Fractional Order Darwinian Particle Swarm Optimization

% fodpso - MatLab function for Fractional Order Darwinian Particle Swarm
% Optimization (FODPSO).
% Limited to optimization problems of nine variables but can easily
% be extended for many more variables.
%
% xbest = fodpso(func)
% xbest - solution of the optimization problem. The number of columns
% depends on the input func. size(func,2)=number of xi variables
% func - string containing a mathematic expression. Variables are defined
% as xi. For instance, func='2*x1+3*x2' means that it is an optimization problem of
% two variables.
%
% [xbest,fit] = fodpso(func)
% fit - returns the optimized value of func using the xbest solution.
%
% [xbest,fit] = fodpso(func,xmin)
% xmin - minimum value of xi. size(xmin,2)=number of xi variables. Default
% -100.
%
% [xbest,fit] = fodpso(func,xmin,xmax)
% xmax - maximum value of xi. size(xmax,2)=number of xi variables. Default
% 100.
%
% [xbest,fit] = fodpso(func,xmin,xmax,type)
% type - minimization 'min' or maximization 'max' of the problem. Default
% 'min'.
%
% [xbest,fit] = fodpso(func,xmin,xmax,type,population)
% population - number of particles within each swarm. Default 20.
%
% [xbest,fit] = fodpso(func,xmin,xmax,type,population,nswarm)
% nswarms - number of starting swarms. Default 5.
%
% [xbest,fit] = fodpso(func,xmin,xmax,type,population,nswarms,iterations)
% iterations - number of iterations. Default 500.
%
% [xbest,fit] = fodpso(func,xmin,xmax,type,population,nswarms,iterations,alfa)
% alfa - fractional coefficient. Default 0.6.
%
% Example: [xbest,fit,time] = fodpso('10+5*x1^2-0.8*x2',[-10 -20],[20 40],'min')
%
% Micael S. Couceiro
% v1.0
% 04/05/2014
%
% Original PSO developed by:
% Kennedy, J. and Eberhart, R. C. (1995).
% "Particle swarm optimization".
% Proceedings of the IEEE 1995 International Conference on Neural Networks, pp. 1942-1948.
%
% Fractional Order Darwinian PSO developed by:
% Micael S. Couceiro, Rui P. Rocha,
% N. M. Fonseca Ferreira & J. A. Tenreiro Machado. (2012) .
% "Introducing the Fractional Order Darwinian PSO".
% Signal, Image and Video Processing, Fractional Signals and Systems.
% Springer.