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ortools-clone/ortools/sat/python/cp_model.py
2018-09-01 08:48:43 +02:00

1422 lines
48 KiB
Python

# Copyright 2010-2017 Google
# 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
from six import iteritems
from ortools.sat import cp_model_pb2
from ortools.sat import sat_parameters_pb2
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 cp_model_test.py for examples.
INT_MIN = -9223372036854775808 # hardcoded to be platform independent.
INT_MAX = 9223372036854775807
INT32_MIN = -2147483648
INT32_MAX = 2147483647
# 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 AssertIsInt64(x):
"""Asserts that x is integer and x is in [min_int_64, max_int_64]."""
if not isinstance(x, numbers.Integral):
raise TypeError('Not an integer: %s' % x)
if x < INT_MIN or x > INT_MAX:
raise OverflowError('Does not fit in an int64: %s' % x)
def AssertIsInt32(x):
"""Asserts that x is integer and x is in [min_int_32, max_int_32]."""
if not isinstance(x, numbers.Integral):
raise TypeError('Not an integer: %s' % x)
if x < INT32_MIN or x > INT32_MAX:
raise OverflowError('Does not fit in an int32: %s' % x)
def AssertIsBoolean(x):
"""Asserts that x is 0 or 1."""
if not isinstance(x, numbers.Integral) or x < 0 or x > 1:
raise TypeError('Not an boolean: %s' % x)
def CapInt64(v):
"""Restrict v within [INT_MIN..INT_MAX] range."""
if v > INT_MAX:
return INT_MAX
if v < INT_MIN:
return INT_MIN
return v
def CapSub(x, y):
"""Saturated arithmetics. Returns x - y truncated to the int64 range."""
if not isinstance(x, numbers.Integral):
raise TypeError('Not integral: ' + str(x))
if not isinstance(y, numbers.Integral):
raise TypeError('Not integral: ' + str(y))
AssertIsInt64(x)
AssertIsInt64(y)
if y == 0:
return x
if x == y:
if x == INT_MAX or x == INT_MIN:
raise OverflowError(
'Integer NaN: subtracting INT_MAX or INT_MIN to itself')
return 0
if x == INT_MAX or x == INT_MIN:
return x
if y == INT_MAX:
return INT_MIN
if y == INT_MIN:
return INT_MAX
return CapInt64(x - y)
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 IntegerExpression(object):
"""Holds an integer expression."""
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):
raise TypeError('Cannot interpret literals in a integer expression.')
else:
raise TypeError('Unrecognized integer 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
AssertIsInt64(arg)
return _ProductCst(self, arg)
elif isinstance(arg, IntegerExpression):
return _Product(self, arg)
else:
raise TypeError('Not an integer expression: ' + str(arg))
def __rmul__(self, arg):
AssertIsInt64(arg)
if arg == 1:
return self
return _ProductCst(self, arg)
def __div__(self, _):
raise NotImplementedError('IntegerExpression.__div__')
def __truediv__(self, _):
raise NotImplementedError('IntegerExpression.__truediv__')
def __mod__(self, _):
raise NotImplementedError('IntegerExpression.__mod__')
def __neg__(self):
return _ProductCst(self, -1)
def __eq__(self, arg):
if arg is None:
return False
if isinstance(arg, numbers.Integral):
AssertIsInt64(arg)
return BoundIntegerExpression(self, [arg, arg])
else:
return BoundIntegerExpression(self - arg, [0, 0])
def __ge__(self, arg):
if isinstance(arg, numbers.Integral):
AssertIsInt64(arg)
return BoundIntegerExpression(self, [arg, INT_MAX])
else:
return BoundIntegerExpression(self - arg, [0, INT_MAX])
def __le__(self, arg):
if isinstance(arg, numbers.Integral):
AssertIsInt64(arg)
return BoundIntegerExpression(self, [INT_MIN, arg])
else:
return BoundIntegerExpression(self - arg, [INT_MIN, 0])
def __lt__(self, arg):
if isinstance(arg, numbers.Integral):
AssertIsInt64(arg)
if arg == INT_MIN:
raise ArithmeticError('< INT_MIN is not supported')
return BoundIntegerExpression(self, [INT_MIN, CapInt64(arg - 1)])
else:
return BoundIntegerExpression(self - arg, [INT_MIN, -1])
def __gt__(self, arg):
if isinstance(arg, numbers.Integral):
AssertIsInt64(arg)
if arg == INT_MAX:
raise ArithmeticError('> INT_MAX is not supported')
return BoundIntegerExpression(self, [CapInt64(arg + 1), INT_MAX])
else:
return BoundIntegerExpression(self - arg, [1, INT_MAX])
def __ne__(self, arg):
if arg is None:
return True
if isinstance(arg, numbers.Integral):
AssertIsInt64(arg)
if arg == INT_MAX:
return BoundIntegerExpression(self, [INT_MIN, INT_MAX - 1])
elif arg == INT_MIN:
return BoundIntegerExpression(self, [INT_MIN + 1, INT_MAX])
else:
return BoundIntegerExpression(
self, [INT_MIN,
CapInt64(arg - 1),
CapInt64(arg + 1), INT_MAX])
else:
return BoundIntegerExpression(self - arg, [INT_MIN, -1, 1, INT_MAX])
class _ProductCst(IntegerExpression):
"""Represents the product of a IntegerExpression by a constant."""
