Introducing dynamic diversity into a discrete particle swarm optimization

Particle swarm optimization (PSO) is an evolutionary metaheuristic inspired by the flocking behaviour of birds, which has successfully been used to solve several kinds of problems, although there are few studies aimed at solving discrete optimization problems. One disadvantage of PSO is the risk of a premature search convergence. To prevent this, we propose to introduce diversity into a discrete PSO by adding a random velocity. The degree of the introduced diversity is not static (i.e. preset before running PSO) but instead changes dynamically according to the heterogeneity of the population (i.e. if the search has converged or not). We solve the response time variability problem (RTVP) to test these two new ideas. The RTVP is an NP-hard combinatorial scheduling problem that has recently appeared in the literature. It occurs whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the instants at which they receive the necessary resources is minimized. The most efficient algorithm for solving non-small instances of the RTVP published to date is a classical PSO algorithm, referred to by the authors as PSO-M1F. In this paper, we propose 10 discrete PSO algorithms for solving the RTVP: one based on the ideas described above (PSO-c"3dyn) and nine based on strategies proposed in the literature and adapted for solving a discrete optimization problem such as the RTVP. We compare all 11 PSO algorithms and the computational experiment shows that, on average, the best results obtained are due to our proposal of dynamic control mechanism for introducing diversity.