Abstract-This paper proposes a new method for a modified particle swarm optimization algorithm (MPSO) combined with a simulated annealing algorithm (SA). MPSO is known as an efficient approach with a high performance of solving optimization problems in many research fields. It is a population intelligence algorithm inspired by social behavior simulations of bird flocking. Considerable research work on classical method PSO (Particle Swarm Optimization) has been done to improve the performance of this method. Therefore, the proposed hybrid optimization algorithms MPSO-SA use the combination of MPSO and simulated annealing SA. This method has the advantage to provide best results comparing with all heuristics methods PSO and SA. In this matter, a benchmark of eighteen well-known functions is given. These functions present different situations of finding the global minimum with gradual difficulties. Numerical results presented, in this paper, show the robustness of the MPSO-SA algorithm. Numerical comparisons with these three algorithms: Simulated Annealing, Modified Particle swarm optimization and MPSO-SA prove that the hybrid algorithm offers best results.

Meta-heuristic PSO has limits, such as premature convergence and high running time, especially for complex optimization problems. In this paper, a description of three parallel models based on the PSO algorithm is developed, on the basis of combining two concepts: parallelism and neighborhood, which are designed according to three different approaches in order to avoid the two disadvantages of the PSO algorithm. The third model, SPM (Spherical-neighborhood Parallel Model), is designed to improve the obtained results from the two parallel NPM (Neighborhood Parallel Model) and MPM (Multi-PSO Parallel Model) models. The experimental results presented in this paper show that SPM model performed much better than both NPM and MPM models in terms of computing time and solution quality.