1177 lines
39 KiB
Python
1177 lines
39 KiB
Python
# Copyright 2010-2017 Google
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Propose a natural linear API on top of cp_model_pb2 python proto.
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This file implements a easy to use API on top of the cp_model_pb2 API
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defined in ../ .
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"""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import collections
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import numbers
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from six import iteritems
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from ortools.sat import cp_model_pb2
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from ortools.sat import sat_parameters_pb2
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from ortools.sat import pywrapsat
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# The classes below allow linear expressions to be expressed naturally with the
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# usual arithmetic operators +-*/ and with constant numbers, which makes the
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# python API very intuitive. See cp_model_test.py for examples.
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INT_MIN = -9223372036854775808 # hardcoded to be platform independent.
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INT_MAX = 9223372036854775807
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INT32_MIN = -2147483648
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INT32_MAX = 2147483647
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# Cp Solver status (exported to avoid importing cp_model_cp2).
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UNKNOWN = cp_model_pb2.UNKNOWN
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MODEL_INVALID = cp_model_pb2.MODEL_INVALID
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MODEL_SAT = cp_model_pb2.MODEL_SAT
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MODEL_UNSAT = cp_model_pb2.MODEL_UNSAT
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OPTIMAL = cp_model_pb2.OPTIMAL
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# Variable selection strategy
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CHOOSE_FIRST = cp_model_pb2.DecisionStrategyProto.CHOOSE_FIRST
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CHOOSE_LOWEST_MIN = cp_model_pb2.DecisionStrategyProto.CHOOSE_LOWEST_MIN
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CHOOSE_HIGHEST_MAX = cp_model_pb2.DecisionStrategyProto.CHOOSE_HIGHEST_MAX
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CHOOSE_MIN_DOMAIN_SIZE = (
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cp_model_pb2.DecisionStrategyProto.CHOOSE_MIN_DOMAIN_SIZE)
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CHOOSE_MAX_DOMAIN_SIZE = (
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cp_model_pb2.DecisionStrategyProto.CHOOSE_MAX_DOMAIN_SIZE)
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# Domain reduction strategy
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SELECT_MIN_VALUE = cp_model_pb2.DecisionStrategyProto.SELECT_MIN_VALUE
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SELECT_MAX_VALUE = cp_model_pb2.DecisionStrategyProto.SELECT_MAX_VALUE
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SELECT_LOWER_HALF = cp_model_pb2.DecisionStrategyProto.SELECT_LOWER_HALF
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SELECT_UPPER_HALF = cp_model_pb2.DecisionStrategyProto.SELECT_UPPER_HALF
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def AssertIsInt64(x):
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"""Asserts that x is integer and x is in [min_int_64, max_int_64]."""
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if not isinstance(x, numbers.Integral):
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raise TypeError('Not an integer: %s' % x)
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if x < INT_MIN or x > INT_MAX:
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raise OverflowError('Does not fit in an int64: %s' % x)
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def AssertIsInt32(x):
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"""Asserts that x is integer and x is in [min_int_32, max_int_32]."""
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if not isinstance(x, numbers.Integral):
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raise TypeError('Not an integer: %s' % x)
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if x < INT32_MIN or x > INT32_MAX:
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raise OverflowError('Does not fit in an int32: %s' % x)
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def AssertIsBoolean(x):
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"""Asserts that x is 0 or 1."""
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if not isinstance(x, numbers.Integral) or x < 0 or x > 1:
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raise TypeError('Not an boolean: %s' % x)
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def CapInt64(v):
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if v > INT_MAX:
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return INT_MAX
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if v < INT_MIN:
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return INT_MIN
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return v
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def CapSub(x, y):
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"""Saturated arithmetics. Returns x - y truncated to the int64 range."""
