Interaction Variable Neighborhood Particle Swarm Optimization

Particle swarm optimization (PSO) is a population-based optimization algorithm by simulating bird flocking. Due to its fast convergent speed, it is easily trapped into a local optimum when optimizing multi-modal high dimensional problems. To deal with this problem, topological structure design is proposed. However, the previous structures are all with fixed manner, while it can not reflect the problem characters. Therefore, in this article, two interactive dynamic topological structures are designed with the small-world models. .In the process to seek the food, some useful information will be transferred among individuals with some topological structures; however, these structures are often changed due to some unpredicted reasons. Inspired by this phenomenon, the Watts and Strogatz small-world model is incorporated into the methodology of PSO, thus resulting a new variant of PSO, WS model-based PSO (WSPSO). In WSPSO, the neighborhood topologyare adjusted dynamically.Although the stochastic linkage mechanism of WS model increases the population diversity, it will destroy the connectivity among particles. To overcome this shortcoming, Newman and Watts proposed a new model in which the old linkages are not removed, only the new edges are added among particles. Therefore, in this article, Newman and Watts model is also employed to increase the population diversity, simulation results show it is effective.The historical best position among neighborhood plays an important role in affecting the performance of PSO. In this article, the group decision strategy is introduced into WSPSO and NWPSO, respectively. In these two variants, the historical best position is replaced by one decided position to further increase the population diversity. Simulation results show all of them are superior to other two variants of PSO significantly when dealing with multi-modal high dimension problems.