This paper proposes a new variant of particle swarm optimization (PSO), namely, multiple learning PSO with space transformation perturbation (MLPSO-STP), to improve the performance of PSO. The proposed MLPSO-STP uses a novel learning strategy and STP. The novel learning strategy allows each particle to learn from the average information on the personal historical best position (pbest) of all particles and from the information on multiple best positions that are randomly chosen from the top 100p% of pbest. This learning strategy enables the preservation of swarm diversity to prevent premature convergence. Meanwhile, STP increases the chance to find optimal solutions. The performance of MLPSO-STP is comprehensively evaluated in 21 unimodal and multimodal benchmark functions with or without rotation. Compared with eight popular PSO variants and seven state-of-the-art metaheuristic search algorithms, MLPSO-STP performs more competitively on the majority of the benchmark functions. Finally, MLPSO-STP shows satisfactory performance in optimizing the operating conditions of an ethylene cracking furnace to improve the yields of ethylene and propylene. 
Multiple learning particle swarm optimization with space transformation perturbation and its application in ethylene cracking furnace optimization