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if not isinstance(x, numbers.Integral):
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raise TypeError('Not integral: ' + str(x))
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if not isinstance(y, numbers.Integral):
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raise TypeError('Not integral: ' + str(y))
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AssertIsInt64(x)
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AssertIsInt64(y)
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if y == 0:
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return x
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if x == y:
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if x == INT_MAX or x == INT_MIN:
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raise OverflowError(
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'Integer NaN: subtracting INT_MAX or INT_MIN to itself')
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return 0
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if x == INT_MAX or x == INT_MIN:
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return x
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if y == INT_MAX:
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return INT_MIN
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if y == INT_MIN:
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return INT_MAX
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return CapInt64(x - y)
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def DisplayBounds(bounds):
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"""Displays a flattened list of intervals."""
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out = ''
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for i in range(0, len(bounds), 2):
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if i != 0:
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out += ', '
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if bounds[i] == bounds[i + 1]:
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out += str(bounds[i])
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else:
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out += str(bounds[i]) + '..' + str(bounds[i + 1])
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return out
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def ShortName(model, i):
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"""Returns a short name of an integer variable, or its negation."""
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if i < 0:
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return 'Not(%s)' % ShortName(model, -i - 1)
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v = model.variables[i]
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if v.name:
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return v.name
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elif len(v.domain) == 2 and v.domain[0] == v.domain[1]:
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return str(v.domain[0])
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else:
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return '[%s]' % DisplayBounds(v.domain)
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class IntegerExpression(object):
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"""Holds an integer expression."""
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def GetVarValueMap(self):
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"""Scan the expression, and return a list of (var_coef_map, constant)."""
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coeffs = collections.defaultdict(int)
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constant = 0
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to_process = [(self, 1)]
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while to_process: # Flatten to avoid recursion.
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expr, coef = to_process.pop()
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if isinstance(expr, _ProductCst):
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to_process.append((expr.Expression(), coef * expr.Coefficient()))
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elif isinstance(expr, _SumArray):
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for e in expr.Array():
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to_process.append((e, coef))
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constant += expr.Constant() * coef
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elif isinstance(expr, IntVar):
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coeffs[expr] += coef
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elif isinstance(expr, _NotBooleanVariable):
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raise TypeError('Cannot interpret literals in a integer expression.')
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else:
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raise TypeError('Unrecognized integer expression: ' + str(expr))
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return coeffs, constant
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def __hash__(self):
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return object.__hash__(self)
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def __add__(self, expr):
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return _SumArray([self, expr])
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def __radd__(self, arg):
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return _SumArray([self, arg])
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def __sub__(self, expr):
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return _SumArray([self, -expr])
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def __rsub__(self, arg):
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return _SumArray([-self, arg])
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def __mul__(self, arg):
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if isinstance(arg, numbers.Integral):
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if arg == 1:
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return self
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AssertIsInt64(arg)
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return _ProductCst(self, arg)
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elif isinstance(arg, IntegerExpression):
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return _Product(self, arg)
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else:
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raise TypeError('Not an integer expression: ' + str(arg))
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def __rmul__(self, arg):
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AssertIsInt64(arg)
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if arg == 1:
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return self
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return _ProductCst(self, arg)
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def __div__(self, _):
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raise NotImplementedError('IntegerExpression.__div__')
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def __truediv__(self, _):
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raise NotImplementedError('IntegerExpression.__truediv__')
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def __mod__(self, _):
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raise NotImplementedError('IntegerExpression.__mod__')
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def __neg__(self):
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return _ProductCst(self, -1)
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def __eq__(self, arg):
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if isinstance(arg, numbers.Integral):
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AssertIsInt64(arg)
