Abstract
This paper views an optimal solution (tour) of the n-station acyclic Travelling Selesman problem as consisting of n−1 elements of the distance matrix. Considering lower bound for elements a theoretical basis for identifying and eliminating non-optimal elements was suggested. This concept of element elimination was then used to define optimality conditions. Finally, an iterative algorithm which converges at the optimal sequence, was proposed and applied to some numerical examples.
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Referemces
Archelus FJ and Chandra R. “On n/F set-up Time Dependent problems”, Engineering optimization, 7 (1983) 59–67.
Baker K R. “Introduction to Sequencing and Scheduling”, John Wiley and Sons Inc., New York (1974).
Bland R G and Shallcross D F “Large Travelling Salesman Problems. Arising From Experiments in X-ray Chrystallography; A Preliminary Report on Computation”, Operations Research Letters, 8 (1989) 125–128.
Bond S C, Pulley Blank W R and Comuejols G. “TRAVEL: An Interactive TSP Package for IBM Personal Computer”, Operations Research Letters, 63 (1997) 141–144.
Chandru Viyaga, Lee C and Uzsoy R. “Minimizing Total Completion Time On a Batch Processing Machine with Job Families”, Operations Research Letters 13 (1993) 61–65.
Chatterjee S, Carrera C and Lynch L A “Genetic Algorithms and Travelling Salesman Problems”. European Journal of Operations Research, 93 (1996) 490–510
Demenlemeester E L and Herroeln W S “Modelling set-up Times, Process Batches and Transfer Batches Using Activity Network Logic”, European Journal of Operational Research, 89 (1996) 355–365.
Foo F C and Wager J G “Set-up Time in Cyclic and Acyclic Group Scheduling Systems”, International Journal of Production Research, 21 (1983) 63–73.
Gavett J W “Three Heuristic Rules for Sequencing Jobs to a Single Production Facility”, Management Science, 11 (1965) B–166–B–176.
Lenstra J K “Sequencing by Enumeration Methods”, Mathematish Centrum, Amsterdam (1977).
Little J D C, Murty K G, Sweeney D W and Karel C. “An Algorithm for the Travelling Salesman Problem”, Operations Research Journal, 11 (1963) 972–989.
Mak K and Matron A J “A Modified Lin-Kemighan Travelling Salesman Heuristic”, Operations Research letters, 13 (1993) 127–132.
Malandraki C and Dial R B. “A Restricted Dynamic Programming Heuristic Algorithm for the Time Dependent Travelling Salesman Problem”, European Journal of Operational Research, 90 (1996) 45–55.
Miller D L and Pekny J F. “Results From a parallel Branch and Bound Algorithm For Assymmetric Travelling Salesman Problem”, Operation Research Letters, 8 (1989) 129–135.
Padberg M and Rinaldi G. “Optimization of 532-city Symmetric Travelling Salsman Problem by Branch and Cut”, Operation Research Letters, 6 (1987) 141–144.
White C H and Wilson R C. “Sequence Dependent Set-up Times and Job Sequencing”, International Journal of Production Research, 15 (1977) 191–202.
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Charles-Owaba, O.E. Optimality Conditions to the Acyclic Travelling Salesman Problem. OPSEARCH 38, 531–542 (2001). https://doi.org/10.1007/BF03398656
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DOI: https://doi.org/10.1007/BF03398656