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A pattern recognition lexi search approach to generalized time-dependent travelling salesman problem

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Abstract

In this paper the “Generalized Time-dependent Travelling Salesman Problem” is a three dimensional travelling salesman problem where the cost matrix C (i, j, k) is the cost of the salesman visiting from city i to city j at time (facility) k. The cost matrix C(i,j,k) [i,j = 1,2,3,…..,n;k = 1,2,3,…..,m] is given. There are n cities and N = {1, 2, 3,…, n}. We are given a partition of cities into groups and we require to find a minimum length tour that includes at least one city from each group. The problem is to find a feasible tour for m(<n) cities for the salesman with minimum total cost with given number of cities from each group with the restriction that he visits only one pair of cities at each point of time(facility) i.e., at a particular time he has to travel from one city to another city. We propose a Lexi Search algorithm based on Pattern Recognition Technique for solving “Generalized Time-dependent Traveling Salesman Problem” with an illustrative example. For this problem a computer program is developed for the algorithm and is tested. It is observed that it takes less time for solving fairly higher dimension problem also.

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Acknowledgements

The first author expresses my deep sense of reverence and gratitude to the research supervisor Prof. M. Sundara Murthy, Department of Mathematics, S.V.U. College of Engineering, Tirupati for suggesting this problem for investigation. It is solely due to his immense interest, competence and exceptional guidance, critical analysis, transcendent and concrete suggestions enlightened discussions, which cumulatively are responsible for the successful execution of this work.

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Authors and Affiliations

  1. Department of Mathematics, Sreenivasa Institute of Technology and Management Studies, Chittoor, India

    U. Balakrishna

  2. Department of Mathematics, S.V.U. College of Engineering, Tirupati, India

    M. Sundara Murthy

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  1. U. Balakrishna
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  2. M. Sundara Murthy
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Correspondence to U. Balakrishna.

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Balakrishna, U., Sundara Murthy, M. A pattern recognition lexi search approach to generalized time-dependent travelling salesman problem. OPSEARCH 49, 191–208 (2012). https://doi.org/10.1007/s12597-012-0074-5

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