A first approach to Fuzzy Multi-Objective Shortest Path Problems
Irene Marinas (University of Oviedo, Spain)
Friday 18th November, 2022 15:00-16:00 Maths 116
Abstract
One of the most studied classical optimization problems is the shortest path problem (SPP). The value of paths is normally measured in terms of a single attribute (cost, duration, time, risk...) defined in each arc of the graph. However, in many cases, a single attribute is insufficient to define the preference between routes. As a result, Multi-Objective Shortest Path (MOSP) problems arise, in which various attributes are defined on the edges and thus on the paths. This scenario leads to solution sets that can be exponentially sized relative to the input size of the problem.
Moreover, in traditional SPPs, there is exact information about the parameters of the problem. However, real-world environments require dealing with uncertainty and so fuzzy notions can be used. In Fuzzy SPP, the classic costs between nodes are replaced by fuzzy numbers.
The main aim of this work is to find a way to provide an unique solution to the MOSP problem, rather than a set of optimal paths, while dealing with the fuzzy costs. The approach proposed is based on ranking methods.
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