Superior solution guided particle swarm optimization combined with local search techniques

• A superior solutions guided particle swarm optimization is proposed (SSG-PSO).
• A novel individual level based mutation strategy is incorporated into SSG-PSO.
• SSG-PSO is combined with four gradient-based or derivative-free local search methods.

Particle swarm optimization (PSO) is an evolutionary algorithm known for its simplicity and effectiveness in solving various optimization problems. PSO should have strong yet balanced exploration and exploitation capabilities to enhance its performance. A superior solution guided PSO (SSG-PSO) framework integrated with an individual level based mutation operator and different local search techniques is proposed in this study. In SSG-PSO, a collection of superior solutions is maintained and updated with the evolutionary process, such that each particle can comprehensively learn from the recorded superior solutions. In addition, to maintain the diversity of the particle swarm, SSG-PSO is combined with an individual level based mutation operator, which will be invoked when a particle is trapped in a local optimum (determined by the fitness and position states of the particle), thereby improving the adaptation and flexibility of each individual particle. Moreover, two gradient-based local search techniques, namely, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) and Davidon–Fletcher–Powell (DFP) Quasi–Newton methods, and two derivative-free local search techniques, namely, pattern search and Nelder–Mead simplex search, are incorporated into SSG-PSO. The performances of SSG-PSO and that of its local search enhanced variants are extensively and comparatively studied on a suit of benchmark optimization functions.