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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) DIGITEO - Yann COLLETTE
// Copyright (C) 2012 - DIGITEO - Allan CORNET
//
// This file is released under the 3-clause BSD license. See COPYING-BSD.
/////////////////////////////////////////////
// example of use of the genetic algorithm //
/////////////////////////////////////////////
function demo_genetic_algo()
// Definition of the Rastrigin test problem
//
// Rastrigin function
//
function Res = min_bd_rastrigin()
Res = [-1 -1]';
endfunction
function Res = max_bd_rastrigin()
Res = [1 1]';
endfunction
function Res = opti_rastrigin()
Res = [0 0]';
endfunction
function y = rastrigin(x)
y = x(1)^2 + x(2)^2 - cos(12 * x(1)) - cos(18 * x(2));
endfunction
func = "rastrigin";
deff("y = f(x)","y = " + func + "(x)");
PopSize = 100;
Proba_cross = 0.7;
Proba_mut = 0.1;
NbGen = 10;
NbCouples = 110;
Log = %T;
nb_disp = 10; // Nb point to display from the optimal population
pressure = 0.05;
ga_params = init_param();
// Parameters to adapt to the shape of the optimization problem
ga_params = add_param(ga_params, "minbound", eval("min_bd_" + func + "()"));
ga_params = add_param(ga_params, "maxbound", eval("max_bd_" + func + "()"));
ga_params = add_param(ga_params, "dimension", 2);
ga_params = add_param(ga_params, "beta", 0);
ga_params = add_param(ga_params, "delta", 0.1);
// Parameters to fine tune the Genetic algorithm. All these parameters are optional for continuous optimization
// If you need to adapt the GA to a special problem, you
ga_params = add_param(ga_params, "init_func", init_ga_default);
ga_params = add_param(ga_params, "crossover_func", crossover_ga_default);
ga_params = add_param(ga_params, "mutation_func", mutation_ga_default);
ga_params = add_param(ga_params, "codage_func", coding_ga_identity);
ga_params = add_param(ga_params, "selection_func", selection_ga_elitist);
ga_params = add_param(ga_params, "nb_couples", NbCouples);
ga_params = add_param(ga_params, "pressure", pressure);
Min = get_param(ga_params, "minbound");
Max = get_param(ga_params, "maxbound");
x0 = (Max - Min) .* rand(size(Min,1),size(Min,2)) + Min;
//////////////////////////////////////////
x = Min(1):(Max(1)-Min(1))/20:Max(1); y = Min(2):(Max(2)-Min(2))/20:Max(2);
function y = rastriginV(x1 , x2)
// Vectorized function for contouring.
y = x1.^2 + x2.^2 - cos(12 * x1) - cos(18 * x2);
endfunction
x = linspace(-1, 1, 100);
y = linspace(-1, 1, 100);
[XX1, XX2] = meshgrid(x, y);
Z = rastriginV(XX1, XX2);
///////////////////////
// Genetic Algorithm //
///////////////////////
printf("\n");
printf(gettext("%s: optimization starting, please wait ...\n"),"GA");
[pop_opt, fobj_pop_opt, pop_init, fobj_pop_init] = optim_ga(f, PopSize, NbGen, Proba_mut, Proba_cross, Log, ga_params);
my_handle = scf(100001);
clf(my_handle, "reset");
if (size(pop_opt(1)', 2) == 2) then
subplot(2, 1, 1);
drawlater;
xset("fpf", " ");
contour(x, y, Z', 5);
_axes = gca();
_axes.data_bounds = [Min(1) Max(1) Min(2) Max(2)];
xtitle("Genetic Algorithm - real variable", "x1", "x2");
printf("plotting init population ...\n");
for i = 1:length(pop_init)
plot(pop_init(i)(1), pop_init(i)(2), "r.");
end
printf("plotting result population ...\n");
for i = 1:length(pop_opt)
plot(pop_opt(i)(1), pop_opt(i)(2), "g.");
end
drawnow;
end
printf("Genetic Algorithm: %d points from pop_opt\n", nb_disp);
for i = 1 : nb_disp
printf("Individual %d: x(1) = %f x(2) = %f -> f = %f\n", i, pop_opt(i)(1), pop_opt(i)(2), fobj_pop_opt(i));
end
/////////////////////////////////////////
// Genetic Algorithm for binary codage //
/////////////////////////////////////////
clear f;
deff("y=f(x)","BinLen = get_param(ga_params,''binary_length''); ..
tmp = convert_to_float(x, BinLen, Max, Min); ..
y = "+func+"(tmp);","n");
ga_params = add_param(ga_params, "binary_length", 8);
ga_params = set_param(ga_params, "crossover_func", crossover_ga_binary);
ga_params = set_param(ga_params, "mutation_func", mutation_ga_binary);
ga_params = set_param(ga_params, "codage_func", coding_ga_binary);
ga_params = add_param(ga_params, "multi_cross", %T);
ga_params = add_param(ga_params, "multi_cross_nb", 3);
printf(gettext("%s: optimization starting, please wait ...\n"),"GA");
[pop_opt, fobj_pop_opt, pop_init, fobj_pop_init] = optim_ga(f, PopSize, NbGen, Proba_mut, Proba_cross, Log, ga_params);
if (size(pop_opt(1)',2)==2) then
subplot(2, 1, 2);
drawlater;
xset("fpf", " ");
contour(x, y, Z', 5);
_axes = gca();
_axes.data_bounds = [Min(1) Max(1) Min(2) Max(2)];
xtitle("Genetic Algorithm - binary variables","x1","x2");
printf("plotting init population ...\n");
for i = 1 : length(pop_init)
plot(pop_init(i)(1), pop_init(i)(2), "r.");
end
printf("plotting result population ...\n");
for i = 1 : length(pop_opt)
plot(pop_opt(i)(1), pop_opt(i)(2), "g.");
end
drawnow;
end
printf("Genetic Algorithm - binary: %d points from pop_opt\n", nb_disp);
for i = 1 : nb_disp
printf("Individual %d: x(1) = %f x(2) = %f -> f = %f\n", i, pop_opt(i)(1), pop_opt(i)(2), fobj_pop_opt(i));
end
demo_viewCode("GAdemo.sce");
endfunction
demo_genetic_algo();
clear demo_genetic_algo;
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