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//////////////////////////////////////////////////////
// example of use of the simulated annealing method //
//////////////////////////////////////////////////////
function demo_sa_1()
my_handle = scf(100001);
clf(my_handle,"reset");
demo_viewCode("SAdemo.sce");
my_handle.info_message = _("Please wait ...");
lines(0);
old_funcprot = funcprot();
funcprot(0);
////////////////////////
// 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";
Proba_start = 0.8;
It_intern = 1000;
It_extern = 30;
It_Pre = 100;
alpha = 0.9;
DoSA = %T;
DoFSA = %F;
DoVFSA = %F;
DoCSA = %F;
DoHuang = %F;
//////////////////////////////////////////
Min = eval("min_bd_"+func+"()");
Max = eval("max_bd_"+func+"()");
x0 = (Max - Min).*rand(size(Min,1),size(Min,2)) + Min;
deff("y=f(x)","y="+func+"(x)");
/////////////////////////
// Simulated Annealing //
/////////////////////////
if DoSA then
printf("\nSA: geometrical decrease temperature law\n");
sa_params = init_param();
sa_params = add_param(sa_params,"min_delta",-0.1*(Max-Min));
sa_params = add_param(sa_params,"max_delta", 0.1*(Max-Min));
sa_params = add_param(sa_params,"neigh_func", neigh_func_default); // Optional
sa_params = add_param(sa_params,"accept_func", accept_func_default); // Optional
sa_params = add_param(sa_params,"temp_law", temp_law_default); // Optional
sa_params = add_param(sa_params,"min_bound",Min);
sa_params = add_param(sa_params,"max_bound",Max);
sa_params = add_param(sa_params,"alpha",alpha); // for the decreasing temperature law
T0 = compute_initial_temp(x0, f, Proba_start, It_Pre, sa_params);
printf("Initial temperature T0 = %f\n", T0);
[x_opt, f_opt, sa_mean_list, sa_var_list, temp_list] = optim_sa(x0, f, It_extern, It_intern, T0, Log = %T, sa_params);
printf("optimal solution:\n"); disp(x_opt);
printf("value of the objective function = %f\n", f_opt);
if is_handle_valid(my_handle) then
drawlater;
subplot(2,1,1);
xtitle("Geometrical annealing","Iteration","Mean / Variance");
t = 1:length(sa_mean_list);
plot(t,sa_mean_list,"r",t,sa_var_list,"g");
legend(["Mean","Variance"]);
subplot(2,1,2);
xtitle("Temperature evolution","Iteration","Temperature");
for i=1:length(t)-1
plot([t(i) t(i+1)], [temp_list(i) temp_list(i)],"k-");
end
drawnow;
my_handle.info_message = "";
end
end
/////////
// FSA //
/////////
if DoFSA then
printf("SA: the FSA algorithm\n");
sa_params = init_param();
sa_params = add_param(sa_params,"min_delta",-0.1*(Max-Min));
sa_params = add_param(sa_params,"max_delta", 0.1*(Max-Min));
sa_params = add_param(sa_params,"neigh_func", neigh_func_default); // Required for compute_initial_temp
sa_params = add_param(sa_params,"accept_func", accept_func_default); // Optional
sa_params = add_param(sa_params,"temp_law", temp_law_fsa); // Required to transform SA into FSA
sa_params = add_param(sa_params,"min_bound",Min);
sa_params = add_param(sa_params,"max_bound",Max);
T0 = compute_initial_temp(x0, f, Proba_start, It_Pre, sa_params);
sa_params = remove_param(sa_params,"neigh_func");
sa_params = add_param(sa_params,"neigh_func", neigh_func_fsa); // Required to transform SA into FSA
printf("Initial temperature T0 = %f\n", T0);
[x_opt, f_opt, sa_mean_list, sa_var_list, temp_list] = optim_sa(x0, f, It_extern, It_intern, T0, Log = %T, sa_params);
printf("optimal solution:\n"); disp(x_opt);
printf("value of the objective function = %f\n", f_opt);
scf();
drawlater;
subplot(2,1,1);
xtitle("FSA","Iteration","Mean / Variance");
t = 1:length(sa_mean_list);
plot(t,sa_mean_list,"r",t,sa_var_list,"g");
legend(["Mean","Variance"]);
subplot(2,1,2);
xtitle("Temperature evolution","Iteration","Temperature");
for i=1:length(t)-1
plot([t(i) t(i+1)], [temp_list(i) temp_list(i)],"k-");
end
drawnow;
end
//////////
// VFSA //
//////////
if DoVFSA then
printf("SA: the VFSA algorithm\n");
sa_params = init_param();
sa_params = add_param(sa_params,"min_delta",-0.1*(Max-Min));
sa_params = add_param(sa_params,"max_delta", 0.1*(Max-Min));
sa_params = add_param(sa_params,"accept_func", accept_func_vfsa); // Required to transform SA into FSA
sa_params = add_param(sa_params,"neigh_func", neigh_func_default); // Required for compute_initial_temp
