Abstract
In this article, we are interested in solving a combinatorial optimization problem, the shortest path problem in a multi-attribute graph, by the out-ranking methods. A multi-attribute graph has simultaneously qualitative and quantitative criteria. This situation gives rise to incomparable paths thus forming the Pareto front. Outranking methods in Multi-criteria Decision Making (MCDM) are the only methods that can take into account this situation (incomparability of actions). After presenting the categories of Multi-criteria Decision Making (MCDM) and the difficulties related to the problems of the shortest paths, we propose an evolutionary algorithm based on the outranking methods to solve the problem of finding “best” paths in a multi-attribute graph with non-additive criteria. Our approach is based on the exploration of induced subgraphs of the outranking graph. Properties have been established to serve as algorithmic basis. Numerical experiments have been carried out and the results presented in this article.
Highlights
The concept of relations was born out of difficulties encountered with diverse concrete outranking problems [1]
After presenting the categories of Multi-criteria Decision Making (MCDM) and the difficulties related to the problems of the shortest paths, we propose an evolutionary algorithm based on the outranking methods to solve the problem of finding “best” paths in a multi-attribute graph with non-additive criteria
We present the basic concepts related to Multi-criteria Decision Making, multi-attribute graphs, difficulties in finding the shortest multicriteria path and the SPARTE (Solution au PARadoxe de voTE—Solution to the voting paradox) outranking method which is very close to the ELECTRE (ELimination Et Choix Traduisant la REalité—elimination and choice expressing reality) outranking method
Summary
The concept of relations was born out of difficulties encountered with diverse concrete outranking problems [1]. The weaknesses that result from this method are the reduction of the multicriteria problem into a unique criterion problem The consequence of this reduction is that all the actions are comparable, a property that is not always desirable to have because one observes that for a human decision-maker, there are situations involving incomparable alternatives [9]. We present the basic concepts related to Multi-criteria Decision Making, multi-attribute graphs, difficulties in finding the shortest multicriteria path and the SPARTE (Solution au PARadoxe de voTE—Solution to the voting paradox) outranking method which is very close to the ELECTRE (ELimination Et Choix Traduisant la REalité—elimination and choice expressing reality) outranking method. We present in the third part our numerical experiments and the results obtained
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