#!/usr/bin/env python
#-*- coding:utf-8 -*-
##
## globalconstraints.py
##
"""
Global constraints conveniently express non-primitive constraints.
Using global constraints
------------------------
Solvers can have specialised implementations for global constraints. CPMpy has GlobalConstraint
expressions so that they can be passed to the solver as is when supported.
If a solver does not support a global constraint (see solvers/) then it will be automatically
decomposed by calling its `.decompose()` function.
The `.decompose()` function returns two arguments:
- a list of simpler constraints replacing the global constraint
- if the decomposition introduces *new variables*, then the second argument has to be a list
of constraints that (totally) define those new variables
As a user you **should almost never subclass GlobalConstraint()** unless you know of a solver that
supports that specific global constraint, and that you will update its solver interface to support it.
For all other use cases, it sufficies to write your own helper function that immediately returns the
decomposition, e.g.:
.. code-block:: python
def alldifferent_except0(args):
return [ ((var1!= 0) & (var2 != 0)).implies(var1 != var2) for var1, var2 in all_pairs(args)]
Numeric global constraints
--------------------------
CPMpy also implements __Numeric Global Constraints__. For these, the CPMpy GlobalConstraint does not
exactly match what is implemented in the solver, but for good reason!!
For example solvers may implement the global constraint `Minimum(iv1, iv2, iv3) == iv4` through an API
call `addMinimumEquals([iv1,iv2,iv3], iv4)`.
However, CPMpy also wishes to support the expressions `Minimum(iv1, iv2, iv3) > iv4` as well as
`iv4 + Minimum(iv1, iv2, iv3)`.
Hence, the CPMpy global constraint only captures the `Minimum(iv1, iv2, iv3)` part, whose return type
is numeric and can be used in any other CPMpy expression. Only at the time of transforming the CPMpy
model to the solver API, will the expressions be decomposed and auxiliary variables introduced as needed
such that the solver only receives `Minimum(iv1, iv2, iv3) == ivX` expressions.
This is the burden of the CPMpy framework, not of the user who wants to express a problem formulation.
Subclassing GlobalConstraint
----------------------------
If you do wish to add a GlobalConstraint, because it is supported by solvers or because you will do
advanced analysis and rewriting on it, then preferably define it with a standard decomposition, e.g.:
.. code-block:: python
class my_global(GlobalConstraint):
def __init__(self, args):
super().__init__("my_global", args)
def decompose(self):
return [self.args[0] != self.args[1]] # your decomposition
If it is a __numeric global constraint__ meaning that its return type is numeric (see `Minimum` and `Element`)
then set `is_bool=False` in the super() constructor and preferably implement `.value()` accordingly.
Alternative decompositions
--------------------------
For advanced use cases where you want to use another decomposition than the standard decomposition
of a GlobalConstraint expression, you can overwrite the 'decompose' function of the class, e.g.:
.. code-block:: python
def my_circuit_decomp(self):
return [self.args[0] == 1], [] # does not actually enforce circuit
circuit.decompose = my_circuit_decomp # attach it, no brackets!
vars = intvar(1,9, shape=10)
constr = circuit(vars)
Model(constr).solve()
The above will use 'my_circuit_decomp', if the solver does not
natively support 'circuit'.
===============
List of classes
===============
.. autosummary::
:nosignatures:
AllDifferent
AllDifferentExcept0
AllEqual
Circuit
Inverse
Table
Xor
Cumulative
GlobalCardinalityCount
"""
import copy
import warnings # for deprecation warning
import numpy as np
from ..exceptions import CPMpyException, IncompleteFunctionError, TypeError
from .core import Expression, Operator, Comparison
from .variables import boolvar, intvar, cpm_array, _NumVarImpl, _IntVarImpl
from .utils import flatlist, all_pairs, argval, is_num, eval_comparison, is_any_list, is_boolexpr, get_bounds
from .globalfunctions import * # XXX make this file backwards compatible
# Base class GlobalConstraint
[docs]class GlobalConstraint(Expression):
"""
Abstract superclass of GlobalConstraints
Like all expressions it has a `.name` and `.args` property.
Overwrites the `.is_bool()` method.
"""
[docs] def is_bool(self):
""" is it a Boolean (return type) Operator?
"""
return True
[docs] def decompose(self):
"""
Returns a decomposition into smaller constraints.
The decomposition might create auxiliary variables
and use other global constraints as long as
it does not create a circular dependency.
To ensure equivalence of decomposition, we split into contraining and defining constraints.
Defining constraints (totally) define new auxiliary variables needed for the decomposition,
they can always be enforced top-level.
