temp_law_csa

The classical temperature decrease law

Calling Sequence

T_out = temp_law_csa(T_in,step_mean,step_var,temp_stage,n,param)

Arguments

:T_in the temperature at the current stage : :step_mean the mean value of the objective function computed during

the current stage

: :step_var the variance value of the objective function computed

during the current stage

: :temp_stage the index of the current temperature stage : :n the dimension of the decision variable (the x in f(x)) : :param not used for this temperature law : :T_out the temperature for the temperature stage to come :

Description

• This function implements the classical annealing temperature schedule (the one for which the convergence of the simulated annealing has been proven).

Examples

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;

`mprintf`_('SA: the CSA algorithm\n');

T0 = `compute_initial_temp`_(x0, rastrigin, Proba_start, It_Pre, `neigh_func_default`_);
`mprintf`_('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_csa, `neigh_func_csa`_);

`mprintf`_('optimal solution:\n'); `disp`_(x_opt);
`mprintf`_('value of the objective function = %f\n', f_opt);

`scf`_();
`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');
`plot`_(t,temp_list,'k-');

See Also

• optim_sa A Simulated Annealing optimization method
• temp_law_huang The Huang temperature decrease law for the simulated annealing
• neigh_func_default A SA function which computes a neighbor of a given point