Many Objective Particle Swarm Optimisation: An Investigation into Strengthening Convergence by Controlling Dominance Area

The application of single and multi-objective particle swarm optimisation (PSO) is widespread, however in many-objective optimisation (problems with four or more competing objectives) traditional PSO has been less well examined. Recent progress on many-objective evolutionary optimisers has lead to the adoption of a variety of non-Pareto quality measures, it is therefore of interest to see how well PSO copes in this domain, and how non-Pareto quality measures perform when integrated into PSO. Here we review the current state of the art in multi- and many-objective PSO optimisation. We compare and contract the performance of canonical PSO, using a wide range of many-objective quality measures, on a number of different parametrised test functions for up to 30 competing objectives. We examine quality measures as selection operators for guides when truncated non-dominated archives of guides are maintained, and maintenance operators, for choosing which solutions should be maintained as guides from one generation to the next. We investigate in detail two Pareto strengthening methods, Controlling Dominance Area of Solutions (CDAS) and Self-Controlling Dominance Area of Solutions (S-CDAS). We find that CDAS and S-CDAS perform exceptionally well as a quality measures to determine archive membership for global and local guides. However, for convergence only at the cost of diversity and spread across the optimal front, single objective canonical PSO run using a linear sum of objectives, has the best performance overall