Derating NichePSO

Abstract

The search for multiple solutions is applicable to many fields (Engineering [54][67], Science [75][80][79][84][86], Economics [13][59], and others [51]). Multiple solutions allow for human judgement to select the best solution from a group of solutions that best match the search criteria. Finding multiple solutions to an optimisation problem has shown to be difficult to solve. Evolutionary computation (EC) and more recently Particle Swarm Optimisation (PSO) algorithms have been used in this field to locate and maintain multiple solutions with fair success. This thesis develops and empirically analyses a new method to find multiple solutions within a convoluted search space. The method is a hybrid of the NichePSO [14] and the sequential niche technique (SNT)[8]. The original SNT was developed using a Genetic Algorithm (GA). It included restrictions such as knowing or approximating the number of solutions that exist. A further pitfall of the SNT is that it introduces false optima after modifying the search space, thereby reducing the accuracy of the solutions. However, this can be resolved with a local search in the unmodified search space. Other sequential niching algorithms require that the search be repeated sequentially until all solutions are found without considering what was learned in previous iterations, resulting in a blind and wasteful search. The NichePSO has shown to be more accurate than GA based algorithms [14][15]. It does not require knowledge of the number of solutions in the search space prior to the search process. However, the NichePSO does not scale well for problems with many optima [16]. The method developed in this thesis, referred to as the derating NichePSO, combines SNT with the NichePSO. The main objective of the derating NichePSO is to eliminate the inaccuracy of SNT and to improve the scalability of the NichePSO. The derating NichePSO is compared to the NichePSO, deterministic crowding [23] and the original SNT using various multimodal functions. The performance of the derating NichePSO is analysed and it is shown that the derating NichePSO is more accurate than SNT and more scalable than the NichePSO.