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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.
////////////////////////////////////////
// Demo of the NSGA Genetic Algorithm //
////////////////////////////////////////
function demo_NSGA()
/////////////////////////
// Deb 1 test function //
// Convex Pareto set //
/////////////////////////
function Res = min_bd_deb_1(n)
if ~isdef("n","local") then n = 10; end;
Res = zeros(n, 1);
endfunction
function Res = max_bd_deb_1(n)
if ~isdef("n", "local") then n = 10; end;
Res = ones(n, 1);
endfunction
function f = get_opti_deb_1(x)
f1_x1 = x(1);
g_x2 = 1;
h = 1 - sqrt(f1_x1 / g_x2);
f(1,1) = f1_x1;
f(1,2) = g_x2 * h;
endfunction
function f = deb_1(x)
f1_x1 = x(1);
g_x2 = 1 + 9 * sum((x(2:$)-x(1)).^2) / (length(x) - 1);
h = 1 - sqrt(f1_x1 / g_x2);
f(1,1) = f1_x1;
f(1,2) = g_x2 * h;
endfunction
funcname = "deb_1";
// example of use of the genetic algorithm
PopSize = 100;
Proba_cross = 0.7;
Proba_mut = 0.1;
NbGen = 4;
NbCouples = 110;
Log = %T;
nb_disp = 10; // Nb point to display from the optimal population
Sigma = 0.02; // Sigma_share = Pareto_length / Pop_Size
Pow = 1;
pressure = 0.1;
ga_params = init_param();
// Parameters to adapt to the shape of the optimization problem
ga_params = add_param(ga_params, "minbound", eval("min_bd_" + funcname + "(2)"));
ga_params = add_param(ga_params, "maxbound", eval("max_bd_" + funcname + "(2)"));
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, 'selection_func', selection_ga_random);
ga_params = add_param(ga_params, "nb_couples", NbCouples);
ga_params = add_param(ga_params, "pressure", pressure);
clear y
deff("y = fobjs(x)","y = " + funcname + "(x);");
////////////////////
// NSGA Algorithm //
////////////////////
printf("\n");
printf(gettext("%s: optimization starting, please wait ...\n"),"NSGA");
[pop_opt, fobj_pop_opt, pop_init, fobj_pop_init] = optim_nsga(fobjs, PopSize, NbGen, Proba_mut, Proba_cross, Log, ga_params, Sigma, Pow);
[f_pareto,pop_pareto] = pareto_filter(fobj_pop_opt,pop_opt);
my_handle = scf(100001);
clf(my_handle,"reset");
if (size(fobj_pop_opt, 2) == 2) then
drawlater;
subplot(2, 1, 1);
printf("plotting init population ...\n");
plot(fobj_pop_init(:,1),fobj_pop_init(:,2),"r.");
if isdef("get_opti_"+funcname) then
t = 0:0.01:1;
for i=1:length(t)
y_t(i,:) = eval("get_opti_" + funcname + "(t(" + string(i) + "))");
end
plot(y_t(:,1), y_t(:,2), "k-");
end
legend(["Init pop.","Pareto front."]);
xtitle("Objective function space","f1","f2");
subplot(2, 1, 2);
printf("plotting final population ...\n");
plot(fobj_pop_opt(:,1), fobj_pop_opt(:,2), "g.");
printf("plotting Pareto population ...\n");
plot(f_pareto(:,1), f_pareto(:,2), "k.");
if isdef("get_opti_"+funcname) then
t = 0 : 0.01 : 1;
for i = 1 : size(t,"*")
y_t(i,:) = eval("get_opti_" + funcname + "(t(" + string(i) + "))");
end
plot(y_t(:,1), y_t(:,2), "k-");
end
legend(["Final pop.", "Pareto pop.", "Pareto front."]);
xtitle("Objective function space", "f1", "f2");
drawnow;
end
demo_viewCode("NSGAdemo.sce");
endfunction
demo_NSGA();
clear demo_NSGA;
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