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return BoundIntegerExpression(self, [arg, arg])
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else:
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return BoundIntegerExpression(self - arg, [0, 0])
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def __ge__(self, arg):
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if isinstance(arg, numbers.Integral):
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AssertIsInt64(arg)
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return BoundIntegerExpression(self, [arg, INT_MAX])
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else:
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return BoundIntegerExpression(self - arg, [0, INT_MAX])
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def __le__(self, arg):
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if isinstance(arg, numbers.Integral):
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AssertIsInt64(arg)
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return BoundIntegerExpression(self, [INT_MIN, arg])
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else:
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return BoundIntegerExpression(self - arg, [INT_MIN, 0])
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def __lt__(self, arg):
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if isinstance(arg, numbers.Integral):
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AssertIsInt64(arg)
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if arg == INT_MIN:
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raise ArithmeticError('< INT_MIN is not supported')
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return BoundIntegerExpression(self, [INT_MIN, CapInt64(arg - 1)])
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else:
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return BoundIntegerExpression(self - arg, [INT_MIN, -1])
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def __gt__(self, arg):
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if isinstance(arg, numbers.Integral):
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AssertIsInt64(arg)
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if arg == INT_MAX:
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raise ArithmeticError('> INT_MAX is not supported')
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return BoundIntegerExpression(self, [CapInt64(arg + 1), INT_MAX])
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else:
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return BoundIntegerExpression(self - arg, [1, INT_MAX])
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def __ne__(self, arg):
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if isinstance(arg, numbers.Integral):
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AssertIsInt64(arg)
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if arg == INT_MAX:
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return BoundIntegerExpression(self, [INT_MIN, INT_MAX - 1])
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elif arg == INT_MIN:
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return BoundIntegerExpression(self, [INT_MIN + 1, INT_MAX])
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else:
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return BoundIntegerExpression(
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self, [INT_MIN,
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CapInt64(arg - 1),
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CapInt64(arg + 1), INT_MAX])
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else:
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return BoundIntegerExpression(self - arg, [INT_MIN, -1, 1, INT_MAX])
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class _ProductCst(IntegerExpression):
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"""Represents the product of a IntegerExpression by a constant."""
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def __init__(self, expr, coef):
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AssertIsInt64(coef)
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if isinstance(expr, _ProductCst):
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self.__expr = expr.Expression()
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self.__coef = expr.Coefficient() * coef
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else:
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self.__expr = expr
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self.__coef = coef
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def __str__(self):
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if self.__coef == -1:
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return '-' + str(self.__expr)
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else:
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return '(' + str(self.__coef) + ' * ' + str(self.__expr) + ')'
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def __repr__(self):
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return 'ProductCst(' + repr(self.__expr) + ', ' + repr(self.__coef) + ')'
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def Coefficient(self):
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return self.__coef
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def Expression(self):
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return self.__expr
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class _SumArray(IntegerExpression):
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"""Represents the sum of a list of IntegerExpression and a constant."""
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def __init__(self, array):
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self.__array = []
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self.__constant = 0
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for x in array:
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if isinstance(x, numbers.Integral):
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AssertIsInt64(x)
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self.__constant += x
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elif isinstance(x, IntegerExpression):
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self.__array.append(x)
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else:
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raise TypeError('Not an integer expression: ' + str(x))
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def __str__(self):
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if self.__constant == 0:
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return '({})'.format(' + '.join(map(str, self.__array)))
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else:
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return '({} + {})'.format(' + '.join(map(str, self.__array)),
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self.__constant)
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def __repr__(self):
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return 'SumArray({}, {})'.format(', '.join(map(repr, self.__array)),
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self.__constant)
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def Array(self):
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return self.__array
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def Constant(self):
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return self.__constant
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class IntVar(IntegerExpression):
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"""Represents a IntegerExpression containing only a single variable."""
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def __init__(self, model, bounds, name, is_present_index=None):
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"""See CpModel.NewIntVar and .NewOptionalIntVar below."""
