Standard Particle Swarm Optimisation 2011 at CEC-2013: A baseline for future PSO improvements

In this work we benchmark, for the first time, the latest Standard Particle Swarm Optimisation algorithm (SPSO-2011) against the 28 test functions designed for the Special Session on Real-Parameter Single Objective Optimisation at CEC-2013. SPSO-2011 is a major improvement over previous PSO versions, with an adaptive random topology and rotational invariance constituting the main advancements. Results showed an outstanding performance of SPSO-2011 for the family of unimodal and separable test functions, with a fast convergence to the global optimum, while good performance was observed for four rotated multimodal functions. Conversely, SPSO-2011 showed the weakest performance for all composition problems (i.e. highly complex functions specially designed for this competition) and certain multimodal test functions. In general, a fast convergence towards the region of the global optimum was achieved, requiring less than 10E+03 function evaluations. However, for most composition and multimodal functions SPSO2011 showed a limited capability to “escape” from sub-optimal regions. Despite this limitation, a desirable feature of SPSO-2011 was its scalable behaviour, which observed up to 50-dimensional problems, i.e. keeping a similar performance across dimensions with no need for increasing the population size. Therefore, it seems advisable that future PSO improvements be focused on enhancing the algorithm's ability to solve non-separable and asymmetrical functions, with a large number of local minima and a second global minimum located far from the true optimum. This work is the first effort towards providing a baseline for a fair comparison of future PSO improvements.