UDE-III：一种面向约束优化问题的增强型统一差分进化算法
UDE-III: An Enhanced Unified Differential Evolution Algorithm for Constrained Optimization Problems
AI总结：
针对实参数约束优化问题，本文提出增强型统一差分进化算法UDE-III，通过双种群策略、多试验向量生成、排序变异、自适应参数与约束处理及停滞应对机制，在CEC 2024基准测试上表现优于UDE-II。
摘要：
本文提出了一种增强型统一差分进化算法，命名为UDE-III，用于求解实参数约束优化问题（COPs）。所提出的UDE-III是改进型UDE（即IUDE，也称为UDE-II）的显著增强版本，后者曾在CEC 2018实参数约束优化问题竞赛中获得第一名。为设计UDE-III，我们针对性地解决了UDE-II的诸多缺陷。具体而言，UDE-III采用三种试验向量生成策略：DE/rand/1、DE/current-to-rand/1和DE/current-to-pbest/1。该算法基于双种群方法，每一代都会将当前种群划分为两个子种群。在顶部子种群中，每个目标向量都会使用全部三种试验向量生成策略；而在底部子种群中则采用策略自适应机制，每个目标向量仅使用一种试验向量生成策略。UDE-III的变异操作基于排序变异，同时采用了SHADE的参数自适应原理，约束处理机制则结合了可行性规则与epsilon约束处理技术。我们发现停滞问题是UDE-II的主要缺陷，为克服这一问题，我们受文献中提出的最佳丢弃向量选择（BDVS）策略启发，在UDE-III中集成了一种新策略来解决停滞问题。此外，与UDE-II不同，UDE-III将两个子种群的规模作为设计要素，并且在策略自适应、排序变异和约束处理技术方面均对UDE-II进行了改进。我们在CEC 2024实参数约束优化问题竞赛提供的28个30维基准问题上对所提出的UDE-III算法进行了测试，实验结果证明了UDE-III相较于UDE-II的优越性。
英文摘要：
In this paper, an enhanced unified differential evolution algorithm, named UDE-III, is presented for real parameter-constrained optimization problems (COPs). The proposed UDE-III is a significantly enhanced version of the Improved UDE (i.e., IUDE or UDE-II), which secured the 1st rank in the CEC 2018 competition on real parameter COPs. To design UDE-III, we extensively targeted the weaknesses of UDE-II. Specifically, UDE-III uses three trial vector generation strategies - DE/rand/1, DE/current-to-rand/1, and DE/current-to-pbest/1. It is based on a dual population approach, and for each generation, it divides the current population into two sub-populations. In the top sub-population, it employs all three trial vector generation strategies on each target vector. On the other hand, the bottom sub-population employs strategy adaptation and one trial vector generation strategy is implemented on each target vector. The mutation operation in UDE-III is based on ranking-based mutation. Further, it employs the parameter adaptation principle of SHADE. The constraint handling principle in UDE-III is based on a combination of the feasibility rule and epsilon-constraint handling technique. We observed that stagnation is a major weakness of UDE-II. To overcome this weakness, we took inspiration from the best-discarded vector selection (BDVS) strategy proposed in the literature and integrated a novel strategy in UDE-III to address stagnation. Additionally, unlike UDE-II, UDE-III considers the size of the two sub-populations to be a design element. Moreover, in comparison to UDE-II, UDE-III improves upon the strategy adaptation, ranking-based mutation, and the constraint handling technique. The proposed UDE-III algorithm is tested on the 28 benchmark 30D problems provided for the CEC 2024 competition on real parameter COPs. The experimental results demonstrate the superiority of UDE-III over UDE-II.
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