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self.__model = model
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self.__index = len(model.variables)
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self.__var = model.variables.add()
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self.__var.domain.extend(bounds)
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self.__var.name = name
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self.__negation = None
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if is_present_index is not None:
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self.__var.enforcement_literal.append(is_present_index)
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def Index(self):
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return self.__index
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def __str__(self):
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return self.__var.name
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def __repr__(self):
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return '%s(%s)' % (self.__var.name, DisplayBounds(self.__var.domain))
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def Not(self):
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for bound in self.__var.domain:
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if bound < 0 or bound > 1:
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raise TypeError('Cannot call Not on a non boolean variable: %s' % self)
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if not self.__negation:
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self.__negation = _NotBooleanVariable(self)
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return self.__negation
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class _NotBooleanVariable(IntegerExpression):
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"""Negation of a boolean variable."""
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def __init__(self, boolvar):
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self.__boolvar = boolvar
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def Index(self):
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return -self.__boolvar.Index() - 1
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def Not(self):
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return self.__boolvar
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def __str__(self):
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return 'not(%s)' % str(self.__boolvar)
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class _Product(IntegerExpression):
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"""Represents the product of two IntegerExpressions."""
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def __init__(self, left, right):
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self.__left = left
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self.__right = right
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def __str__(self):
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return '(' + str(self.__left) + ' * ' + str(self.__right) + ')'
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def __repr__(self):
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return 'Product(' + repr(self.__left) + ', ' + repr(self.__right) + ')'
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def Left(self):
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return self.__left
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def Right(self):
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return self.__right
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class BoundIntegerExpression(object):
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"""Represents a constraint: IntegerExpression in domain."""
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def __init__(self, expr, bounds):
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self.__expr = expr
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self.__bounds = bounds
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def __str__(self):
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if len(self.__bounds) == 2:
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lb = self.__bounds[0]
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ub = self.__bounds[1]
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if lb > INT_MIN and ub < INT_MAX:
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if lb == ub:
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return str(self.__expr) + ' == ' + str(lb)
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else:
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return str(lb) + ' <= ' + str(self.__expr) + ' <= ' + str(ub)
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elif lb > INT_MIN:
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return str(self.__expr) + ' >= ' + str(lb)
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elif ub < INT_MAX:
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return str(self.__expr) + ' <= ' + str(ub)
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else:
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return 'True (unbounded expr ' + str(self.__expr) + ')'
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else:
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return str(self.__expr) + ' in [' + DisplayBounds(self.__bounds) + ']'
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def Expression(self):
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return self.__expr
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def Bounds(self):
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return self.__bounds
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class Constraint(object):
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"""Base class for constraints."""
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def __init__(self, constraints):
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self.__index = len(constraints)
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self.__constraint = constraints.add()
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def OnlyEnforceIf(self, boolvar):
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self.__constraint.enforcement_literal.append(boolvar.Index())
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def Index(self):
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return self.__index
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def ConstraintProto(self):
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return self.__constraint
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class IntervalVar(object):
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"""Represents a Interval variable."""
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def __init__(self, model, start_index, size_index, end_index,
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is_present_index, name):
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self.__model = model
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self.__index = len(model.constraints)
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self.__ct = self.__model.constraints.add()
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self.__ct.interval.start = start_index
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self.__ct.interval.size = size_index
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self.__ct.interval.end = end_index
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if is_present_index is not None:
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self.__ct.enforcement_literal.append(is_present_index)
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if name:
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self.__ct.name = name
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def Index(self):
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return self.__index
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def __str__(self):
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return self.__ct.name
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def __repr__(self):
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interval = self.__ct.interval
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if self.__ct.enforcement_literal:
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return '%s(start = %s, size = %s, end = %s, is_present = %s)' % (
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self.__ct.name, ShortName(self.__model, interval.start),
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ShortName(self.__model, interval.size),
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ShortName(self.__model, interval.end),
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ShortName(self.__model, self.__ct.enforcement_literal[0]))
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else:
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return '%s(start = %s, size = %s, end = %s)' % (
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self.__ct.name, ShortName(self.__model, interval.start),
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ShortName(self.__model, interval.size),
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ShortName(self.__model, interval.end))
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class CpModel(object):
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"""Wrapper class around the cp_model proto."""
