A novel hybrid algorithm with marriage of particle swarm optimization and extremal optimization

Particle swarm optimization (PSO) has received increasing interest from the optimization community due to its simplicity in implementation and its inexpensive computational overhead. However, PSO has premature convergence, especially in complex multimodal functions. Extremal Optimization (EO) is a recently developed local-search heuristic method and has been successfully applied to some NP-hard combinatorial optimization problems. To overcome the limitation of PSO, this paper proposes a novel hybrid algorithm, called hybrid PSO-EO algorithm, through introducing EO to PSO for the first time. The hybrid approach elegantly combines the exploration ability of PSO with the exploitation ability of EO. We also present a new hybrid mutation operator in EO that enhances the exploratory capabilities of our algorithm. The proposed approach is validated using six complex unimodal/multimodal benchmark functions. The simulation results demonstrate that the proposed approach is capable of avoiding premature convergence and is superior to three search algorithms, i.e., standard PSO, Population-based EO (PEO) and standard Genetic Algorithm (GA). Thus, the hybrid PSO-EO algorithm can be considered a good alternative to solve complex numerical function optimization problems.