temp_law_huang — The Huang temperature decrease law for the simulated annealing
T_out = temp_law_huang(T_in,step_mean,step_var,temp_stage,n,param)
the temperature at the current stage
the mean value of the objective function computed during the current stage
the variance value of the objective function computed during the current stage
the index of the current temperature stage
the dimension of the decision variable (the x in f(x))
a float corresponding to the lambda parameter of the Huang temperature decrease law (0.01 by default)
the temperature for the temperature stage to come
function y = rastrigin(x)
y = x(1)^2+x(2)^2-cos(12*x(1))-cos(18*x(2));
endfunction
x0 = [-1, -1];
Proba_start = 0.8;
It_intern = 1000;
It_extern = 30;
It_Pre = 100;
printf('SA: the Huang temperature decrease law\n');
T0 = compute_initial_temp(x0, rastrigin, Proba_start, It_Pre, neigh_func_default);
printf('Initial temperatore T0 = %f\n', T0);
[x_opt, f_opt, sa_mean_list, sa_var_list, temp_list] = optim_sa(x0, rastrigin, It_extern, It_intern, T0, Log = %T, temp_law_huang, neigh_func_default);
printf('optimal solution:\n'); disp(x_opt);
printf('value of the objective function = %f\n', f_opt);
scf();
subplot(2,1,1);
xtitle('Huang 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');
plot(t,temp_list,'k-');