Dynamic multiobjective optimization problems (DMOPs) are optimization problems with multiple conflicting optimization objectives, and these objectives change over time. Transfer learning-based approaches have been proven to be promising; however, a slow solving speed is one of the main obstacles preventing such methods from solving real-world problems. One of the reasons for the slow running speed is that low-quality individuals occupy a large amount of computing resources, and these individuals may lead to negative transfer. Combining high-quality individuals, such as knee points, with transfer learning is a feasible solution to this problem. However, the problem with this idea is that the number of high-quality individuals is often very small, so it is difficult to acquire substantial improvements using conventional transfer learning methods. In this paper, we propose a knee point-based transfer learning method, called KT-DMOEA, for solving dynamic multiobjective optimization problems. In the proposed method, a trend prediction model (TPM) is developed for producing the estimated knee points. Then, an imbalance transfer learning method is proposed to generate a high-quality initial population by using these estimated knee points. The advantage of this approach is that the seamless integration of a small number of high-quality individuals and the imbalance transfer learning technique can greatly improve the computational efficiency while maintaining the quality of the solution. The experimental results and performance comparisons with some chosen state-of-the-art algorithms demonstrate that the proposed design is capable of significantly improving the performance of dynamic optimization.

中文翻译：

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用于动态多目标优化的基于膝点的不平衡转移学习

动态多目标优化问题 (DMOP) 是具有多个相互冲突的优化目标的优化问题，并且这些目标会随着时间而变化。基于迁移学习的方法已被证明是有前途的；然而，缓慢的求解速度是阻碍此类方法解决现实世界问题的主要障碍之一。运行速度慢的原因之一是低素质的个体占用了大量的计算资源，这些个体可能会导致负迁移。将膝点等高质量个体与迁移学习相结合是解决此问题的可行方案。然而，这种想法的问题在于，高质量个体的数量通常很少，因此使用传统的迁移学习方法很难获得实质性的改进。在本文中，我们提出了一种基于拐点的转移学习方法，称为 KT-DMOEA，用于解决动态多目标优化问题。在所提出的方法中，开发了一种趋势预测模型（TPM）来产生估计的拐点。然后，提出了一种不平衡迁移学习方法，通过使用这些估计的拐点来生成高质量的初始种群。这种方法的优点是少量优质个体的无缝融合和不平衡迁移学习技术可以在保持解的质量的同时大大提高计算效率。