膜系统下的一种多目标优化算法

提出一种基于膜优化理论的多目标优化算法，该算法受膜计算的启发，结合膜结构、多重集和反应规则来求解多目标优化问题。为了增强算法的适应能力，采用了遗传算法中的交叉与变异机制，同时在膜中引入外部档案集，并采用非支配排序和拥挤距离方法对外部档案集进行更新操作来提高搜索解的多样性。仿真实验采用标准的KUR和ZDT系列多目标问题对所提出的算法进行测试，通过该算法得出的非支配解集能够较好地逼近真实的Pareto前沿，说明所提算法在求解多目标优化问题上具有可行性和有效性。

Multi-objective optimization algorithm based on membrane system

In this paper, we propose a multi-objective optimization algorithm based on the theory of membrane optimization. Inspired by membrane computing, this algorithm combines membrane structure, multiple sets, and reaction rules to solve multi-objective optimization problems. We employ the crossover and mutation mechanism in this genetic algorithm to enhance its adaptability. We also introduce an external archive set into the membrane and design a non-dominated sorting and crowding distance method to improve the diversity of the global search solution and thereby update the introduced archive. We used multi-objective problems including KUR and ZDT to evaluate the performance of our proposed algorithm. Our results show that the non-dominated solution set derived from the proposed algorithm can better approach the real Pareto front, which confirms that the proposed algorithm is feasible and effective in solving multi-objective optimization problems.