Multi-domain diversity preservation to mitigate particle stagnation and enable better pareto coverage in mixed-discrete particle swarm optimization

This paper makes important advancements to a Particle Swarm Optimization (PSO) algorithm, which seeks to address the major complex attributes of engineering optimization problems, namely multiple objectives, high nonlinearity, high dimensionality, constraints, and mixed-discrete variables. To introduce these capabilities while keeping PSO competitive with other powerful multi-objective algorithms (e.g., NSGA-II, SPEA, and PAES), it is important to not only preserve population diversity (for mitigating stagnation), but also explicit diversity preservation to facilitate improved coverage of Pareto frontiers (particularly non-convex frontiers). A new multi-domain preservation technique is presented in this paper for this purpose. In this technique, an adoptive repulsion is applied to each global leader to slow down excessive clustering of particles towards popular global leaders, and instead promote all global leaders to attract a fair distribution of follower particles. In addition, the global leader selection is now modified to follow a stochastic strategy based on the half-normal distribution. Specifically, two different population diversity measures are explored: (i) based on the smallest hypercube enclosing the entire population, and (ii) based on the smallest hypercube enclosing the subset of particles following each of the global leaders. Both strategies are investigated using a suite of benchmark problems. Compared to the original MO-MDPSO, the new MO-MDPSO algorithm exhibits better robustness, thereby illustrating the potential of the modified diversity metric.