基于动态变量相关性消减的多目标多任务进化算法

Multi-Objective Multitasking Evolutionary Algorithm with Dynamic Correlation Reduction

摘要: 多目标多任务优化(MTO)是进化计算领域的重要分支。变量相关性对遗传操作的挑战一直影响着多目标多任务优化的效率，但这一问题尚未得到认真考虑。为此，本文提出了一种基于动态变量相关性消减的多目标多任务进化算法(MTO-DCR)，通过结合学习到的变量协方差矩阵进行坐标变换以减少变量相关性。具体而言，MTO-DCR首先通过坐标变换动态减少变量相关性以生成后代。为学习变量相关性，针对每个任务分别维护了独立的协方差自适应搜索。此外，提出了一种基于缩放变换的领域迁移策略，用于将源任务中表现优异的个体迁移到目标任务中。为验证所提MTO-DCR的有效性和效率，构建了一组具有可控非可分性和难度的可扩展MOMTOP测试实例进行实验研究。结果分析及与最新算法(MO-SBO、MO-MaTDE和MO-EMaTO-MKT)的对比表明，所提MTO-DCR能够有效处理具有相关变量的MTO问题。

Abstract: Multi-objective multi-task optimization (MTO) is an important branch of evolutionary computation. The challenge of variable dependency in genetic operations has consistently impacted the efficiency of multi-objective multi-task optimization, yet this issue has not been thoroughly addressed. To this end, this paper proposes a multi-objective multi-task evolutionary algorithm based on dynamic variable dependency reduction (MTO-DCR), which reduces variable dependency through coordinate transformation using a learned covariance matrix. Specifically, MTO-DCR dynamically reduces variable dependency via coordinate transformation to generate offspring. To learn variable dependencies, independent covariance adaptive searches are maintained for each task. Additionally, a domain transfer strategy based on scaling transformation is proposed to migrate well-performing individuals from source tasks to target tasks. To validate the effectiveness and efficiency of the proposed MTO-DCR, a set of scalable MOMTOP test instances with controllable non-separability and difficulty levels is constructed for experimental studies. Results analysis and comparisons with state-of-the-art algorithms (MO-SBO, MO-MaTDE, and MO-EMaTO-MKT) demonstrate that the proposed MTO-DCR effectively handles MTO problems with correlated variables.