Inner Product Based Particle Swarm Optimization

Standard Particle Swarm Optimization (SPSO)is a well-known and very competitive swarm optimization approach, which is designed by Particle Swarm Central. In all PSO variants, the relative position relation between the individual and the global optimal position has important influences on the performance of algorithms. In this paper, an alternative Standard Particle Swarm Optimization (SPSO 2007)is proposed, which is based on the inner product of difference vectors. One particle will confuse which solution it should learn from when the global best and the personal best positions have comparable attractions to different directions during its velocity updating process. Even the oscillation phenomenon will appear that the global best solution draws the particle close to it at one generation and the personal best solution draws the particle back to it at next generation. In order to overcome this phenomenon particle adopts different velocity update strategies when the angle between difference vectors is either acute or obtuse of two directions in this paper. Two difference vectors refer to the current particle to the global and the personal best solutions. The vector level and the component level inner product based PSOs are proposed, denoted as IPSPSO2007V and IPSPSO2007C respectively. They are analyzed firstly and then compared with SPSO2007 with IEEE CEC2015 benchmarks, which indicate that two inner product based PSOs show promising performance.