Particle swarm optimization (PSO) is widely used in industrial and academic research to solve optimization problems. Recent developments of PSO show a direction towards adaptive PSO (APSO). APSO changes its behaviour during the optimization process based on information gathered at each iteration. It has been shown that APSO is able to solve a wide range of difficult optimization problems efficiently and effectively. In classical PSO, all parameters are fixed for the entire swarm. In particular, all particles share the same settings of their velocity weights. We propose four APSO variants in which every particle has its own velocity weights. We use PSO to optimize the settings of the velocity weights of every particle at every iteration, thereby creating a step-optimized PSO (SOPSO). We implement four known PSO variants (global best PSO,
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