Abstract

A two-stage R2 indicator-based evolution algorithm (TS-R2EA) was proposed in the recent years. A good balance between convergence and diversity can be achieved, due to the R2 indicator and reference vector-guided selection strategy. However, TSR2-EA is sensitive to problem geometries. In order to address this issue, a weight vector-based selection strategy is introduced, and a weight vector adaptive strategy based on population partition is proposed. In the selection strategy, each candidate solution is ranked according to the scalarizing function values in the corresponding neighbor, and the candidate solutions with good performance can be selected. In the adaptive strategy, the population is partitioned by associating each individual with its closest weight vector, and the weight vectors with a worse performance are adjusted. Similar to TS-R2EA, these strategies are combined with the R2 indicator to solve multi-objective optimization problems. The performance of proposed algorithm has been validated and compared with four related algorithms on a variety of benchmark test problems. The experimental results have demonstrated that the proposed algorithm has high competition and is less sensitive to problem geometries.

中文翻译：

---

基于R2指标和权重向量的进化算法用于多目标优化

摘要

近年来，提出了一种基于R2指标的两阶段演化算法（TS-R2EA）。由于采用了R2指标和参考矢量指导的选择策略，因此可以在收敛和多样性之间实现良好的平衡。但是，TSR2-EA对问题的几何形状很敏感。为了解决这个问题，提出了一种基于权向量的选择策略，并提出了一种基于种群划分的权向量自适应策略。在选择策略中，根据对应邻域中的标量函数值对每个候选解进行排序，从而可以选择性能好的候选解。在自适应策略中，通过将每个个体与其最接近的权重向量相关联来对总体进行划分，并调整性能较差的权重向量。与TS-R2EA类似，这些策略与R2指标结合起来解决了多目标优化问题。在各种基准测试问题上，所提出算法的性能已得到验证，并与四种相关算法进行了比较。实验结果表明，该算法竞争激烈，对问题的几何形状不敏感。