Title: Enhanced non-dominated sorting genetic algorithms for fuzzy multi-objective multi-route shortest path problem

Authors: Aniket S. Todkar; Jayesh M. Dhodiya

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

Abstract: This study examines a fuzzy multi-objective multi-route short path problem (FMOMRSPP) by transforming it into a crisp multi-objective multi-route shortest path problem (MOMRSPP) using possibility distribution. Using α-level sets, fuzzy judgement is categorised for the decision maker (DM) to optimise fuzzy objective function scenarios. This paper proposes aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and AL-based NSGA-III to obtain a Pareto-optimal solution that meets DM AL for the FMOMRSPP. A numerical example has been provided to demonstrate the usage of the presented methodologies. A comparison is presented between the proposed and several other approaches. The sensitivity of objective functions is also investigated with ALs and shape parameters. The coverage is determined to evaluate the effectiveness of the proposed methods.

Keywords: multi-objective multi-route shortest path problem; MOMRSPP; NSGA-II; NSGA-III; aspiration level.

DOI: 10.1504/IJMOR.2025.148626

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.1, pp.90 - 122

Received: 09 Sep 2023
Accepted: 21 Nov 2023
Published online: 16 Sep 2025 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article