Internal behavior analysis of GA and PSO using problem-specific distance functions

Evolutionary computations such as a genetic algorithm (GA) and particle swarm optimization (PSO), which is inspired by the evolutionary computations, are based on exploiting a population of potential solutions. Their goal is to evolve through a time randomly generated initial population toward an improved final population, which may contain the optimal or near-optimal solutions. The converge rate depends on population diversity. Here diversity means a collection of solutions coming from different points of the search space, and each solution contains a characteristic needed in the optimal or near-optimal solution. Thus, we developed problem-specific distance functions (PSDF), which are a set of collected measurements pointing out the internal behavior (similarity and difference) between the current optimal-solution to the rest of the population. In this paper, we examined and compared the internal behavior of GA and PSO based on PSDF for the three well-known mathematical benchmark functions: DeJong Fl, Rastrigin and Rosenbrock. Our results have shown that PSO has more steady and smooth mean distance function value as compared to GA for all the three mathematical benchmark functions. In the case of GA, the mean distance function kept oscillating between the bounded values, which needed a considerable number of generations for convergence. In the case of PSO, the mean distance function started with a large value, but smoothly converged to an optimum value in few generations