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def __init__(self):
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self.__model = cp_model_pb2.CpModelProto()
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self.__constant_map = {}
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self.__optional_constant_map = {}
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# Integer variable.
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def NewIntVar(self, lb, ub, name):
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"""Creates an integer variable with domain [lb, ub]."""
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return IntVar(self.__model, [lb, ub], name)
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def NewEnumeratedIntVar(self, bounds, name):
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"""Creates an integer variable with an enumerated domain.
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Args:
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bounds: A flattened list of disjoint intervals.
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name: The name of the variable.
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Returns:
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a variable whose domain is union[bounds[2*i]..bounds[2*i + 1]].
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To create a variable with domain [1, 2, 3, 5, 7, 8], pass in the
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array [1, 3, 5, 5, 7, 8].
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"""
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return IntVar(self.__model, bounds, name)
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def NewOptionalIntVar(self, lb, ub, is_present, name):
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"""Creates an optional integer variable."""
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is_present_index = self.GetOrMakeBooleanIndex(is_present)
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return IntVar(self.__model, [lb, ub], name, is_present_index)
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def NewOptionalEnumeratedIntVar(self, bounds, is_present, name):
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"""Creates an optional enumerated integer variable."""
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is_present_index = self.GetOrMakeBooleanIndex(is_present)
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return IntVar(self.__model, bounds, name, is_present_index)
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def NewBoolVar(self, name):
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"""Creates a 0-1 variable with the given name."""
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return IntVar(self.__model, [0, 1], name)
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|
# 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)."""
|
|
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 constraints from a sparse list of arcs that encode the graph.
|
|
|
|
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:
|
|
The constraint proto.
|
|
|
|
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):
|
|
"""Adds AllowedAssignments(variables, [tuples])."""
|
|
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:
|
|
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):
|
|
"""Adds AddForbiddenAssignments(variables, [tuples])."""
|
|
|
|
if not variables:
|
|
raise ValueError('AddForbiddenAssignments expects a non empty variables '
|
|
'array')
|
|
|
|
index = len(self.__model.constraints)
|
|
self.AddAllowedAssignments(variables, tuples)
|
|
self.__model.constraints[index].table.negated = True
|
|
|
|
def AddAutomata(self, transition_variables, starting_state, final_states,
|
|
transition_triples):
|
|
"""Adds an automata constraint.
|
|
|
|
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).
|
|
|
|
|
|
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)."""
|
|
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)."""
|
|
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 AddMapDomain(self, var, bool_var_array, offset=0):
|
|
"""Creates 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 = target.Index()
|
|
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 = target.Index()
|
|
return ct
|
|
|
|
def AddDivisionEquality(self, target, num, denom):
|
|
"""Creates 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 = target.Index()
|
|
return ct
|
|
|
|
def AddModuloEquality(self, target, var, mod):
|
|
"""Creates 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 = target.Index()
|
|
return ct
|
|
|
|
def AddProdEquality(self, target, args):
|
|
"""Creates 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 = target.Index()
|
|
return ct
|
|
|
|
# Scheduling support
|
|
|
|
def NewIntervalVar(self, start, size, end, name):
|
|
start_index = self.GetOrMakeIndex(start)
|
|
size_index = self.GetOrMakeIndex(size)
|
|
end_index = self.GetOrMakeIndex(end)
|
|
self.AssertIntVarIsNotOptional(start_index)
|
|
self.AssertIntVarIsNotOptional(size_index)
|
|
self.AssertIntVarIsNotOptional(end_index)
|
|
return IntervalVar(self.__model, start_index, size_index, end_index, None,
|
|
name)
|
|
|
|
def NewOptionalIntervalVar(self, start, size, end, is_present, name):
|
|
is_present_index = self.GetOrMakeBooleanIndex(is_present)
|
|
start_index = self.GetOrMakeOptionalIndex(start, is_present)
|
|
size_index = self.GetOrMakeIndex(size) # Currently, not optional.
