Environmental Knowledge-Driven Transfer Strategy With Collaborative Learning for Dynamic Constrained Multi-Objective Optimization
针对现有迁移学习方法仅用欧氏距离度量环境相似性易误判的问题，提出两种结构相似性度量，并利用协同学习从历史最优解中提取隐式共享解和专属解，提升知识迁移质量，实验表明该方法显著优于七种先进算法。
In recent years, transfer learning-based dynamic constrained multi-objective optimization algorithms (TL-DCMOAs) have shown great promise in handling dynamic constrained multi-objective optimization problems (DCMOPs). In existing TL-DCMOAs, environmental similarity is typically assessed by measures based on Euclidean distance. However, such measures merely capture overall numerical differences between two environments, which are sensitive to local fluctuations in environmental information, potentially leading to misjudgments of environmental similarity. Besides, most existing TL-DCMOAs leverage historical constrained and unconstrained Pareto-optimal solutions as knowledge, but neglect relations and implicit solutions behind them for acquiring knowledge. To address the above issues, an environmental knowledge-driven transfer strategy with collaborative learning (EKTS-CL) is proposed in this article. Specifically, we design two structural similarity measures (SSMs) which consider the mean, variance, and covariance of environmental information, to comprehensively assess the environmental structural discrepancies with respect to concentration, divergence, and correlation, respectively. Using SSMs, the most structurally similar historical unconstrained Pareto-optimal solutions (UPS) and constrained Pareto-optimal solutions (CPS) can be obtained. Additionally, true CPS and UPS share partial solutions across all environments or the majority of environments of a DCMOP. From the obtained CPS and UPS that separately approximate the true CPS and UPS of the current environment, we extract implicit shared solutions and exclusive ones through collaborative learning, providing high-quality knowledge than the obtained plain solutions for knowledge transfer. Our experimental results include comprehensive comparisons with seven state-of-the-art DCMOAs, and show that the proposed EKTS-CL brings significant performance improvements in solving DCMOPs.