Inverse optimization on the evaluations of alternatives in the Promethee II ranking method

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science Pub Date : 2025-03-31 DOI:10.1016/j.omega.2025.103325

Alexandre Flachs, Yves De Smet

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引用次数: 0

Abstract

In multi-criteria decision aid, one usually distinguishes three main families of methods: aggregating, outranking and interactive approaches. Among the outranking methods, Promethee II allows decision makers to obtain a complete ranking of the alternatives regarding multiple – usually conflicting – criteria. Despite its popularity and the various theoretical contributions that have been made to it, few work has been focused on the influence of the alternatives’ evaluations on the final ranking.

In this contribution, this issue is addressed by proposing a solution to the following question: given a ranking of the alternatives, what are the minimal modifications required on the evaluations of a given alternative in order to improve its position? A novel exact algorithmic procedure is proposed to answer this question even when multiple criteria are involved. In such cases the solution takes the form of a Pareto optimal front. A proof of the correctness of the algorithm and a complexity analysis are provided. Finally, experimental tests of the method on a real life dataset is discussed along with some indications on how it could be presented to decision makers.

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Prometheeⅱ排序法中备选方案评价的逆优化

在多标准决策辅助中，人们通常区分三种主要的方法：聚合、超越排序和交互方法。在排名方法中，普罗米修斯II允许决策者根据多个通常相互冲突的标准获得备选方案的完整排名。尽管它很受欢迎，也有各种各样的理论贡献，但很少有研究关注备选方案的评价对最终排名的影响。在这篇文章中，这个问题是通过提出以下问题的解决方案来解决的：给定一个备选方案的排名，为了改善其位置，对给定备选方案的评价需要进行的最小修改是什么？提出了一种新颖的精确算法程序来回答这个问题，即使涉及多个标准。在这种情况下，解决方案采用帕累托最优前沿的形式。给出了算法的正确性证明和复杂度分析。最后，讨论了该方法在现实生活数据集上的实验测试，以及如何将其呈现给决策者的一些指示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Omega-international Journal of Management Science 管理科学-运筹学与管理科学

CiteScore

13.80

自引率

11.60%

发文量

130

审稿时长

56 days

期刊介绍： Omega reports on developments in management, including the latest research results and applications. Original contributions and review articles describe the state of the art in specific fields or functions of management, while there are shorter critical assessments of particular management techniques. Other features of the journal are the "Memoranda" section for short communications and "Feedback", a correspondence column. Omega is both stimulating reading and an important source for practising managers, specialists in management services, operational research workers and management scientists, management consultants, academics, students and research personnel throughout the world. The material published is of high quality and relevance, written in a manner which makes it accessible to all of this wide-ranging readership. Preference will be given to papers with implications to the practice of management. Submissions of purely theoretical papers are discouraged. The review of material for publication in the journal reflects this aim.