Example one: estimating the parameters of a dynamic model
In this illustrative example, the parameters of a simple dynamic mathematical model are estimated using MATLAB and using all three of the global optimization algorithms that are available for download here. Just extract it, browse to that directory in MATLAB, and run the main.m script. If you have any problems or suggestions, please let me know [my email: brecht.donckels[at]biomath.ugent.be]!
Download example here.
Get more information on these and many other (global) optimization in these books...
Simplex-Simulated annealing (SIMPSA)
Algorithms based on simulated annealing employ a stochastic generation of solution vectors and employ similarities between the physical process of annealing (i.e. melting a solid by heating it, followed by slow cooling and crystallization into a minimum free energy state) and a minimization problem. During the cooling process, transitions are accepted to occur from a low to a high energy level through a Boltzmann probability distribution. For an optimization problem, this corresponds to "wrong-way" movements. This implementation contains an algorithm that was described in Cardoso et al. (1996) and is based on the combination of the non-linear smplex and simulated annealing algorithms (the SIMPSA algorithm).
Particle swarm optimization
Particle swarm optimization (PSO) is a population based stochastic optimization technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling. In PSO, each particle moves in the search space and updates its velocity according to best previous positions already found by himself and its neighbors, trying to find an even better position.
Shuffled complex evolution
The SCE method is based on a synthesis of four concepts that have proved successful for global optimization: (a) combination of probabilistic and deterministic approaches; (b) clustering; (c) systematic evolution of a complex of points spanning the space, in the direction of global improvement; and (d) competitive evolution.