Particle Swarm Optimization assisted by Gaussian Processes for Multimodal Function Optimization

In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, standard Particle Swarm Optimization (PSO) meets a special challenge for a very large number of problem function evaluations. Applying models as a surrogate of the real fitness function is proved effective way to address this challenge. This study proposes a model assisted PSO, which uses a Gaussian Process (GP) approximation model. In this algorithm, the training datasets for establishing a GP are generated by the first two generations particle information. Once the GP model is obtained, the function value is evaluated using trained GP model instead of real function evaluation, so that the total number of function evaluation is clearly reduced. In order to improve the predictive capacity of GP, the training datasets are dynamically renewed through sorting datasets and replacing the worst dataset during iterative process. Numerical results from simulations on several 20 dimensional complex multimodal functions are presented. Furthermore, a comparison of the new algorithm with the standard PSO is also made. Results show that the new algorithm is much more efficient than standard PSO. Keywords-particle swarm optimization; surrogate; gaussian process; multimodal function optimization