IEEE Trans Cybern. 2023 Apr;53(4):2480-2493. doi: 10.1109/TCYB.2021.3125071. Epub 2023 Mar 16.
In multiobjective decision making, most knee identification algorithms implicitly assume that the given solutions are well distributed and can provide sufficient information for identifying knee solutions. However, this assumption may fail to hold when the number of objectives is large or when the shape of the Pareto front is complex. To address the above issues, we propose a knee-oriented solution augmentation (KSA) framework that converts the Pareto front into a multimodal auxiliary function whose basins correspond to the knee regions of the Pareto front. The auxiliary function is then approximated using a surrogate and its basins are identified by a peak detection method. Additional solutions are then generated in the detected basins in the objective space and mapped to the decision space with the help of an inverse model. These solutions are evaluated by the original objective functions and added to the given solution set. To assess the quality of the augmented solution set, a measurement is proposed for the verification of knee solutions when the true Pareto front is unknown. The effectiveness of KSA is verified on widely used benchmark problems and successfully applied to a hybrid electric vehicle controller design problem.
在多目标决策中，大多数膝盖识别算法隐含地假设给定的解决方案分布良好，并且可以为识别膝盖解决方案提供足够的信息。然而，当目标数量很大或 Pareto 前沿的形状很复杂时，这种假设可能不成立。为了解决上述问题，我们提出了一种面向膝盖的解决方案增强 (KSA) 框架，该框架将 Pareto 前沿转换为一个多峰辅助函数，其盆地对应于 Pareto 前沿的膝盖区域。然后使用替代方法对辅助函数进行近似，并通过峰检测方法识别其盆地。然后在检测到的盆地中在目标空间中生成附加解决方案，并在逆模型的帮助下映射到决策空间。这些解决方案由原始目标函数进行评估，并添加到给定的解决方案集中。为了评估增强后的解决方案集的质量，在不知道真实 Pareto 前沿的情况下，提出了一种用于验证膝盖解决方案的度量方法。KSA 在广泛使用的基准问题上得到了验证，并成功应用于混合动力电动汽车控制器设计问题。
