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A Framework for the Design and Analysis of an Evolutionary Algorithm for Multi Travelling Salesman Problem


  • Department of Mathematics, Sri Chandrasekharendra Saraswathi Viswa Mahavidyalaya SCSVMV University, Enathur, Kanchipuram – 631561, Tamil Nadu, India
  • Department of Mathematics Division, Vellore Institute of Technology (VIT) University, Vandalur - Kelambakkam Road, Chennai – 600127, Tamil Nadu, India


This paper mainly deals with the design of an evolutionary algorithm for a Multi Travelling Salesman problem. The solution for this problem in multi application fields becomes a highly NP hard type problems which is in need of an efficient solution. The aim of the study is to find an optimal schedule of a salesman which is formed as a multiple objective problem. The mathematical model for the Multi Objective in Multi Travelling salesman problem is stated with the corresponding notations. To get an optimal schedule an evolutionary based approach is proposed to meet the criteria.The proposed algorithm is modelled and stimulated as a program and tested with a suitable example. The output results are given as a grant chart, with the optimal sequence schedule of each salesman.


And Approach, Criteria, Evolutionary, Expense, Minimized Minim Maximize, Multi Travelling, Optimal Schedule, Optimal, Profit, Salesman, Time The.

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  • Mohammadi A, Omidvar MN, Li X, Deb K. Integrating user preferences and decomposition methods for multi-objective optimization. In Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation; 2014 Jul. p. 421–8.
  • Carter AE, Ragsdale CT. A new approach to solving the multiple travelling salesperson problem using genetic algorithms.European Journal of Operational Research. 2006 Nov; 175(1):246–57.
  • Kiraly A, Abonyi J. Optimization of multiple travelling salesmen problem by a novel representation based genetic algorithm. 10th International Symposium of Hungarian Researchers on Computational Intelligence and Informatics; 2016 Mar 26. p. 315–26.
  • Gutting G, Punnen AP. The travelling salesman problem and its variations combinatorial optimization. Kluwer Academic Publishers, Dordrecht, the Nederland’s; 2002.
  • Hu G, Yang S, Li Y, Khan SU. A hybridized vector optimal algorithm for multi-objective optimal designs of electromagnetic devices. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Magnetics. 2016 Mar; 52(3).
  • Jain H, Deb K. An evolutionary multi-objective optimization algorithm using reference-point based non-dominated sorting approach, part II: handling constraints and extending to an adaptive approach. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Evolutionary Computation. 2013; 18(4):602–22.
  • Huang Y et al. Incremental temporal reasoning in job shop scheduling repair. Institute of Electrical and Electronics Engineers (IEEE) International Conference on Industrial Engineering and Engineering Management (IEEM); 2010 Dec. p. 1276–80.
  • Cheng J, Yen G, Zhang G. A multi-objective evolutionary algorithm with enhanced mating and environmental selections. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Evolutionary Computation. 2015; 19(4):592–605.
  • Odili JB, Kadar MNM. Solving the travelling salesman’s problem using the african buffalo optimization. Hinduri Publishing Corporation, Computational Intelligence and Neuroscience. 2015 Aug 27; 2016:12.
  • Peker M, Sen B, Kumru PY. An efficient solving of the travelling salesman problem: the ant colony system having parameters optimized by the Taguchi method. Turkish Journal of Electrical Engineering and Computer Sciences.2013; 21:2015–36.
  • Cheng R, Jin Y, Narukawa K, Sendhoff B. A multiobjective evolutionary algorithm using gaussian process based inverse modelling. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Evolutionary Computation. 2015; 19(6):838–56.
  • Cavill R, Smith S, Tyrell A. Multi-chromosomal genetic programming. In Proceedings of the Conference on Genetic and Evolutionary Computation, Association for Computing Machinery (ACM) New York, USA; 2005. p. 1753–9.
  • Singh S, Lodi EA. Comparison study of multiple travelling salesmen problem using genetic algorithm. International Journal of Computer Science and Network Security (IJCSNS). 2014 Jul; 14(7):107–10.
  • Bandyopadhyay S, Mukherjee A. An algorithm for multi-objective optimization with reduced objective computations: A study in differential evolution. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Evolutionary Computation. 2015; 19(3):400–13.
  • Ponnambalam SG, Aravindan P, Rajesh SV. A tabu search algorithm for job shop scheduling. International Journal of Advanced Manufacturing Technology. 2000; 16:765–71.
  • Petrovic S, Fayad C. A genetic algorithm for job shop scheduling with load balancing. School of Computer Science and Information Technology, University of Nottingham; 2005.
  • Rajakumar S, Arunachalam VP, Selladurai V. Workflow balancing in parallel machine scheduling with precedence constraints using genetic algorithm. Journal of Manufacturing Technology Management. 2006; 17:239–54.
  • Bektas T. The multiple travelling salesman problems: an overview of formulations and solution procedures. Omega.2006; 34:209–19.
  • Tang L, Liu J, Rong A, Yang Z. A multiple travelling salesman problem model for hot rolling scheduling in shanghaied boatman iron and steel complex. European Journal of Operational Research. 2000; 124:267–82.
  • Park YB. A hybrid genetic algorithm for the vehicle scheduling problem with due times and time deadlines.International Journal of Productions Economics. 2001; 73(2):175–88.
  • Zhu Z, Zhang G, Li M, Liu X. Evolutionary multi-objective workflow scheduling in cloud. Institute of Electrical and Electronics Engineers (IEEE) Transactions on Parallel and Distributed Systems. 2016 May; 27(5):1344–57.


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