Title: Aspiration level-based non-dominated sorting genetic algorithm-II and III for multi-objective shortest path problem in a trapezoidal environment

Authors: Aniket Todkar; Jayesh M. Dhodiya

Addresses: Department of Mathematics and Humanities, SV National Institute of Technology, Surat, Gujrat, India ' Department of Mathematics and Humanities, SV National Institute of Technology, Surat, Gujrat, India

Abstract: The present article provides aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and AL-based NSGA-III utilising an exponential membership function (EMF) with possibility distribution to tackle fuzzy multi-objective shortest path problem (FMOSPP). In this study, fuzzy judgement for trapezoidal fuzzy number is classified for the decision-maker (DM) to optimise fuzzy objective function scenarios like optimistic, most likely lower, most likely upper, and pessimistic at the same time, utilising α-level sets. A numerical demonstration and a dataset have been offered to portray the application of the recommended methodologies. This study suggests that AL-based NSGA-II and AL-based NSGA-III can handle FMOSPP effectively and efficiently with optimal outputs. These methods provide solutions as per DM's AL. Thus it is very effective to manage real-world multi-objective shortest path problems (MOSPPs).

Keywords: multi-objective shortest path problem; MOSPP; aspiration level; exponential membership function; EMF; α-level set; trapezoidal fuzzy number; genetic algorithm.

DOI: 10.1504/IJMOR.2024.137054

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.2, pp.223 - 253

Received: 27 May 2022
Accepted: 04 Jul 2022
Published online: 01 Mar 2024 *

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