# optim_nsga

A multi-objective Niched Sharing Genetic Algorithm

## Calling Sequence

    [pop_opt,fobj_pop_opt,pop_init,fobj_pop_init] = optim_nsga(ga_f,pop_size,nb_generation,p_mut,p_cross,Log,param,sigma,pow)

## Arguments

ga_f

  the function to be optimized. The prototype if y = f(x) or y = list(f,p1,p2,...).

pop_size

  the size of the population of individuals (default value: 100).

nb_generation

  the number of generations (equivalent to the number of iterations in classical optimization) to be computed (default value: 10).

p_mut

  the mutation probability (default value: 0.1).

p_cross

  the crossover probability (default value: 0.7).

Log

  if %T, we will display to information message during the run of the genetic algorithm.

param

  a list of parameters.

  - 'codage_func': the function which will perform the coding and decoding of individuals (default function: codage_identity).

  - 'init_func': the function which will perform the initialization of the population (default function: init_ga_default).

  - 'dimension', 'minbounds' and 'maxbounds': parameters used by the initialization function to define the initial population.

  - 'crossover_func': the function which will perform the crossover between two individuals (default function: crossover_ga_default).

  - 'mutation_func': the function which will perform the mutation of one individual (default function: mutation_ga_default).

  - 'selection_func': the function whcih will perform the selection of individuals at the end of a generation (default function: selection_ga_elitist).

  - 'nb_couples': the number of couples which will be selected so as to perform the crossover and mutation (default value: 100).

  - 'pressure': the value the efficiency of the worst individual (default value: 0.05).

sigma

  the radius of the sharing area.

pow

  the power coefficient of the penalty formula.

pop_opt

  the population of optimal individuals.

fobj_pop_opt

  the set of objective function values associated to pop_opt (optional).

pop_init

  the initial population of individuals (optional).

fobj_pop_init

  the set of objective function values associated to pop_init (optional).

## Description

- This function implements the classical "Niched Sharing Genetic Algorithm". For a demonstration, see SCI/modules/genetic_algorithms/demos/NSGAdemo.sce

## Examples

    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

    PopSize     = 100;
    Proba_cross = 0.5;
    Proba_mut   = 0.3;
    NbGen       = 4;
    NbCouples   = 110;
    Log         = %T;
    nb_disp     = 10; // Nb point to display from the optimal population
    pressure    = 0.1;

    ga_params = init_param();
    ga_params = add_param(ga_params,'dimension',2);
    ga_params = add_param(ga_params,'minbound',zeros(2,1));
    ga_params = add_param(ga_params,'maxbound',ones(2,1));

    [pop_opt, fobj_pop_opt, pop_init, fobj_pop_init] = optim_nsga(deb_1, PopSize,NbGen, Proba_mut, Proba_cross, Log, ga_params)

## See Also

- optim_moga
- optim_ga
- optim_nsga2