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Aspiration level-based non-dominated sorting genetic algorithm II & III to solve fuzzy multi-objective shortest path problem

Todkar Aniket S. (Department of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat, India), anikettodkar@gmail.com
Dhodiya Jayesh M. (Department of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat, India), jdhodiya@yahoo.com

The present article provides aspiration level-based non-dominated sorting genetic algorithm-II and III techniques for solving a fuzzy multi-objective shortest path problem utilizing an exponential membership function with a possibility distribution. Furthermore, in this study, using α-level sets, fuzzy judgement was categorized for the decision maker to simultaneously optimize fuzzy objective functions scenarios as optimistic, most likely, and pessimistic. A numerical illustration is presented together with a data set to demonstrate the use of the suggested techniques. A comparison is performed between the suggested methodology and several other approaches. The sensitivity of the objective functions is also investigated using aspiration levels and shape parameters. The coverage is computed to assess the effectiveness of the proposed methods. This research concludes that the suggested approaches can manage fuzzy multi-objective shortest path problems competently and efficiently with a solid yield, allowing the decision maker to make a decision based on its aspiration level.

Keywords: Multi-objective shortest path problem, fuzzy membership function, α-level set, triangular fuzzy number, aspiration level