Advances on Particle Swarm Optimization in Solving Discrete Optimization Problems

Abstract

AbstractParticle Swarm Optimization (PSO) is a well-known optimization method which optimizes a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity. PSO initially proposed for continuous optimization and, to till, different discrete optimizations methods are developed adapting PSO in different time periods. The major concerns to solve discrete optimization task with PSO are the adaptation of particle encoding, velocity measurement and position update. The aim of this study is to demonstrate the evolution of PSO in solving discrete optimizations conceiving different adaptations in its operations. This study explains adaptation of PSO for four different discrete optimization problems: knapsack problem (KP), traveling salesman problem (TSP), vehicle routing problem (VRP), and university course scheduling problem (UCSP). The selected problems are well diverse having different constraints and objectives; KP seems a simplest one and UCSP is the most complex optimization task. The rhythmic presentation of PSO adaptation in solving KP, TSP, VRP and UCSP in this chapter may be a proper demonstration of PSO transformation from its original continuous domain to different discrete domains. The study will be made easy to understand other PSO-based discrete optimization methods as well as will be helpful to solve any new discrete optimization task adopting PSO.KeywordsParticle swarm optimizationKnapsack problemTraveling salesman problemVehicle routing problemUniversity course scheduling problem