Solving constrained optimization via a modified genetic particle swarm optimization

The genetic particle swarm optimization (GPSO) was derived from the original particle swarm optimization (PSO), which is incorporated with the genetic reproduction mechanisms, namely crossover and mutation. Based on which a modified genetic particle swarm optimization (MGPSO) was introduced to solve constrained optimization problems. In which the differential evolution (DE) was incorporated into GPSO to enhance search performance. At each generation GPSO and DE generated a position for each particle, respectively, and the better one was accepted to be a new position for the particle. To compare and ranking the particles, the lexicographic order ranking was introduced. Moreover, DE was incorporated to the original PSO with the same method, which was used to be compared with MGSPO. MGPSO were experimented with well-known benchmark functions. By comparison with original PSO algorithms and the evolution strategy, the simulation results have shown its robust and consistent effectiveness.