The hybrid algorithm based on the Hook-Jeeves search method and the local constriction approach particle swarm optimization (PSO) with linear varying inertia weight (HJ-LLPSO) for unconstrained optimization was put forward. HJ-LLPSO is very easy to implement in practice since it does not require gradient computation. The modification of the particle swarm optimization intends to produce faster and more accurate convergence. The main purpose is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybrid strategy. In a suit of 6 test function problems taken from the literature, computational results via a comprehensive experimental study show that the hybrid HJ-LLPSO approach outperforms other two relevant search techniques (i.e., the original PSO and PSO combined with chaos) in terms of solution quality and convergence rate. As evidenced by the overall assessment based on computational experience, the new algorithm is extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization.

The hybrid Powell-LLPSO algorithm based on the Powell search method and the local constriction approach particle swarm optimization with linear varying inertia weight for unconstrained optimization was proposed. Powel-LLPSO is very easy to implement in practice since does not require gradient computation. The modification of both the Powell search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybrid strategy. In a suit of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid Powell-LLPSO approach outperforms other three relevant search techniques (the original PSO, the guaranteed convergence particle swarm optimization (GCPSO) and hybrid NM-PSO) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the Powell-LLPSO algorithm was compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the Powell-LLPSO algorithm in the performance of accuracy, robustness and function evaluation.