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
|
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2008 - Yann COLLETTE <yann.collette@renault.com>
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
function [pop_opt, fobj_pop_opt, pop_init, fobj_pop_init] = optim_nsga(ga_f, pop_size, nb_generation, p_mut, p_cross, Log, param, sigma, pow)
[nargout, nargin] = argn();
if ~isdef('param','local') then
param = [];
end
[codage_func,err] = get_param(param,'codage_func',coding_ga_identity);
[init_func,err] = get_param(param,'init_func',init_ga_default);
[crossover_func,err] = get_param(param,'crossover_func',crossover_ga_default);
[mutation_func,err] = get_param(param,'mutation_func',mutation_ga_default);
[selection_func,err] = get_param(param,'selection_func',selection_ga_elitist);
[nb_couples,err] = get_param(param,'nb_couples',100);
[pressure,err] = get_param(param,'pressure',0.05);
if ~isdef('ga_f','local') then
error(gettext("optim_moga: ga_f is mandatory"));
end
if ~isdef('pop_size','local') then
pop_size = 100;
end
if ~isdef('nb_generation','local') then
nb_generation = 10;
end
if ~isdef('p_mut','local') then
p_mut = 0.1;
end
if ~isdef('p_cross','local') then
p_cross = 0.1;
end
if ~isdef('Log','local') then
Log = %F;
end
if ~isdef('sigma','local') then
sigma = 0.01;
end
if ~isdef('pow','local') then
pow = 2;
end
// Initialization of the population
if (Log) then
printf(gettext("%s: Initialization of the population\n"),"optim_nsga");
end
Pop = list();
Pop = init_func(pop_size,param);
if (nargout==4) then
pop_init = Pop;
end
// Code the individuals
Pop = codage_func(Pop,'code',param);
for i=1:length(Pop)
MO_FObj_Pop(i,:) = ga_f(Pop(i));
end
// Compute the domination rank
for i=1:size(MO_FObj_Pop,1)
Index = 0;
for j=1:size(MO_FObj_Pop,1)
Index = Index + double(and(MO_FObj_Pop(i,:)<=MO_FObj_Pop(j,:)) & or(MO_FObj_Pop(i,:)<MO_FObj_Pop(j,:)));
end
FObj_Pop(i) = - (Index + 1);
end
if (nargout==4) then
fobj_pop_init = MO_FObj_Pop;
end
// The genetic algorithm
for i=1:nb_generation
if (Log) then
printf(gettext("%s: iteration %d / %d"), "optim_nsga", i, nb_generation);
end
// Computation of the niching penality
for j=1:size(MO_FObj_Pop,1)
Niching(j) = 0;
for k=1:size(MO_FObj_Pop,1)
Distance = sqrt(sum((MO_FObj_Pop(j,:) - MO_FObj_Pop(k,:)).^2));
if Distance < sigma then
Niching(j) = Niching(j) + (1 - Distance / sigma)^pow;
end
end
end
// Apply niching penality to fobj
FObj_Pop = FObj_Pop ./ Niching;
FObj_Pop_Max = max(FObj_Pop);
FObj_Pop_Min = min(FObj_Pop);
// Normalization of the efficiency
Efficiency = (1 - pressure) * (FObj_Pop - FObj_Pop_Min) / max([FObj_Pop_Max - FObj_Pop_Min %eps]) + pressure;
//
// Selection
//
Indiv1 = list();
Indiv2 = list();
Wheel = cumsum(Efficiency);
for j=1:nb_couples
// Selection of the first individual in the couple
Shoot = rand(1,1)*Wheel($);
Index = find(Wheel<=Shoot);
if length(Index)>1 then Index = Index($); end;
if isempty(Index) then Index = 1; end;
Indiv1(j) = Pop(Index);
MO_FObj_Indiv1(j,:) = MO_FObj_Pop(Index,:);
// Selection of the second individual in the couple
