论文标题
使用MIP方法比较多数和多目标优化解决方案集的优势移动计算
Dominance Move calculation using a MIP approach for comparison of multi and many-objective optimization solution sets
论文作者
论文摘要
优势移动（DOM）是一个二进制质量指标，可用于多目标优化。它可以比较解决方案集的同时代表一些重要功能，例如收敛，差异，均匀性和基数。 DOM具有直观的概念，并考虑了一个弱帕累托（Pareto）占主导地位所需的一组最小动作。尽管具有上述特性，但很难计算DOM。原始配方仅在生物原则的情况下提供了一种有效而精确的方法来计算它。这项工作提出了一种新的方法来计算和扩展DOM以处理三个或更多目标。这个想法是使用混合整数编程（MIP）方法来计算DOM。在生物目标空间中进行了一些初始实验，以验证模型正确性。此外，使用三个，五个和十个目标函数进行了其他实验，以显示模型在较高维度的情况下的表现。使用IBEA，MOEAD，NSGAIII，NSGAII和SPEA2等算法来生成溶液集，但是任何其他算法都可以与DOM指示器一起使用。结果证实了MIP DOM在超过三个目标函数的问题中的有效性。讨论了最终的注释，考虑因素和未来的研究，以利用某些解决方案集，并改善模型及其在其他情况下的使用。
Dominance move (DoM) is a binary quality indicator that can be used in multiobjective optimization. It can compare solution sets while representing some important features such as convergence, spread, uniformity, and cardinality. DoM has an intuitive concept and considers the minimum move of one set needed to weakly Pareto dominate the other set. Despite the aforementioned properties, DoM is hard to calculate. The original formulation presents an efficient and exact method to calculate it in a biobjective case only. This work presents a new approach to calculate and extend DoM to deal with three or more objectives. The idea is to use a mixed integer programming (MIP) approach to calculate DoM. Some initial experiments, in the biobjective space, were done to verify the model correctness. Furthermore, other experiments, using three, five, and ten objective functions were done to show how the model behaves in higher dimensional cases. Algorithms such as IBEA, MOEAD, NSGAIII, NSGAII, and SPEA2 were used to generate the solution sets, however any other algorithms could be used with DoM indicator. The results have confirmed the effectiveness of the MIP DoM in problems with more than three objective functions. Final notes, considerations, and future research are discussed to exploit some solution sets particularities and improve the model and its use for other situations.