"""
raise NotImplementedError("Decomposition for", self, "not available")
[docs] def get_bounds(self):
"""
Returns the bounds of a Boolean global constraint.
Numerical global constraints should reimplement this.
"""
return 0, 1
# Global Constraints (with Boolean return type)
[docs]def alldifferent(args):
warnings.warn("Deprecated, use AllDifferent(v1,v2,...,vn) instead, will be removed in stable version", DeprecationWarning)
return AllDifferent(*args) # unfold list as individual arguments
[docs]class AllDifferent(GlobalConstraint):
"""All arguments have a different (distinct) value
"""
def __init__(self, *args):
super().__init__("alldifferent", flatlist(args))
[docs] def decompose(self):
"""Returns the decomposition
"""
return [var1 != var2 for var1, var2 in all_pairs(self.args)], []
[docs] def value(self):
return len(set(a.value() for a in self.args)) == len(self.args)
[docs]class AllDifferentExcept0(GlobalConstraint):
"""
All nonzero arguments have a distinct value
"""
def __init__(self, *args):
super().__init__("alldifferent_except0", flatlist(args))
[docs] def decompose(self):
# equivalent to (var1 == 0) | (var2 == 0) | (var1 != var2)
return [(var1 == var2).implies(var1 == 0) for var1, var2 in all_pairs(self.args)], []
[docs] def value(self):
vals = [a.value() for a in self.args if a.value() != 0]
return len(set(vals)) == len(vals)
[docs]def allequal(args):
warnings.warn("Deprecated, use AllEqual(v1,v2,...,vn) instead, will be removed in stable version", DeprecationWarning)
return AllEqual(*args) # unfold list as individual arguments
[docs]class AllEqual(GlobalConstraint):
"""All arguments have the same value
"""
def __init__(self, *args):
super().__init__("allequal", flatlist(args))
[docs] def decompose(self):
"""Returns the decomposition
"""
# arg0 == arg1, arg1 == arg2, arg2 == arg3... no need to post n^2 equalities
return [var1 == var2 for var1, var2 in zip(self.args[:-1], self.args[1:])], []
[docs] def value(self):
return len(set(a.value() for a in self.args)) == 1
[docs]def circuit(args):
warnings.warn("Deprecated, use Circuit(v1,v2,...,vn) instead, will be removed in stable version", DeprecationWarning)
return Circuit(*args) # unfold list as individual arguments
[docs]class Circuit(GlobalConstraint):
"""The sequence of variables form a circuit, where x[i] = j means that j is the successor of i.
"""
def __init__(self, *args):
flatargs = flatlist(args)
if any(is_boolexpr(arg) for arg in flatargs):
raise TypeError("Circuit global constraint only takes arithmetic arguments: {}".format(flatargs))
super().__init__("circuit", flatargs)
if len(flatargs) < 2:
raise CPMpyException('Circuit constraint must be given a minimum of 2 variables')
[docs] def decompose(self):
"""
Decomposition for Circuit
Not sure where we got it from,
MiniZinc has slightly different one:
https://github.com/MiniZinc/libminizinc/blob/master/share/minizinc/std/fzn_circuit.mzn
"""
succ = cpm_array(self.args)
n = len(succ)
order = intvar(0,n-1, shape=n)
constraining = []
constraining += [AllDifferent(succ)] # different successors
constraining += [AllDifferent(order)] # different orders
constraining += [order[n-1] == 0] # symmetry breaking, last one is '0'
defining = [order[0] == succ[0]]
defining += [order[i] == succ[order[i-1]] for i in range(1,n)] # first one is successor of '0', ith one is successor of i-1
return constraining, defining
[docs] def value(self):
pathlen = 0
idx = 0
visited = set()
arr = [argval(a) for a in self.args]
while idx not in visited:
if idx is None:
return False
if not (0 <= idx < len(arr)):
break
visited.add(idx)
pathlen += 1
idx = arr[idx]
return pathlen == len(self.args) and idx == 0
[docs]class Inverse(GlobalConstraint):
"""
Inverse (aka channeling / assignment) constraint. 'fwd' and
'rev' represent inverse functions; that is,
fwd[i] == x <==> rev[x] == i
"""
def __init__(self, fwd, rev):
flatargs = flatlist([fwd,rev])
if any(is_boolexpr(arg) for arg in flatargs):
raise TypeError("Only integer arguments allowed for global constraint Inverse: {}".format(flatargs))
assert len(fwd) == len(rev)
super().__init__("inverse", [fwd, rev])
