Particle Swarm Optimization and Differential Evolution Methods Hybridized with Pattern Search for Solving Optimization Problems

Derivative-free methods are being explored recently due to the increased complexity of the models used in the optimization problems, and the impossibility/inconvenience of using derivatives in several situations. However, those methods show some limitations due to their low convergence rate, and when the problem is high-dimensional. Metaheuristics are another commonly adopted type of search technique. Despite their robustness, metaheuristics require a large number of objective function evaluations to find an accurate solution. The combination of derivative-free optimization methods with population-based metaheuristics is analyzed here. Specifically, Particle Swarm Optimization and Differential Evolution are hybridized with Pattern Search technique. Also, an improvement of the conventional pattern search is proposed. Finally, computational experiments are performed to comparatively analyze the hybrid methods and the proposed pattern search.