1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
|
# This file is part of DEAP.
#
# DEAP is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as
# published by the Free Software Foundation, either version 3 of
# the License, or (at your option) any later version.
#
# DEAP is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with DEAP. If not, see <http://www.gnu.org/licenses/>.
import random
import numpy
import pytest
from deap import algorithms
from deap import base
from deap import benchmarks
from deap.benchmarks.tools import hypervolume
from deap import cma
from deap import creator
from deap import tools
FITCLSNAME = "FIT_TYPE"
INDCLSNAME = "IND_TYPE"
HV_THRESHOLD = 116.0 # 120.777 is Optimal value
def teardown_():
# Messy way to remove a class from the creator
del creator.__dict__[FITCLSNAME]
del creator.__dict__[INDCLSNAME]
@pytest.fixture
def setup_teardown_single_obj():
creator.create(FITCLSNAME, base.Fitness, weights=(-1.0,))
creator.create(INDCLSNAME, list, fitness=creator.__dict__[FITCLSNAME])
yield
teardown_()
@pytest.fixture
def setup_teardown_multi_obj():
creator.create(FITCLSNAME, base.Fitness, weights=(-1.0, -1.0))
creator.create(INDCLSNAME, list, fitness=creator.__dict__[FITCLSNAME])
yield
teardown_()
@pytest.fixture
def setup_teardown_multi_obj_numpy():
creator.create(FITCLSNAME, base.Fitness, weights=(-1.0, -1.0))
creator.create(INDCLSNAME, numpy.ndarray, fitness=creator.__dict__[FITCLSNAME])
yield
teardown_()
def test_cma(setup_teardown_single_obj):
NDIM = 5
strategy = cma.Strategy(centroid=[0.0]*NDIM, sigma=1.0)
toolbox = base.Toolbox()
toolbox.register("evaluate", benchmarks.sphere)
toolbox.register("generate", strategy.generate, creator.__dict__[INDCLSNAME])
toolbox.register("update", strategy.update)
pop, _ = algorithms.eaGenerateUpdate(toolbox, ngen=100)
best, = tools.selBest(pop, k=1)
assert best.fitness.values < (1e-8,), "CMA algorithm did not converged properly."
def test_nsga2(setup_teardown_multi_obj):
NDIM = 5
BOUND_LOW, BOUND_UP = 0.0, 1.0
MU = 16
NGEN = 100
toolbox = base.Toolbox()
toolbox.register("attr_float", random.uniform, BOUND_LOW, BOUND_UP)
toolbox.register("individual", tools.initRepeat, creator.__dict__[INDCLSNAME], toolbox.attr_float, NDIM)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("evaluate", benchmarks.zdt1)
toolbox.register("mate", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)
toolbox.register("mutate", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)
toolbox.register("select", tools.selNSGA2)
pop = toolbox.population(n=MU)
fitnesses = toolbox.map(toolbox.evaluate, pop)
for ind, fit in zip(pop, fitnesses):
ind.fitness.values = fit
pop = toolbox.select(pop, len(pop))
for gen in range(1, NGEN):
offspring = tools.selTournamentDCD(pop, len(pop))
offspring = [toolbox.clone(ind) for ind in offspring]
for ind1, ind2 in zip(offspring[::2], offspring[1::2]):
if random.random() <= 0.9:
toolbox.mate(ind1, ind2)
toolbox.mutate(ind1)
toolbox.mutate(ind2)
del ind1.fitness.values, ind2.fitness.values
invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
pop = toolbox.select(pop + offspring, MU)
hv = hypervolume(pop, [11.0, 11.0])
# hv = 120.777 # Optimal value
assert hv > HV_THRESHOLD, "Hypervolume is lower than expected %f < %f" % (hv, HV_THRESHOLD)
for ind in pop:
assert not (any(numpy.asarray(ind) < BOUND_LOW) or any(numpy.asarray(ind) > BOUND_UP))
def test_mo_cma_es(setup_teardown_multi_obj_numpy):
def distance(feasible_ind, original_ind):
"""A distance function to the feasibility region."""
