Research On Multi-objective Charged System Search Algorithm

Many problems in daily life and engineering involve the simultaneous optimization of several conflicting objectives, and those are the so-called multi-objective optimization problems (MOPs).In most cases, multi-objective optimization problems don’t have a unique optimal solution but a set of solutions representing different trade-offs amongst the objectives. As a result of computational and space limitations, a multi-objective optimizer is often unable to retain all generated trade-off solutions and instead must endeavor to keep the solutions that best cover the trade-off front. Recently, the research on multi-objective optimization problems has been a highly discussed issue in the field of optimization and evolutionary computation.We mainly focus on two aspects of multi-objective optimization problems in our work:on one hand, the run-time complexity of the construction methods of multi-objective non-dominated set is deeply investigated from the theoretical view of multi-objective optimization; on the other hand, how to figure out efficient optimization algorithms is further considered in the context from the view of algorithm design. Specifically, our work includes the following issues:(1) The concepts of domination relationship and domination relationship matrix have been defined, after which a method of reducing domination relationship matrix (RDRM) is presented to extract non-dominated solutions to improve the optimization efficiency. The proposed method has been theoretically proved to be correct and its computational complexity has been analyzed, and the experimental results have illustrated its efficiency.(2) For the design of optimization algorithm, the mechanism of the state-of-the-art charged system search (CSS) algorithm has been deeply investigated. The theoretical evidence that CSS algorithm can be used to solve multi-objective optimization problems has been given, along with the feasible idea of combination.(3) The novel CSS algorithm is integrated into the framework of multi-objective optimization by proposing a new technique of circular sorting of non-domination preference, in which RDRM is utilized to reduce the run-time of grading solutions and the circular sorting of maximum-minimum crowding-distance is used to select elite individuals for CSS algorithm.The above strategies shape the algorithm of CSS-based multi-objective optimization using the method of circular sorting non-domination preference. Experimental results show that the proposed algorithm is efficient and valid.(4) As to the quality measure of solutions, most existed indicator except of Hypervolume indicator can merely measure the quality of obtained solutions instead of being used as selection operators in the optimization procedure while Hypervolume indicator has some vital drawbacks. Therefore, a new measure indicator-Δp contribution indicator is proposed, which is not only used as quality measure of solutions but also employed as selection indicator. The proposed indicator is exactly combined with CSS algorithm for multi-objective optimization, thus propels the formation of multi-objective charged system search algorithm based on Δp contribution indicator. Experimental results demonstrate that the proposed algorithm is excellent in multi-objective optimization and can achieve good results.