Browsing by Author "Cai, Z."

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    A comparative study of constraint-handling techniques in constrained multiobjective evolutionary optimization
    (IEEE Press, 2016-07-25) Li, Jiapeng; Wang, Yong; Yang, Shengxiang; Cai, Z.
    Solving constrained multiobjective optimization problems is one of the most challenging areas in the evolutionary computation research community. To solve a constrained multiobjective optimization problem, an algorithm should tackle the objective functions and the constraints simultaneously. As a result, many constraint-handling techniques have been proposed. However, most of the existing constraint-handling techniques are developed to solve test instances (e.g., CTPs) with low dimension and large feasible region. On the other hand, experimental comparisons on different constraint-handling techniques remain scarce. In view of these two issues, in this paper we first construct 18 test instances, each of which exhibits different properties. Afterward, we choose three representative constraint-handling techniques and combine them with nondominated sorting genetic algorithm II to study the performance difference on various conditions. By the experimental studies, we point out the advantages and disadvantages of different constraint-handling techniques.
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    Differential evolution with a two-stage optimization mechanism for numerical optimization
    (IEEE Press, 2016-07-25) Liu, Zhizhong; Wang, Yong; Yang, Shengxiang; Cai, Z.
    Differential Evolution (DE) is a popular paradigm of evolutionary algorithms, which has been successfully applied to solve different kinds of optimization problems. To design an effective DE, it is necessary to consider different requirements of the exploration and exploitation at different evolutionary stages. Motivated by this consideration, a new DE with a two-stage optimization mechanism, called TSDE, has been proposed in this paper. In TSDE, based on the number of fitness evaluations, the whole evolutionary process is divided into two stages, namely the former stage and the latter stage. TSDE focuses on improving the search ability in the former stage and emphasizes the convergence in the latter stage. Hence, different trial vector generation strategies have been utilized at different stages. TSDE has been tested on 25 benchmark test functions from IEEE CEC2005 and 30 benchmark test functions from IEEE CEC2014. The experimental results suggest that TSDE performs better than four other state-of-the-art DE variants.
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    A weighted biobjective transformation technique for locating multiple optimal solutions of nonlinear equation systems
    (IEEE Press, 2017) Yang, Shengxiang; Gong, Wenyin; Wang, Yong; Cai, Z.
    Due to the fact that a nonlinear equation system may contain multiple optimal solutions, solving nonlinear equation systems is one of the most important challenges in numerical computation. When applying evolutionary algorithms to solve nonlinear equation systems, two issues should be considered: i) how to transform a nonlinear equation system into a kind of optimization problem, and ii) how to develop an optimization algorithm to solve the transformed optimization problem. In this paper, we tackle the first issue by transforming a nonlinear equation system into a weighted biobjective optimization problem. By the above transformation, not only do all the optimal solutions of an original nonlinear equation system become the Pareto optimal solutions of the transformed biobjective optimization problem, but also their images are different points on a linear Pareto front in the objective space. In addition, we suggest an adaptive multiobjective differential evolution, the goal of which is to effectively locate the Pareto optimal solutions of the transformed biobjective optimization problem. Once these solutions are found, the optimal solutions of the original nonlinear equation system can also be obtained correspondingly. By combining the weighted biobjective transformation technique with the adaptive multiobjective differential evolution, we propose a generic framework for the simultaneous locating of multiple optimal solutions of nonlinear equation systems. Comprehensive experiments on 38 nonlinear equation systems with various features have demonstrated that our framework provides very competitive overall performance compared with several state-of-the-art methods.