def __init__(self, expr, coef):
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(IntegerExpression):
"""Represents the sum of a list of IntegerExpression and a constant."""
def __init__(self, array):
self.__array = []
self.__constant = 0
for x in array:
if isinstance(x, numbers.Integral):
AssertIsInt64(x)
self.__constant += x
elif isinstance(x, IntegerExpression):
self.__array.append(x)
else:
raise TypeError('Not an integer 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(IntegerExpression):
"""Represents a IntegerExpression containing only a single variable."""
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):
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(IntegerExpression):
"""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 _Product(IntegerExpression):
"""Represents the product of two IntegerExpressions."""
def __init__(self, left, right):
self.__left = left
self.__right = right
def __str__(self):
return '(' + str(self.__left) + ' * ' + str(self.__right) + ')'
def __repr__(self):
return 'Product(' + repr(self.__left) + ', ' + repr(self.__right) + ')'
def Left(self):
return self.__left
def Right(self):
return self.__right
class BoundIntegerExpression(object):
"""Represents a constraint: IntegerExpression in domain."""
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."""
def __init__(self, constraints):
self.__index = len(constraints)
self.__constraint = constraints.add()
def OnlyEnforceIf(self, boolvar):
if isinstance(boolvar, numbers.Integral) and boolvar == 1:
# Always true. Do nothing.
pass
else:
self.__constraint.enforcement_literal.append(boolvar.Index())
def Index(self):
return self.__index
def ConstraintProto(self):
return self.__constraint
class IntervalVar(object):
"""Represents a Interval variable."""
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."""
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))
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))
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 BoundIntegerExpression to the model."""
if isinstance(ct, BoundIntegerExpression):
coeffs_map, constant = ct.Expression().GetVarValueMap()
bounds = [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:
AssertIsInt32(arc[0])
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:
AssertIsInt64(v)
model_ct.table.values.extend(t)
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)
self.AddAllowedAssignments(variables, tuples_list)
self.__model.constraints[index].table.negated = True
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 automata 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 automata.
starting_state: The initial state of the automata.
final_states: A non empty list of admissible final states.
transition_triples: A list of transition for the automata, 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('AddAutomata expects a non empty transition_variables '
'array')
if not final_states:
raise ValueError('AddAutomata expects some final states')
if not transition_triples:
raise ValueError('AddAutomata expects some transtion triples')
ct = Constraint(self.__model.constraints)
model_ct = self.__model.constraints[ct.Index()]
model_ct.automata.vars.extend(
[self.GetOrMakeIndex(x) for x in transition_variables])
AssertIsInt64(starting_state)
model_ct.automata.starting_state = starting_state
for v in final_states:
AssertIsInt64(v)
model_ct.automata.final_states.append(v)
for t in transition_triples:
if len(t) != 3:
raise TypeError('Tuple ' + str(t) + ' has the wrong arity (!= 3)')
AssertIsInt64(t[0])
AssertIsInt64(t[1])
AssertIsInt64(t[2])
model_ct.automata.transition_tail.append(t[0])
model_ct.automata.transition_label.append(t[1])
model_ct.automata.transition_head.append(t[2])
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 the 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(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 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):
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):
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, IntegerExpression):
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 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 EvaluateIntegerExpression(expression, solution):
"""Evaluate an integer 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):
raise TypeError('Cannot interpret literals in a integer expression.')
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 CpSolverSolutionCallback(pywrapsat.SolutionCallback):
"""Nicer solution callback that uses the CpSolver class."""
def __init__(self):
pywrapsat.SolutionCallback.__init__(self)
def BooleanValue(self, lit):
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.' % literal)
def Value(self, expression):
"""Returns the value of an integer expression."""
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):
raise TypeError('Cannot interpret literals in a integer expression.')
return value
class CpSolver(object):
"""Main solver class."""
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 SolveWithSolutionObserver(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 integer expression after solve."""
if not self.__solution:
raise RuntimeError('Solve() has not be called.')
return EvaluateIntegerExpression(expression, self.__solution)
def BooleanValue(self, literal):
"""Returns the boolean value of an integer expression 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 StatusName(self, status):
"""Returns the name of the status returned by Solve()."""
return cp_model_pb2.CpSolverStatus.Name(status)
def NumBooleans(self):
return self.__solution.num_booleans
def NumConflicts(self):
return self.__solution.num_conflicts
def NumBranches(self):
return self.__solution.num_branches
def WallTime(self):
return self.__solution.wall_time
def UserTime(self):
return self.__solution.user_time