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Abstract: This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence. [Copyright &y& Elsevier]

In practical applications, solving multimodal multiobjective optimization problems (MMOPs), which have multiple Pareto optimal sets (PSs) in the decision space mapping to the same Pareto front (PF) in the objective space, has great significance for decision makers. The issue of how to maintain diversity in both decision space and objective space remains a key problem for existing multimodal multiobjective evolutionary algorithms. To address this issue, a novel grey prediction evolution algorithm for multimodal multiobjective optimization, termed MMGPE, is proposed in this paper. This is the first time that the grey prediction evolution algorithm (GPE), which is a recently proposed competitive optimization algorithm with strong exploration capability, is improved for MMOPs. These improvements are conducted in the following four aspects: (1) an initialization operator based on particle swarm optimization, (2) an adaptive parameter setting strategy depending on the domain of decision variables of MMOPs, (3) an accelerating convergence mechanism inspired by the niche principle, and (4) an environmental selection operator based on a nondominated sorting mechanism and a special crowding distance approach. The performance of MMGPE is compared with two state-of-the-art multiobjective evolutionary algorithms and four multimodal multiobjective evolutionary algorithms on 11 multimodal multiobjective test functions. MMGPE is also applied to solve a practical problem. The results show the MMGPE's effectiveness and superiority in achieving the goal of finding multiple PSs while obtaining a well-distributed PF. [ABSTRACT FROM AUTHOR]