[docs] def decompose(self):
from .python_builtins import all
fwd, rev = self.args
rev = cpm_array(rev)
return [all(rev[x] == i for i, x in enumerate(fwd))], []
[docs] def value(self):
fwd = [argval(a) for a in self.args[0]]
rev = [argval(a) for a in self.args[1]]
return all(rev[x] == i for i, x in enumerate(fwd))
[docs]class Table(GlobalConstraint):
"""The values of the variables in 'array' correspond to a row in 'table'
"""
def __init__(self, array, table):
array = flatlist(array)
if not all(isinstance(x, Expression) for x in array):
raise TypeError("the first argument of a Table constraint should only contain variables/expressions")
super().__init__("table", [array, table])
[docs] def decompose(self):
from .python_builtins import any, all
arr, tab = self.args
return [any(all(ai == ri for ai, ri in zip(arr, row)) for row in tab)], []
[docs] def value(self):
arr, tab = self.args
arrval = [argval(a) for a in arr]
return arrval in tab
# syntax of the form 'if b then x == 9 else x == 0' is not supported (no override possible)
# same semantic as CPLEX IfThenElse constraint
# https://www.ibm.com/docs/en/icos/12.9.0?topic=methods-ifthenelse-method
[docs]class IfThenElse(GlobalConstraint):
def __init__(self, condition, if_true, if_false):
if not is_boolexpr(condition) or not is_boolexpr(if_true) or not is_boolexpr(if_false):
raise TypeError("only boolean expression allowed in IfThenElse")
super().__init__("ite", [condition, if_true, if_false])
[docs] def value(self):
condition, if_true, if_false = self.args
if argval(condition):
return argval(if_true)
else:
return argval(if_false)
[docs] def decompose(self):
condition, if_true, if_false = self.args
return [condition.implies(if_true), (~condition).implies(if_false)], []
def __repr__(self):
condition, if_true, if_false = self.args
return "If {} Then {} Else {}".format(condition, if_true, if_false)
[docs]class InDomain(GlobalConstraint):
"""
The "InDomain" constraint, defining non-interval domains for an expression
"""
def __init__(self, expr, arr):
assert not (is_boolexpr(expr) or any(is_boolexpr(a) for a in arr)), \
"The expressions in the InDomain constraint should not be boolean"
super().__init__("InDomain", [expr, arr])
[docs] def decompose(self):
"""
Returns two lists of constraints:
1) constraints representing the comparison
2) constraints that (totally) define new auxiliary variables needed in the decomposition,
they should be enforced toplevel.
"""
from .python_builtins import any
expr, arr = self.args
lb, ub = expr.get_bounds()
defining = []
#if expr is not a var
if not isinstance(expr,_IntVarImpl):
aux = intvar(lb, ub)
defining.append(aux == expr)
expr = aux
expressions = any(isinstance(a, Expression) for a in arr)
if expressions:
return [any(expr == a for a in arr)], defining
else:
return [expr != val for val in range(lb, ub + 1) if val not in arr], defining
[docs] def value(self):
return argval(self.args[0]) in argval(self.args[1])
def __repr__(self):
return "{} in {}".format(self.args[0], self.args[1])
[docs]class Xor(GlobalConstraint):
"""
The 'xor' exclusive-or constraint
"""
def __init__(self, arg_list):
flatargs = flatlist(arg_list)
if not (all(is_boolexpr(arg) for arg in flatargs)):
raise TypeError("Only Boolean arguments allowed in Xor global constraint: {}".format(flatargs))
# convention for commutative binary operators:
# swap if right is constant and left is not
if len(arg_list) == 2 and is_num(arg_list[1]):
arg_list[0], arg_list[1] = arg_list[1], arg_list[0]
flatargs = arg_list
super().__init__("xor", flatargs)
[docs] def decompose(self):
# there are multiple decompositions possible, Recursively using sum allows it to be efficient for all solvers.
decomp = [sum(self.args[:2]) == 1]
if len(self.args) > 2:
decomp = Xor([decomp,self.args[2:]]).decompose()[0]
return decomp, []
[docs] def value(self):
return sum(argval(a) for a in self.args) % 2 == 1
def __repr__(self):
if len(self.args) == 2:
return "{} xor {}".format(*self.args)
return "xor({})".format(self.args)
[docs]class Cumulative(GlobalConstraint):
"""
Global cumulative constraint. Used for resource aware scheduling.