return sum((f - o)**2 for f, o in zip(feasible_ind, original_ind))
def closest_feasible(individual):
"""A function returning a valid individual from an invalid one."""
feasible_ind = numpy.array(individual)
feasible_ind = numpy.maximum(BOUND_LOW, feasible_ind)
feasible_ind = numpy.minimum(BOUND_UP, feasible_ind)
return feasible_ind
def valid(individual):
"""Determines if the individual is valid or not."""
if any(individual < BOUND_LOW) or any(individual > BOUND_UP):
return False
return True
NDIM = 5
BOUND_LOW, BOUND_UP = 0.0, 1.0
MU, LAMBDA = 10, 10
NGEN = 500
numpy.random.seed(128)
# The MO-CMA-ES algorithm takes a full population as argument
population = [creator.__dict__[INDCLSNAME](x) for x in numpy.random.uniform(BOUND_LOW, BOUND_UP, (MU, NDIM))]
toolbox = base.Toolbox()
toolbox.register("evaluate", benchmarks.zdt1)
toolbox.decorate("evaluate", tools.ClosestValidPenalty(valid, closest_feasible, 1.0e+6, distance))
for ind in population:
ind.fitness.values = toolbox.evaluate(ind)
strategy = cma.StrategyMultiObjective(population, sigma=1.0, mu=MU, lambda_=LAMBDA)
toolbox.register("generate", strategy.generate, creator.__dict__[INDCLSNAME])
toolbox.register("update", strategy.update)
for gen in range(NGEN):
# Generate a new population
population = toolbox.generate()
# Evaluate the individuals
fitnesses = toolbox.map(toolbox.evaluate, population)
for ind, fit in zip(population, fitnesses):
ind.fitness.values = fit
# Update the strategy with the evaluated individuals
toolbox.update(population)
# Note that we use a penalty to guide the search to feasible solutions,
# but there is no guarantee that individuals are valid.
# We expect the best individuals will be within bounds or very close.
num_valid = 0
for ind in strategy.parents:
dist = distance(closest_feasible(ind), ind)
if numpy.isclose(dist, 0.0, rtol=1.e-5, atol=1.e-5):
num_valid += 1
assert num_valid >= len(strategy.parents)
# Note that NGEN=500 is enough to get consistent hypervolume > 116,
# but not 119. More generations would help but would slow down testing.
hv = hypervolume(strategy.parents, [11.0, 11.0])
assert hv > HV_THRESHOLD, "Hypervolume is lower than expected %f < %f" % (hv, HV_THRESHOLD)
def test_nsga3(setup_teardown_multi_obj):
NDIM = 5
BOUND_LOW, BOUND_UP = 0.0, 1.0
MU = 16
NGEN = 100
ref_points = tools.uniform_reference_points(2, p=12)
toolbox = base.Toolbox()
toolbox.register("attr_float", random.uniform, BOUND_LOW, BOUND_UP)
toolbox.register("individual", tools.initRepeat, creator.__dict__[INDCLSNAME], toolbox.attr_float, NDIM)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("evaluate", benchmarks.zdt1)
toolbox.register("mate", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)
toolbox.register("mutate", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)
toolbox.register("select", tools.selNSGA3, ref_points=ref_points)
pop = toolbox.population(n=MU)
fitnesses = toolbox.map(toolbox.evaluate, pop)
for ind, fit in zip(pop, fitnesses):
ind.fitness.values = fit
pop = toolbox.select(pop, len(pop))
# Begin the generational process
for gen in range(1, NGEN):
offspring = algorithms.varAnd(pop, toolbox, 1.0, 1.0)
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
# Select the next generation population
pop = toolbox.select(pop + offspring, MU)
hv = hypervolume(pop, [11.0, 11.0])
# hv = 120.777 # Optimal value
assert hv > HV_THRESHOLD, "Hypervolume is lower than expected %f < %f" % (hv, HV_THRESHOLD)
for ind in pop:
assert not (any(numpy.asarray(ind) < BOUND_LOW) or any(numpy.asarray(ind) > BOUND_UP))
|