|
|
end_index = self.GetOrMakeOptionalIndex(end, is_present)
|
|
return IntervalVar(self.__model, start_index, size_index, end_index,
|
|
is_present_index, name)
|
|
|
|
def AddNoOverlap(self, interval_vars):
|
|
"""Adds NoOverlap(interval_vars)."""
|
|
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)."""
|
|
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)."""
|
|
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 GetOrMakeOptionalIndex(self, arg, is_present):
|
|
"""Returns the index of an optional variable or constant (seen as a var)."""
|
|
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.GetOrMakeOptionalIndexFromConstant(arg, is_present)
|
|
else:
|
|
raise TypeError('NotSupported: model.GetOrMakeOptionalIndex(%s, %s)' %
|
|
(arg, is_present))
|
|
|
|
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 GetOrMakeOptionalIndexFromConstant(self, value, is_present):
|
|
self.AssertIsBooleanVariable(is_present)
|
|
if (is_present, value) in self.__optional_constant_map:
|
|
return self.__optional_constant_map[(is_present, value)]
|
|
index = len(self.__model.variables)
|
|
var = self.__model.variables.add()
|
|
var.domain.extend([value, value])
|
|
var.enforcement_literal.append(self.GetOrMakeBooleanIndex(is_present))
|
|
self.__optional_constant_map[(is_present, 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 AssertIntVarIsNotOptional(self, var_index):
|
|
var = self.VarIndexToVarProto(var_index)
|
|
if var.enforcement_literal:
|
|
raise TypeError('Variable %s should not be marked as optional' %
|
|
ShortName(self.__model, var_index))
|
|
|
|
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.PySolutionCallback):
|
|
"""Nicer solution callback that uses the CpSolver class."""
|
|
|
|
def __init__(self):
|
|
self.__current_solution = None
|
|
|
|
def Wrap(self, solution_proto):
|
|
self.__current_solution = solution_proto
|
|
self.NewSolution()
|
|
|
|
def BooleanValue(self, literal):
|
|
if not self.__current_solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateBooleanExpression(literal, self.__current_solution)
|
|
|
|
def Value(self, expression):
|
|
"""Returns the value of an integer expression."""
|
|
if not self.__current_solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateIntegerExpression(expression, self.__current_solution)
|
|
|
|
def ObjectiveValue(self):
|
|
"""Returns the value of the objective."""
|
|
return self.__current_solution.objective_value
|
|
|
|
def NumBooleans(self):
|
|
return self.__current_solution.num_booleans
|
|
|
|
def NumConflicts(self):
|
|
return self.__current_solution.num_conflicts
|
|
|
|
def NumBranches(self):
|
|
return self.__current_solution.num_branches
|
|
|
|
def WallTime(self):
|
|
return self.__current_solution.wall_time
|
|
|
|
def UserTime(self):
|
|
return self.__current_solution.user_time
|
|
|
|
def NewSolution(self):
|
|
pass
|
|
|
|
|
|
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.SolveWithParametersAndSolutionObserver(
|
|
model.ModelProto(), self.parameters, callback))
|
|
return self.__solution.status
|
|
|
|
def SearchForAllSolutions(self, model, callback):
|
|
"""Search for all solutions of a satisfiability problem."""
|
|
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.SolveWithParametersAndSolutionObserver(
|
|
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."""
|
|
if not self.__solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateIntegerExpression(expression, self.__solution)
|
|
|
|
def BooleanValue(self, literal):
|
|
if not self.__solution:
|
|
raise RuntimeError('Solve() has not be called.')
|
|
return EvaluateBooleanExpression(literal, self.__solution)
|
|
|
|
def ObjectiveValue(self):
|
|
"""Returns the objective value found after solve."""
|
|
return self.__solution.objective_value
|
|
|
|
def StatusName(self, status):
|
|
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
|