|
self.__solution = (
|
|
pywrapsat.SatHelper.SolveWithParametersAndSolutionCallback(
|
|
model.ModelProto(), self.parameters, callback))
|
|
# Restore parameters.
|
|
self.parameters.enumerate_all_solutions = enumerate_all
|
|
return self.__solution.status
|
|
|
|
def Value(self, expression):
|
|
"""Returns the value of an linear expression after solve."""
|
|
if not self.__solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateLinearExpression(expression, self.__solution)
|
|
|
|
def BooleanValue(self, literal):
|
|
"""Returns the boolean value of a literal after solve."""
|
|
if not self.__solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateBooleanExpression(literal, self.__solution)
|
|
|
|
def ObjectiveValue(self):
|
|
"""Returns the value of objective after solve."""
|
|
return self.__solution.objective_value
|
|
|
|
def BestObjectiveBound(self):
|
|
"""Returns the best lower (upper) bound found when min(max)imizing."""
|
|
return self.__solution.best_objective_bound
|
|
|
|
def StatusName(self, status):
|
|
"""Returns the name of the status returned by Solve()."""
|
|
return cp_model_pb2.CpSolverStatus.Name(status)
|
|
|
|
def NumBooleans(self):
|
|
"""Returns the number of boolean variables managed by the SAT solver."""
|
|
return self.__solution.num_booleans
|
|
|
|
def NumConflicts(self):
|
|
"""Returns the number of conflicts since the creation of the solver."""
|
|
return self.__solution.num_conflicts
|
|
|
|
def NumBranches(self):
|
|
"""Returns the number of search branches explored by the solver."""
|
|
return self.__solution.num_branches
|
|
|
|
def WallTime(self):
|
|
"""Returns the wall time in seconds since the creation of the solver."""
|
|
return self.__solution.wall_time
|
|
|
|
def UserTime(self):
|
|
"""Returns the user time in seconds since the creation of the solver."""
|
|
return self.__solution.user_time
|
|
|
|
def ResponseStats(self):
|
|
"""Returns some statistics on the solution found as a string."""
|
|
return pywrapsat.SatHelper.SolverResponseStats(self.__solution)
|
|
|
|
|
|
class CpSolverSolutionCallback(pywrapsat.SolutionCallback):
|
|
"""Solution callback.
|
|
|
|
This class implements a callback that will be called at each new solution
|
|
found during search.
|
|
|
|
The method OnSolutionCallback() will be called by the solver, and must be
|
|
implemented. The current solution can be queried using the BooleanValue()
|
|
and Value() methods.
|
|
"""
|
|
|
|
def OnSolutionCallback(self):
|
|
"""Proxy to the same method in snake case."""
|
|
self.on_solution_callback()
|
|
|
|
def BooleanValue(self, lit):
|
|
"""Returns the boolean value of a boolean literal.
|
|
|
|
Args:
|
|
lit: A boolean variable or its negation.
|
|
|
|
Returns:
|
|
The boolean value of the literal in the solution.
|
|
|
|
Raises:
|
|
RuntimeError: if 'lit' is not a boolean variable or its negation.
|
|
"""
|
|
if not self.Response().solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
if isinstance(lit, numbers.Integral):
|
|
return bool(lit)
|
|
elif isinstance(lit, IntVar) or isinstance(lit, _NotBooleanVariable):
|
|
index = lit.Index()
|
|
return self.SolutionBooleanValue(index)
|
|
else:
|
|
raise TypeError(
|
|
'Cannot interpret %s as a boolean expression.' % lit)
|
|
|
|
def Value(self, expression):
|
|
"""Evaluates an linear expression in the current solution.
|
|
|
|
Args:
|
|
expression: a linear expression of the model.
|
|
|
|
Returns:
|
|
An integer value equal to the evaluation of the linear expression
|
|
against the current solution.
|
|
|
|
Raises:
|
|
RuntimeError: if 'expression' is not a LinearExpression.
|
|
"""
|
|
if not self.Response().solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
if isinstance(expression, numbers.Integral):
|
|
return expression
|
|
value = 0
|
|
to_process = [(expression, 1)]
|
|
while to_process:
|
|
expr, coef = to_process.pop()
|
|
if isinstance(expr, _ProductCst):
|
|
to_process.append((expr.Expression(),
|
|
coef * expr.Coefficient()))
|
|
elif isinstance(expr, _SumArray):
|
|
for e in expr.Array():
|
|
to_process.append((e, coef))
|
|
value += expr.Constant() * coef
|
|
elif isinstance(expr, IntVar):
|
|
value += coef * self.SolutionIntegerValue(expr.Index())
|
|
elif isinstance(expr, _NotBooleanVariable):
|
|
value += coef * (1 - self.SolutionIntegerValue(expr.Not().Index()))
|
|
return value
|
|
|
|
|
|
class ObjectiveSolutionPrinter(CpSolverSolutionCallback):
|
|
"""Print intermediate solutions objective and time."""
|
|
|
|
def __init__(self):
|
|
CpSolverSolutionCallback.__init__(self)
|
|
self.__solution_count = 0
|
|
self.__start_time = time.time()
|
|
|
|
def on_solution_callback(self):
|
|
"""Called on each new solution."""
|
|
current_time = time.time()
|
|
objective = self.ObjectiveValue()
|
|
best_bound = self.BestObjectiveBound()
|
|
obj_lb = min(objective, best_bound)
|
|
obj_ub = max(objective, best_bound)
|
|
print('Solution %i, time = %f s, objective = [%i, %i]' %
|
|
(self.__solution_count, current_time - self.__start_time, obj_lb,
|
|
obj_ub))
|
|
self.__solution_count += 1
|