Multi-objective quasi oppositional Jaya algorithm to solve multi-objective solid travelling salesman problem with different aspiration level

Abstract

Multi-Objective Travelling Salesman Problem (MOTSP) is one of the most crucial problems in realistic scenarios and is difficult to solve by classical methods. However, it can be solved by evolutionary methods. This paper presents an Aspiration Level based Multi-Objective Quasi Oppositional Jaya (AL-based MOQO-Jaya) Algorithm for solving the Multi-Objective Solid Travelling Salesman Problem (MOSTSP). Furthermore, fuzzy judgment was characterised by utilizing the possibility and necessity measures to allow the decision-maker (DM) for optimising different scenarios of the Fuzzy Multi-Objective Solid Travelling Salesman Problem (FMOSTSP). A numerical illustration is provided for 10, 80, 100 and 120 cities, and sensitivity analysis is performed with different shape parameters and aspiration levels. Further the results are compared by CPLEX optimizer and Hybrid GA. The results obtained by AL-based MOQO Jaya are more efficient, the run time of AL-based MOQO is 5.8667, 40.9115, 58.4789 and 60.6882 seconds for 10, 80,100 and 120 cities for FMOSTSP which is quite less as compared to CPLEX and Hybrid GA. To access the performance of the proposed method coverage and hypervolume are calculated. This paper concludes that developed approach has solved MOSTSP and FMOSTSP efficiently with an effective output and provides alternative solutions for decision-making to DM.

Keywords:

• Multi-objective solid travelling salesman problem
• multi-objective quasi oppositional Jaya
• exponential membership

Data availability

The data that support the findings of this study are openly available in TSPLIB at http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsplib.html.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Aaishwarya Bajaj

Aaishwarya Bajaj is a research scholar at SVNIT, Surat. She is currently pursuing her Ph.D. on Operation Research and Optimisation through Evolutionary Algorithms. She had cleared GATE examination in 2017. She had done her M.Tech for NIT, Bhopal.

Jayesh Dhodiya

Jayesh M. Dhodiya is an associate professor at SVNIT, Surat. He has published 74 research papers in various reputed International and National Journals. He has been awarded as a Gold Medalist in the Post-graduation Programme. He has cleared Gujarat Public Service Commission examination for Mathematics in 2010. His major area of research interest lies in Operations Research, Mathematical Modelling and Simulation, Computing, Knowledge Management and Image mining.