基于梯度扩散的自适应迁移双层进化优化算法

Adaptive Transfer Bilevel Evolutionary Optimization Algorithm Based on Gradient Diffusion

摘要: 进化双层优化因其广泛的适用性而日益受到关注，其中下层优化任务间的知识迁移在提升上层基于种群的搜索效率方面发挥着重要作用。迁移学习方法提供了灵活的范式，但在跨相关下层优化任务利用信息时，常面临效率低下甚至负迁移的问题。为解决这些问题，本文提出ATEB-GD——一种基于梯度扩散(GD)的自适应迁移进化双层优化算法。具体而言，该方法采用基于梯度扩散的框架来实现有效的下层梯度迁移，其中设计了混合距离度量以量化下层任务相似性，并融入双进度驱动的自适应策略来调控知识迁移的时机与强度。此外，进一步设计了动态更新的权重矩阵，实现相似任务间梯度信息的定向共享，同时双模式更新机制确保仅当满足迁移条件时才执行基于梯度扩散的更新。在两个广泛使用的双层基准测试集上的实验评估表明，与三种先进的进化基线算法相比，所提算法在性能和稳定性方面均表现出显著优势。

Abstract: Evolutionary Bilevel optimization has gained increasing attention due to its broad applicability, where the knowledge transfer among lower-level optimization tasks plays an important role in improving the efficiency of upper-level population-based search. Transfer learning methods provide a flexible paradigm but often suffer from inefficient or even negative transfer when leveraging information across related lower-level optimization tasks. To address these issues, this paper presents ATEB-GD, an adaptive transfer-based evolutionary bilevel optimization algorithm built upon gradient diffusion (GD). In particular, the proposed method employs GD-based framework to effectively transfer lower-level gradients, where a hybrid distance metric is designed to quantify lower-level task similarity, and a dual-progress-driven adaptive strategy is incorporated to regulate the timing and intensity of knowledge transfer. In addition, a dynamically updated weight matrix is further devised to enable directed sharing of gradient information among similar tasks, while a dual-mode update mechanism ensures that DGD-based updates are executed only when transfer conditions are met. Experimental evaluations on two widely used bilevel benchmark suites demonstrate that the proposed algorithm achieves superior performance and stability compared with three state-of-the-art evolutionary baselines.