Abstract
Nowadays, meta-heuristic algorithms based on biological species have grown increasingly familiar. In the general realm of swarm intelligence, the collective intelligence of diverse social insects like “ants, bees, wasps, termites, birds, and fish” has been researched to create a variety of meta-heuristic algorithms. The “traveling salesman problem (TSP)” represents a combinatorial optimization problem in which a salesman starts in one location and goes to all remaining cities in the lowest time feasible. TSP is a prominent problem because its instances may be used to address real-world issues, through the evaluation of the performance of novel algorithms. This paper develops the arithmetic optimization algorithm (AOA) for solving TSP. Here, the performance is evaluated by comparing with several heuristic-based algorithms in terms of convergence analysis. The efficacy of the suggested AOA for solving TSP is demonstrated by experimental findings.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Singh A, Baghel AS (2009) A new grouping genetic algorithm approach to the multiple traveling salesperson problem. Soft Comput 13(1):95–101
Krishna MM, Panda N, Majhi SK (2021) Solving traveling salesman problem using hybridization of rider optimization and spotted hyena optimization algorithm. Expert Syst Appl 115353
Tang L, Liu J, Rong A, Yang Z (2000) A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron and Steel complex. Eur J Oper Res 124(2):267–282
Gilbert KC, Hofstra RB (1992) A new multiperiod multiple traveling salesman problem with heuristic and application to a scheduling problem. Decis Sci 23(1):250–259
Li J, Zhou MC, Sun Q, Dai XZ, Yu X (2015) Colored traveling salesman problem. IEEE Trans Cybern 45(11):2390–2401
Croes GA (1958) A method for solving traveling-salesman problems. Oper Res 6(6):791–812
Panda N, Majhi SK (2021) Oppositional salp swarm algorithm with mutation operator for global optimization and application in training higher order neural networks. Multimedia Tools Appl 1–25
Panda N, Majhi SK, Singh S, Khanna A (2020) Oppositional spotted hyena optimizer with mutation operator for global optimization and application in training wavelet neural network. J Intell Fuzzy Syst 38(5):6677–6690
Bektas T (2006) The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega 34(3):209–219
Panda N, Majhi SK (2021) Effectiveness of swarm-based metaheuristic algorithm in data classification using Pi-Sigma higher order neural network. In: Progress in advanced computing and intelligent engineering, pp 77–88. Springer, Singapore
Panda N, Majhi SK (2019) How effective is spotted hyena optimizer for training multilayer perceptrons. Int J Recent Technol Eng 4915–4927
Florios K, Mavrotas G (2014) Generation of the exact Pareto set in multiobjective traveling salesman and set covering problems’. Appl Math Comput 237:1–19
Wang J, Ersoy O, He M, Wang F (2016) Multi-offspring genetic algorithm and its application to the traveling salesman problem. Appl Soft Comput 43:415–423
Ma M, Li H (2017) A hybrid genetic algorithm for solving bi-objective traveling salesman problems. J Phys Conf Ser 887
Albayrak M, Allahverd N (2011) Development a new mutation operator to solve the traveling salesman problem by aid of genetic algorithms. Expert Syst Appl 38(3):1313–1320
Meng X, Li J, Zhou M, Dai X, Dou J (2018) Population-based incremental learning algorithm for a serial colored traveling salesman problem. IEEE Trans Syst Man Cybernet Syst 48(2):277–288
Chen X, Liu Y, Li X, Wang Z, Wang S, Gao C (2019) A new evolutionary multiobjective model for traveling salesman problem. IEEE Access 7:66964–66979
Hatamlou A (2017) Solving travelling salesman problem using black hole algorithm. Soft Comput 22:8167–8175
Silva BCH, Fernandes IFC, Goldbarg MC, Goldbarg EFG (2020) Quota travelling salesman problem with passengers, incomplete ride and collection time optimization by ant-based algorithms. Comput Oper Res 120
Yuan Y, Cattaruzza D, Ogier M, Semet F (2020) A branch-and-cut algorithm for the generalized traveling salesman problem with time windows. Eur J Oper Res 286(3):849–866
Draft M (2014) A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode’s ideal transfer function based automobile cruise control system. J King Saud University Eng Sci
Wang K-P, Huang L, Zhou C-G, Pang W (2003) Particle swarm optimization for traveling salesman problem. In: Proceedings of the 2003 international conference on machine learning and cybernetics (IEEE Cat. No.03EX693), 2003, vol 3, pp 1583–1585
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Yilmaz S, Sen S (2019) Electric fish optimization: a new heuristic algorithm inspired by electrolocation. Neural Comput Appl 32:11543–11578
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Krishna, M.M., Majhi, S.K. (2022). Developing Arithmetic Optimization Algorithm for Travelling Salesman Problem. In: Mohanty, M.N., Das, S. (eds) Advances in Intelligent Computing and Communication. Lecture Notes in Networks and Systems, vol 430. Springer, Singapore. https://doi.org/10.1007/978-981-19-0825-5_23
Download citation
DOI: https://doi.org/10.1007/978-981-19-0825-5_23
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0824-8
Online ISBN: 978-981-19-0825-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)