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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 2018-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""
Maximization with a boolean variable and constraints.
Maximize:
sum_{i=1}^{n-1} sum_{j=i+1}^{n} w_{ij} x_{i} x_{j}
where:
sum_{i=1}^{n} x_{i} < b
x_{i} in {0,1}
"""
from mystic.solvers import diffev2
from mystic.monitors import VerboseMonitor
from mystic.constraints import impose_sum, discrete, and_
import numpy as np
N = 10
b = 5
bounds = [(0,1)] * N
def objective(x, w):
s = 0
for i in range(len(x)-1):
for j in range(i, len(x)):
s += w[i,j] * x[i] * x[j]
return s
w = np.ones((N,N)) #XXX: replace with actual values of wij
cost = lambda x: -objective(x, w)
c = and_(lambda x: impose_sum(b, x), discrete([0,1])(lambda x:x))
mon = VerboseMonitor(10)
solution = diffev2(cost,bounds,constraints=c,bounds=bounds,itermon=mon,gtol=50, maxiter=5000, maxfun=50000, npop=10)
print(solution)
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