Shoot = rand(1,1)*Wheel($);
Index = find(Wheel<=Shoot);
if length(Index)>1 then Index = Index($); end;
if isempty(Index) then Index = 1; end;
Indiv2(j) = Pop(Index);
MO_FObj_Indiv2(j,:) = MO_FObj_Pop(Index,:);
end
//
// Crossover
//
for j=1:nb_couples
if (p_cross>rand(1,1)) then
[x1, x2] = crossover_func(Indiv1(j), Indiv2(j),param);
Indiv1(j) = x1;
Indiv2(j) = x2;
ToCompute_I1(j) = %T;
ToCompute_I2(j) = %T;
else
ToCompute_I1(j) = %F;
ToCompute_I2(j) = %F;
end
end
//
// Mutation
//
for j=1:nb_couples
if (p_mut>rand(1,1)) then
x1 = mutation_func(Indiv1(j),param);
Indiv1(j) = x1;
ToCompute_I1(j) = %T;
end
if (p_mut>rand(1,1)) then
x2 = mutation_func(Indiv2(j),param);
Indiv2(j) = x2;
ToCompute_I2(j) = %T;
end
end
//
// Computation of the objective functions
//
for j=1:length(Indiv1)
if ToCompute_I1(j) then MO_FObj_Indiv1(j,:) = ga_f(Indiv1(j)); end
if ToCompute_I2(j) then MO_FObj_Indiv2(j,:) = ga_f(Indiv2(j)); end
end
// Reinit ToCompute lists
ToCompute_I1 = ToCompute_I1 & %F;
ToCompute_I2 = ToCompute_I2 & %F;
// Compute the domination rank
for j=1:size(MO_FObj_Indiv1,1)
// We compute the rank for Indiv1
Index1 = 0; Index2 = 0; Index3 = 0;
for k=1:size(MO_FObj_Indiv1,1)
Index1 = Index1 + double(and(MO_FObj_Indiv1(j,:)<=MO_FObj_Indiv1(k,:)) & or(MO_FObj_Indiv1(j,:)<MO_FObj_Indiv1(k,:)));
Index2 = Index2 + double(and(MO_FObj_Indiv1(j,:)<=MO_FObj_Indiv2(k,:)) & or(MO_FObj_Indiv1(j,:)<MO_FObj_Indiv2(k,:)));
end
for k=1:size(MO_FObj_Pop,1)
Index3 = Index3 + and(MO_FObj_Indiv1(j,:)<=MO_FObj_Pop(k,:)) & or(MO_FObj_Indiv1(j,:)<MO_FObj_Pop(k,:));
end
FObj_Indiv1(j) = - (Index1 + Index2 + Index3 + 1);
// We compute the rank for Indiv2
Index1 = 0; Index2 = 0; Index3 = 0;
for k=1:size(MO_FObj_Indiv1,1)
Index1 = Index1 + double(and(MO_FObj_Indiv2(j,:)<=MO_FObj_Indiv1(k,:)) & or(MO_FObj_Indiv2(j,:)<MO_FObj_Indiv1(k,:)));
Index2 = Index2 + double(and(MO_FObj_Indiv2(j,:)<=MO_FObj_Indiv2(k,:)) & or(MO_FObj_Indiv2(j,:)<MO_FObj_Indiv2(k,:)));
end
for k=1:size(MO_FObj_Pop,1)
Index3 = Index3 + double(and(MO_FObj_Indiv2(j,:)<=MO_FObj_Pop(k,:)) & or(MO_FObj_Indiv2(j,:)<MO_FObj_Pop(k,:)));
end
FObj_Indiv2(j) = - (Index1 + Index2 + Index3 + 1);
end
// We compute the rank for Pop
for j=1:size(MO_FObj_Pop,1)
Index1 = 0; Index2 = 0; Index3 = 0;
for k=1:size(MO_FObj_Indiv1,1)
Index1 = Index1 + double(and(MO_FObj_Pop(j,:)<=MO_FObj_Indiv1(k,:)) & or(MO_FObj_Pop(j,:)<MO_FObj_Indiv1(k,:)));
Index2 = Index2 + double(and(MO_FObj_Pop(j,:)<=MO_FObj_Indiv2(k,:)) & or(MO_FObj_Pop(j,:)<MO_FObj_Indiv2(k,:)));
end
for k=1:size(FObj_Pop,1)
Index3 = Index3 + double(and(MO_FObj_Pop(j,:)<=MO_FObj_Pop(k,:)) & or(MO_FObj_Pop(j,:)<MO_FObj_Pop(k,:)));
end
FObj_Pop(j) = - (Index1 + Index2 + Index3 + 1);
end
//
// Recombination
//
[Pop,FObj_Pop,Efficiency,MO_FObj_Pop] = selection_func(Pop,Indiv1,Indiv2,FObj_Pop,FObj_Indiv1,FObj_Indiv2, ...
MO_FObj_Pop,MO_FObj_Indiv1,MO_FObj_Indiv2,param);
if (Log) then
printf(gettext(" - min / max value found = %f / %f\n"), min(FObj_Pop), max(FObj_Pop));
end
end
pop_opt = codage_func(Pop,'decode',param);
fobj_pop_opt = MO_FObj_Pop;
endfunction
|
