Sustainable fixed-charge fuzzy multi-objective 5D shortest path problem using aspiration level-based NSGAS: application to aquatic fish haul system

¹ Department of Mathematics, SV National Institute of Technology, Ichchhanath, Surat 395007, Gujarat, India
² Tatyasaheb Kore Institute of Engineering and Technology, Warananager, Warana University, Warananager 416113, Maharastra, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 September 2024
Accepted: 17 September 2025

Abstract

Sustainability encompasses the interaction between environmental, economic, and social systems at various levels. In transportation systems, vehicles rely on different fuels to meet energy demands. However, these fuels contribute to environmental pollution by releasing greenhouse gases. Considering this context, the present study investigates a sustainable fixed-charge multi-objective multi-driver multi-route multi-conveyance shortest path problem (FCMOMDMRMCSPP). The primary intent is to identify the most efficient route that minimizes cost, time, risk, carbon emissions, and distance while traveling between sources and destinations. Real-world scenarios often involve uncertainties, making it difficult to precisely define the parameters of FCMOMDMRMCSPP. Triangular fuzzy numbers are introduced in the proposed model to address this ambiguity. The possibilistic programming approach is employed to transform the fuzzy problem into a deterministic one. The resulting deterministic model is then solved using two multi-objective genetic algorithms (MOGAs): aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and NSGA-III. An aquatic fish haul system problem has been examined as an application within the framework of the proposed model. For α = 0 and 0.1, the AL-based NSGA-II and III generate 6, 11, and 4 solutions that satisfy the decision-maker’s (DM’s) ALs in cases I, II, and III of the AL and shape parameter combination, respectively. Similarly, for α = 0.5, these methods yield 5, 11, and 4 solutions, while for α = 0.9, they provide 6, 11, and 4 solutions for the same cases. A comparative analysis is conducted between the compromise solutions obtained from the proposed techniques and those derived from the hybrid genetic algorithm, NSGA-II and NSGA-III. A sensitivity analysis of the objective functions concerning the shape parameter and AL is also performed. Finally, the coverage performance measure is computed to assess the effectiveness of the proposed methods.