Padding the dimensions for knowledge transfer in the dynamic vector evaluated particle swarm optimisation algorithm

Most real world problems have more than one objective, with at least two objectives in conflict with one another and at least one objective that is dynamic in nature. The dynamic vector evaluated particle swarm optimisation (DVEPSO) algorithm is a co-operative algorithm, where each sub-swarm solves only one objective function and therefore, each sub-swarm optimises only a sub-set of decision variables. Knowledge is shared amongst the sub-swarms when the particles' velocity is updated, by using the position of the global guide of the subswarm or of another sub-swarm. The global guide can only provide information about the decision variables that are applicable to the objective function that its sub-swarm is optimising. Therefore, padding is required for the other decision variables. This paper investigates various padding approaches, namely using the sub-swarm's global best, using the personal best (pbest) of another particle in the sub-swarm, using the global best (gbest) of another sub-swarm or performing parent-centric crossover on another particle's position, pbest and gbest. Results indicate that using a random gbest or pbest performed well in fast changing environments, and using the sub-swarm's gbest performed well in slowly changing environments.