| 摘要: |
| 多模态多目标优化存在个体拥挤度难以合理定义、个体多样性计算难以动态平衡决策空间和目标空间的挑战, 现有多模态多目标优化算法在性能上尚存在较大提升空间. 为此, 提出了一种个体多样性自适应的多模态多目标差分进化算法(multimodal multiobjective differential evolution algorithm based on adaptive individual diversity, MMODE-AID). 首先, 以个体在决策空间或目标空间的最近邻平均欧氏距离为基础, 通过对个体间相对距离的累乘定义个体的拥挤度, 可以更合理地衡量各个体在相应空间的真实拥挤程度. 其次, 基于决策空间和目标空间各自的整体拥挤度, 得到个体在相应空间的拥挤度相对值, 可以合理地动态平衡进化过程中决策空间和目标空间当前状态对个体多样性计算的影响, 有利于各等效帕累托最优解集的充分搜索. MMODE-AID以差分进化为基础优化框架, 并基于自适应个体多样性评估个体的适应度, 可在子代生成和环境选择时得到在决策空间分布、目标空间分布、收敛性这3方面均表现优异的种群. 为验证MMODE-AID的性能, 将其与7个先进的多模态多目标优化算法在39个基准测试问题和1个实际应用问题上进行对比. 实验结果表明MMODE-AID对于多模态多目标优化问题的求解具有明显竞争优势. MMODE-AID的源代码和原始实验数据已在GitHub上公开: https://github.com/CIA-SZU/ZQ. |
| 关键词: 拥挤度 多样性 多模态多目标优化 差分进化 |
| DOI：10.13328/j.cnki.jos.007578 |
| 分类号:TP18 |
| 基金项目:国家自然科学基金(62572327); 广东省自然科学基金(2025A1515010260) |
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| Multimodal Multiobjective Differential Evolution Algorithm Based on Adaptive Individual Diversity |
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MAO Fei-Qiao, ZHOU Qian, HOU Wei-Jun, ZENG Wen-Jun, LIANG Zheng-Ping
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College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China
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| Abstract: |
| As multimodal multiobjective optimization faces challenges of reasonably defining the individual crowdedness and dynamically balancing the decision space and objective space in individual diversity calculation, there is still significant room for performance improvement in existing multimodal multiobjective optimization algorithms. To this end, this study proposes a multimodal multiobjective differential evolution algorithm based on adaptive individual diversity (MMODE-AID). First, based on the average Euclidean distance of individuals’ nearest neighbors in the decision space or objective space, the crowdedness of individuals can be defined by multiplying the relative distances between individuals, which can more reasonably measure the true crowdedness of each individual in the corresponding space. Second, based on the overall crowdedness of the decision space and objective space, the relative crowdedness of individuals in the corresponding space is obtained, which can reasonably and dynamically balance the influence of the current state of the decision space and objective space on individual diversity calculation during the evolution process, and is conducive to the sufficient search of each equivalent Pareto optimal solution set. By employing differential evolution as the basic optimization framework, MMODE-AID evaluates individual fitness based on adaptive individual diversity. Meanwhile, it can obtain a population with excellent performance in decision space distribution, objective space distribution and convergence during offspring generation and environmental selection. MMODE-AID is compared with seven advanced multimodal multiobjective optimization algorithms on 39 benchmark test problems and one real-world application problem to validate the algorithm’s performance. The experimental results demonstrate that MMODE-AID exhibits significant competitive advantages in solving multimodal multiobjective optimization problems. The source code and original experimental data of MMODE-AID are publicly available on GitHub: https://github.com/CIA-SZU/ZQ. |
| Key words: crowdedness diversity multimodal multiobjective optimization differential evolution |