Ensures no overlap between tasks and never exceeding the capacity of the resource
Supports both varying demand across tasks or equal demand for all jobs
"""
def __init__(self, start, duration, end, demand, capacity):
assert is_any_list(start), "start should be a list"
assert is_any_list(duration), "duration should be a list"
assert is_any_list(end), "end should be a list"
start = flatlist(start)
duration = flatlist(duration)
end = flatlist(end)
assert len(start) == len(duration) == len(end), "Start, duration and end should have equal length"
n_jobs = len(start)
for lb in get_bounds(duration)[0]:
if lb < 0:
raise TypeError("Durations should be non-negative")
if is_any_list(demand):
demand = flatlist(demand)
assert len(demand) == n_jobs, "Demand should be supplied for each task or be single constant"
else: # constant demand
demand = [demand] * n_jobs
super(Cumulative, self).__init__("cumulative", [start, duration, end, demand, capacity])
[docs] def decompose(self):
"""
Time-resource decomposition from:
Schutt, Andreas, et al. "Why cumulative decomposition is not as bad as it sounds."
International Conference on Principles and Practice of Constraint Programming. Springer, Berlin, Heidelberg, 2009.
"""
from ..expressions.python_builtins import sum
arr_args = (cpm_array(arg) if is_any_list(arg) else arg for arg in self.args)
start, duration, end, demand, capacity = arr_args
cons = []
# set duration of tasks
for t in range(len(start)):
cons += [start[t] + duration[t] == end[t]]
# demand doesn't exceed capacity
lb, ub = min(s.lb for s in start), max(s.ub for s in end)
for t in range(lb,ub+1):
demand_at_t = 0
for job in range(len(start)):
if is_num(demand):
demand_at_t += demand * ((start[job] <= t) & (t < end[job]))
else:
demand_at_t += demand[job] * ((start[job] <= t) & (t < end[job]))
cons += [demand_at_t <= capacity]
return cons, []
[docs] def value(self):
argvals = [np.array([argval(a) for a in arg]) if is_any_list(arg)
else argval(arg) for arg in self.args]
if any(a is None for a in argvals):
return None
# start, dur, end are np arrays
start, dur, end, demand, capacity = argvals
# start and end seperated by duration
if not (start + dur == end).all():
return False
# demand doesn't exceed capacity
lb, ub = min(start), max(end)
for t in range(lb, ub+1):
if capacity < sum(demand * ((start <= t) & (t < end))):
return False
return True
[docs]class GlobalCardinalityCount(GlobalConstraint):
"""
GlobalCardinalityCount(vars,vals,occ): The number of occurrences of each value vals[i] in the list of variables vars
must be equal to occ[i].
"""
def __init__(self, vars, vals, occ):
flatargs = flatlist([vars, vals, occ])
if any(is_boolexpr(arg) for arg in flatargs):
raise TypeError("Only numerical arguments allowed for gcc global constraint: {}".format(flatargs))
super().__init__("gcc", [vars,vals,occ])
[docs] def decompose(self):
from .globalfunctions import Count
vars, vals, occ = self.args
return [Count(vars, i) == v for i, v in zip(vals, occ)], []
[docs] def value(self):
from .python_builtins import all
decomposed, _ = self.decompose()
return all(decomposed).value()
[docs]class DirectConstraint(Expression):
"""
A DirectConstraint will directly call a function of the underlying solver when added to a CPMpy solver
It can not be reified, it is not flattened, it can not contain other CPMpy expressions than variables.
When added to a CPMpy solver, it will literally just directly call a function on the underlying solver,
replacing CPMpy variables by solver variables along the way.
See the documentation of the solver (constructor) for details on how that solver handles them.
If you want/need to use what the solver returns (e.g. an identifier for use in other constraints),
then use `directvar()` instead, or access the solver object from the solver interface directly.
"""
def __init__(self, name, arguments, novar=None):
"""
name: name of the solver function that you wish to call
arguments: tuple of arguments to pass to the solver function with name 'name'
novar: list of indices (offset 0) of arguments in `arguments` that contain no variables,
that can be passed 'as is' without scanning for variables
"""
if not isinstance(arguments, tuple):
arguments = (arguments,) # force tuple
super().__init__(name, arguments)
self.novar = novar
[docs] def is_bool(self):
""" is it a Boolean (return type) Operator?
"""
return True
[docs] def callSolver(self, CPMpy_solver, Native_solver):
"""
Call the `directname`() function of the native solver,
with stored arguments replacing CPMpy variables with solver variables as needed.
SolverInterfaces will call this function when this constraint is added.
:param CPMpy_solver: a CPM_solver object, that has a `solver_vars()` function
:param Native_solver: the python interface to some specific solver
:return: the response of the solver when calling the function
"""
# get the solver function, will raise an AttributeError if it does not exist
solver_function = getattr(Native_solver, self.name)
solver_args = copy.copy(self.args)
for i in range(len(solver_args)):
if self.novar is None or i not in self.novar:
# it may contain variables, replace
solver_args[i] = CPMpy_solver.solver_vars(solver_args[i])
# len(native_args) should match nr of arguments of `native_function`
return solver_function(*solver_args)