FU Junhao1,2, LI Ting1,2, GE Hongwei1,2
（1. School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi 214122, China;2. Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, Wuxi 214122, China）
Abstract： The diversity of individuals affects the quality of the solution sets and determines the distribution of the solution sets in solving multi-objective optimization problems. In order to expand the search direction of individuals, increase the diversity of the population and avoid individuals from gathering at the boundary during the mutation process, a chaotic opposition initialization and average mutation update-based differential evolution (COI-AMU_DE) is proposed. Firstly, in order to generate a uniformly distributed initial population, random numbers are subjected to tent chaotic map and opposition-based learning in the initialization process to generate uniformly distributed random numbers. Secondly, a mutation operator is processed to avoid individuals from gathering at the boundary to improve the diversity of population. In each iteration, the average mutation update of the individuals is carried out for legalization, and the weighted sum of the rankings based on the Pareto dominance and the constrained dominance principle (CDP) are calculated. Then the next generation of individuals is selected according to the weighted sum sorting, and the process is repeated until the end condition is satisfied to obtain the result sets. Finally, a total of 38 multi-objective optimization problems in three test suites are selected to evaluate the performance of the proposed algorithm, and it is compared with seven algorithms. The simulation results show that COI-AMU_DE has high comprehensive performance in solving constrained multi-objective optimization problems.
Key words： chaotic opposition initialization; multi-objective optimization; differential evolution; mutant operators; average mutation update
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一种具有反向混沌映射的平均突变修补差分进化算法
付俊豪1,2, 李婷1,2, 葛洪伟1,2
（1. 江南大学 人工智能与计算机学院， 江苏 无锡 214122；2. 江南大学 江苏省模式识别与计算智能工程实验室， 江苏 无锡 214122）
摘要：在求解多目标优化问题上， 个体的多样性影响了求得解集的质量， 决定了解集的分布性。 为了扩大个体的搜索方向， 增大种群的多样性， 同时避免个体在变异过程中聚集在边界处， 提出了一种具有反向混沌映射的平均突变修补差分进化(Opposition chaotic initialization and average mutation repair-based differential evolution, OCI-AMR_DE)算法。 首先， 为了生成均匀分布的初始种群， 在初始化过程中对随机数进行tent混沌映射和反向学习， 以生成均匀分布的随机数。 其次， 对突变算子进行处理以避免个体聚集在边界， 从而提高种群的多样性。 在每次迭代中， 对产生突变的个体进行平均突变修补， 做合法化处理， 计算分别基于Pareto优势和约束优势原则（Constrained dominance principle， CDP）排名的加权和。 然后， 根据加权和排序选择前N个个体进入下一代， 重复上述过程至满足结束条件得到结果集。 最后， 选取3个测试函数集共38个多目标优化问题对所提算法的性能做出评估， 并将其与7种算法进行对比。 实验结果表明， OCI-AMR_DE在解决受约束多目标优化问题方面具有较强的竞争力。
关键词：反向混沌映射； 多目标优化； 差分进化算法； 突变算子； 平均突变修补
引用格式：FU Junhao, LI Ting, GE Hongwei． Chaotic opposition initialization and average mutation update-based differential evolution． Journal of Measurement Science and Instrumentation， 2023， 14（4）： 473-484. DOI： 10．3969／j．issn．1674-8042．2023．04．010
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