sa_params = add_param(sa_params,"temp_law", temp_law_vfsa); // Required to transform SA into FSA
sa_params = add_param(sa_params,"type_accept", "vfsa"); // Required to compute correctly the starting temperature for VFSA
sa_params = add_param(sa_params,"dimension", length(x0)); // Required to compute correctly the starting temperature for VFSA
sa_params = add_param(sa_params,"min_bound",Min);
sa_params = add_param(sa_params,"max_bound",Max);
T0 = compute_initial_temp(x0, f, Proba_start, It_Pre, sa_params);
sa_params = remove_param(sa_params,"neigh_func");
sa_params = add_param(sa_params,"neigh_func", neigh_func_vfsa); // Required to transform SA into VFSA
sa_params = remove_param(sa_params,"type_accept");
sa_params = add_param(sa_params,"type_accept", "sa"); // We go back to the classical method for computing the starting temperature
printf("Initial temperature T0 = %f\n", T0);
[x_opt, f_opt, sa_mean_list, sa_var_list, temp_list] = optim_sa(x0, f, It_extern, It_intern, T0, Log = %T, sa_params);
printf("optimal solution:\n"); disp(x_opt);
printf("value of the objective function = %f\n", f_opt);
scf();
drawlater;
subplot(2,1,1);
xtitle("VFSA","Iteration","Mean / Variance");
t = 1:length(sa_mean_list);
plot(t,sa_mean_list,"r",t,sa_var_list,"g");
legend(["Mean","Variance"]);
subplot(2,1,2);
xtitle("Temperature evolution","Iteration","Temperature");
for i=1:length(t)-1
plot([t(i) t(i+1)], [temp_list(i) temp_list(i)],"k-");
end
drawnow;
end
/////////
// CSA //
/////////
if DoCSA then
printf("SA: the CSA algorithm\n");
sa_params = init_param();
sa_params = add_param(sa_params,"min_delta",-0.1*(Max-Min));
sa_params = add_param(sa_params,"max_delta", 0.1*(Max-Min));
sa_params = add_param(sa_params,"neigh_func", neigh_func_default); // Required for compute_initial_temp
sa_params = add_param(sa_params,"accept_func", accept_func_default); // Optional
sa_params = add_param(sa_params,"temp_law", temp_law_csa); // Required to transform SA into CSA
sa_params = add_param(sa_params,"min_bound",Min);
sa_params = add_param(sa_params,"max_bound",Max);
T0 = compute_initial_temp(x0, f, Proba_start, It_Pre, sa_params);
sa_params = remove_param(sa_params,"neigh_func");
sa_params = add_param(sa_params,"neigh_func", neigh_func_csa); // Required to transform SA into CSA
printf("Initial temperature T0 = %f\n", T0);
[x_opt, f_opt, sa_mean_list, sa_var_list, temp_list] = optim_sa(x0, f, It_extern, It_intern, T0, Log = %T, sa_params);
printf("optimal solution:\n"); disp(x_opt);
printf("value of the objective function = %f\n", f_opt);
scf();
drawlater;
subplot(2,1,1);
xtitle("Classical simulated annealing","Iteration","Mean / Variance");
t = 1:length(sa_mean_list);
plot(t,sa_mean_list,"r",t,sa_var_list,"g");
legend(["Mean","Variance"]);
subplot(2,1,2);
xtitle("Temperature evolution","Iteration","Temperature");
for i=1:length(t)-1
plot([t(i) t(i+1)], [temp_list(i) temp_list(i)],"k-");
end
drawnow;
end
///////////
// Huang //
///////////
if DoHuang then
printf("SA: the Huang annealing\n");
sa_params = init_param();
sa_params = add_param(sa_params,"min_delta",-0.1*(Max-Min));
sa_params = add_param(sa_params,"max_delta", 0.1*(Max-Min));
sa_params = add_param(sa_params,"temp_law", temp_law_huang);
sa_params = add_param(sa_params,"min_bound",Min);
sa_params = add_param(sa_params,"max_bound",Max);
T0 = compute_initial_temp(x0, f, Proba_start, It_Pre, sa_params);
printf("Initial temperature T0 = %f\n", T0);
[x_opt, f_opt, sa_mean_list, sa_var_list, temp_list] = optim_sa(x0, f, It_extern, It_intern, T0, Log = %T, sa_params);
printf("optimal solution:\n"); disp(x_opt);
printf("value of the objective function = %f\n", f_opt);
scf();
drawlater;
subplot(2,1,1);
xtitle("Huang annealing","Iteration","Mean / Variance");
t = 1:length(sa_mean_list);
plot(t,sa_mean_list,"r",t,sa_var_list,"g");
legend(["Mean","Variance"]);
subplot(2,1,2);
xtitle("Temperature evolution","Iteration","Temperature");
for i=1:length(t)-1
plot([t(i) t(i+1)], [temp_list(i) temp_list(i)],"k-");
end
drawnow;
end
funcprot(old_funcprot);
endfunction
demo_sa_1();
clear demo_sa_1;
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