For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity. KeywordsExact and approximate methods for ranked-optimal solutions; K-ranked optimal solutions; Multi-objective integer programming model; Non-dominated point set; Rank-based solution method.

中文翻译：

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基于秩的求解方法及其在多目标整数规划模型非控制点集确定中的应用

对于任何单目标数学规划模型，与基于相同单目标数学规划模型的最优解相比，基于排名的最优解在计算上难以找到。本文提出了几种方法来找到这些基于秩的最优解，并在此基础上概述了一种新的基于秩的解法（RBSM），用于识别多目标整数规划模型的非支配点集。每种方法都通过一个数值示例进行说明，并且对于每种方法，我们都讨论了其局限性，优点和计算复杂性。排序最优解的精确和近似方法; K级最佳解决方案；多目标整数规划模型；非支配点集；基于等级的求解方法。