Multimodal multiobjective problems (MMOPs) exist in scientific research and practical projects, and their Pareto solution sets correspond to the same Pareto front. Existing evolutionary algorithms often fall into local optima when solving such problems, which usually leads to insufficient search solutions and their uneven distribution in the Pareto front. In this work, an improved membrane algorithm is proposed for solving MMOPs, which is based on the framework of P system. More specifically, the proposed algorithm employs three elements from P system: object, reaction rule, and membrane structure. The object is implemented by real number coding and represents a candidate solution to the optimization problem to be solved. The function of the reaction rule of the proposed algorithm is similar to the evolution operation of the evolutionary algorithm. It can evolve the object to obtain a better candidate solution set. The membrane structure is the evolutionary logic of the proposed algorithm. It consists of several membranes, each of which is an independent evolutionary unit. This structure is used to maintain the diversity of objects, so that it provides multiple Pareto sets as output. The effectiveness verification study was carried out in simulation experiments. The simulation results show that compared with other experimental algorithms, the proposed algorithm has a competitive advantage in solving all 22 multimodal benchmark test problems in CEC2019.

中文翻译：

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P系统框架下改进膜算法求解多模态多目标问题

多模态多目标问题（MMOPs）存在于科学研究和实际项目中，它们的帕累托解集对应同一个帕累托前沿。现有的进化算法在解决此类问题时往往会陷入局部最优，这通常会导致搜索解决方案不足及其在帕累托前沿的分布不均匀。在这项工作中，提出了一种基于P系统框架的改进的膜算法来解决MMOPs。更具体地说，所提出的算法采用了 P 系统的三个元素：对象、反应规则和膜结构。该对象通过实数编码实现，表示待解决的优化问题的候选解。该算法的反应规则的作用类似于进化算法的进化操作。它可以对对象进行进化以获得更好的候选解集。膜结构是所提出算法的进化逻辑。它由几个膜组成，每个膜都是一个独立的进化单元。该结构用于保持对象的多样性，使其提供多个帕累托集作为输出。在仿真实验中进行了有效性验证研究。仿真结果表明，与其他实验算法相比，所提算法在解决CEC2019所有22个多模态基准测试问题方面具有竞争优势。该结构用于保持对象的多样性，使其提供多个帕累托集作为输出。在仿真实验中进行了有效性验证研究。仿真结果表明，与其他实验算法相比，所提算法在解决CEC2019所有22个多模态基准测试问题方面具有竞争优势。该结构用于保持对象的多样性，使其提供多个帕累托集作为输出。在仿真实验中进行了有效性验证研究。仿真结果表明，与其他实验算法相比，所提算法在解决CEC2019所有22个多模态基准测试问题方面具有竞争优势。