Abstract
The final solution set given by almost all existing preference-based multi-objective evolutionary algorithms (MOEAs) lies a certain distance away from the decision makers’ preference information region. Therefore, we propose a multi-objective optimization algorithm, referred to as the double-grid interactive preference based MOEA (DIP-MOEA), which explicitly takes the preferences of decision makers (DMs) into account. First, according to the optimization objective of the practical multi-objective optimization problems and the preferences of DMs, the membership functions are mapped to generate a decision preference grid and a preference error grid. Then, we put forward two dominant modes of population, preference degree dominance and preference error dominance, and use this advantageous scheme to update the population in these two grids. Finally, the populations in these two grids are combined with the DMs’ preference interaction information, and the preference multi-objective optimization interaction is performed. To verify the performance of DIP-MOEA, we test it on two kinds of problems, i.e., the basic DTLZ series functions and the multi-objective knapsack problems, and compare it with several different popular preference-based MOEAs. Experimental results show that DIP-MOEA expresses the preference information of DMs well and provides a solution set that meets the preferences of DMs, quickly provides the test results, and has better performance in the distribution of the Pareto front solution set.
摘要
几乎所有现有的基于偏好的多目标进化算法(MOEA)给出的最终解集都与决策者偏好信息的表示存在一定距离。因此,提出一种多目标优化算法,称为双重网格交互式基于偏好的多目标进化算法(DIP-MOEA),该算法明确考虑了决策者偏好。首先根据实际多目标优化问题(MOPs)的优化目标和决策者偏好映射隶属度函数,生成决策偏好度网格和偏好误差网格。其次,提出偏好度支配和偏好误差支配两种种群支配方式,并利用该方案更新两个网格中的种群。最后综合两个网格中的种群并结合决策者偏好交互信息可进行偏好多目标优化交互。为验证DIP-MOEA性能,我们在基本DTLZ系列函数和多目标背包问题上对DIP-MOEA进行测试,并将其与几种流行的基于偏好的多目标进化算法进行比较。实验结果表明,DIP-MOEA能较好表达决策者偏好信息,提供满足决策者偏好的解集,快速求解测试问题结果,并在最终解集的Pareto前沿分布性具有较好表现。
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Luda ZHAO designed the research and drafted the paper. Bin WANG and Yihua HU guided the research. Yicheng LU provided suggestions for the example background and processed the data. Luda ZHAO, Bin WANG, and Xiaoping JIANG revised and finalized the paper.
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Luda ZHAO, Bin WANG, Xiaoping JIANG, Yicheng LU, and Yihua HU declare that they have no conflict of interest.
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Comparison of runtime among several algorithms on the test function boxplot
Project supported by the National Natural Science Foundation of China (No. 72101266), the Military Postgraduate Funding Project, China (No. JY2021B042), and the Hunan Provincial Postgraduate Scientific Research Innovation Project, China (No. CX20200029)
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Zhao, L., Wang, B., Jiang, X. et al. DIP-MOEA: a double-grid interactive preference based multi-objective evolutionary algorithm for formalizing preferences of decision makers. Front Inform Technol Electron Eng 23, 1714–1732 (2022). https://doi.org/10.1631/FITEE.2100508
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DOI: https://doi.org/10.1631/FITEE.2100508