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A General Meta-Heuristic Based Solver for Combinatorial Optimisation Problems

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Abstract

In recent years, there have been many studies in which tailored heuristics and meta-heuristics have been applied to specific optimisation problems. These codes can be extremely efficient, but may also lack generality. In contrast, this research focuses on building a general-purpose combinatorial optimisation problem solver using a variety of meta-heuristic algorithms including Simulated Annealing and Tabu Search. The system is novel because it uses a modelling environment in which the solution is stored in dense dynamic list structures, unlike a more conventional sparse vector notation. Because of this, it incorporates a number of neighbourhood search operators that are normally only found in tailored codes and it performs well on a range of problems. The general nature of the system allows a model developer to rapidly prototype different problems. The new solver is applied across a range of traditional combinatorial optimisation problems. The results indicate that the system achieves good performance in terms of solution quality and runtime.

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References

  1. D. Abramson, “Constructing school timetables using simulated annealing: sequential and parallel algorithms, ” Management Science, vol. 37, pp. 98–113, 1991.

    Google Scholar 

  2. D. Abramson and H. Dang, “School timetables: A case study in simulated annealing, ” in Applied Simulated Annealing, Lecture Notes in Economics and Mathematics Systems, V. Vidal (Ed.), Springer-Verlag, Singapore, 1993, chap. 5, pp. 103–124.

    Google Scholar 

  3. D. Abramson, A. de Silva, M. Randall, and A. Postula, “Special purpose computer architectures for high speed optimisation, ” in Proceedings of the Second Australasian Conference on Parallel and Real Time Systems Conference, Perth, Australia, 1995, pp. 13–20.

  4. D. Abramson, H. Dang, and M. Krishnamoorthy, “A comparison of two methods for solving 0-1 integer programs using a general purpose simulated annealing, ” Annals of Operations Research, vol. 63, pp. 129–150, 1996.

    Google Scholar 

  5. D. Abramson, P. Logothetis, M. Randall, and A. Postula, “Application specific computers for combinatorial optimisation, ” in Proceedings of The Australian Computer Architecture Workshop, Sydney, Australia, 1997, pp. 29–43.

  6. D. Abramson and M. Randall “A simulated annealing code for general integer linear programs, ” Annals of Operations Research, vol. 86, pp. 3–24, 1999.

    Google Scholar 

  7. T. Bäck, “A User's guide to GENEsYs 1.0, ” Department of Computer Science, University of Dortmund, 1992.

  8. R. Battiti and M. Protasi, “Reactive local search for the maximum clique problem, ” International Computer Science Institute, Technical Report TR-95-052, 1995.

  9. J. Beasley, “OR-Library: Distributing Test problems by electronic mail, ” Journal of the Operational Research Society, vol. 41, pp. 1069–1072, 1990.

    Google Scholar 

  10. J. Beasley, M. Krishnamoorthy, D. Abramson, and Y. Sharaiha, “Scheduling aircraft landing–The static case, ” Transportation Science (to appear).

  11. J. Beasley and P. Chu, “A genetic algorithm for the multiconstraint knapsack problem, ” Computers and Operations Research, vol. 24, pp. 17–23, 1997.

    Google Scholar 

  12. J. Beasley and P. Chu, “Constraint handling in genetic algorithms: The set partitioning problem, ” Journal of Heuristics, vol. 4, pp. 323–357, 1998.

    Google Scholar 

  13. A. Brooke, D. Kendrick, A. Meeraus, and R. Raman, GAMS Language Guide, GAMS Development Corporation, Washington, DC, 1997.

    Google Scholar 

  14. R. Burkard, S. Karisch, and F. Rendl, “QAPLIB–A quadratic assignment problem library, ” Journal of Global Optimization, vol. 10, pp. 391–403, 1997.

    Google Scholar 

  15. M. Chams, A. Hertz, and D. de Werra, “Some experiments with simulated annealing for coloring graphs, ” European Journal of Operational Research, vol. 32, pp. 260–266, 1987.

    Google Scholar 

  16. S. Chanas and P. Kobylanski, “A new heuristic algorithm solving the linear ordering problem, ” Institute of Industrial Engineering and Management, Technical Report PL-50-372, 1995.

  17. J. Chandy and B. Prithviraj, “Parallel simulated annealing strategies for VSLI cell placement, ” in Proceedings of the 9th International Conference on VSLI Design, Bangalore, India, 1996.

  18. P. Chu and J. Beasley, “A genetic algorithm for the generalised assignment problem, ” Computers and Operations Research, vol. 24, pp. 17–23, 1997.

    Google Scholar 

  19. D. Connolly, “An improved annealing for the QAP, ” European Journal of Operational Research, vol. 46, pp. 93–100, 1990.

    Google Scholar 

  20. D. Connolly, “General purpose simulated annealing, ” Journal of the Operational Research Society, vol. 43, pp. 495–505, 1992.

    Google Scholar 

  21. A. Ernst and M. Krishnamoorthy, “An exact solution approach based on shortest paths for p-hub median problems, ” Informs Journal on Computing, vol. 10, pp. 100–112.

  22. T. Feo and M. Resende, “Greedy randomised adaptive search procedures, ” Journal of Global Optimization, vol. 51, pp. 109–133, 1995.

    Google Scholar 

  23. P. Gilmore and R. Gomory, “A linear programming approach to the cutting stock problem, ” Operations Research, vol. 9, pp. 849–859, 1961.

    Google Scholar 

  24. F. Glover and M. Laguna, Tabu Search, Kluwer Academic Publishers: Boston MA, 1997.

    Google Scholar 

  25. D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, AddisonWesley: Reading, MA, 1989.

    Google Scholar 

  26. J. Grefenstette, “A User's Guide to GENISIS, ” Navy Center for Applied Research in Artificial Intelligence, Washington, D.C, 1987.

    Google Scholar 

  27. P. Hart, N. Nilsson, and B. Raphael, “A formal basis for the heuristic determination of minimum cost paths, ” IEEE Transactions on SSC, vol. 4, pp. 100–107, 1968.

    Google Scholar 

  28. J. Hopfield, “Neural networks and physical systems with emergent collective computational responsibilities, ” Proceedings National Academy of Sciences, vol. 79, pp. 2554–2558, 1982.

    Google Scholar 

  29. L. Ingber, “Simulated annealing: Practice versus theory, ” Computer Modelling, vol. 18, pp. 29–57, 1993.

    Google Scholar 

  30. L. Ingber, “Adaptive simulated annealing (ASA): Lessons learned, ” Control and Cybernetics, vol. 25, pp. 33–54, 1996.

    Google Scholar 

  31. J. Jaffar and M. Maher, “Constraint logic programming: A survey, ” Journal of Logic Programming, vol. 19/20, pp. 503–585, 1996.

    Google Scholar 

  32. D. Johnson, C. Aragon, L. McGeogh, and C. Scheveon, “Optimisation by simulated annealing: An experimental evaluation, Part I: Graph partitioning, ” Operations Research, vol. 37, pp. 865–892, 1991.

    Google Scholar 

  33. D. Johnson, C. Aragon, L. McGeogh, and C. Scheveon, “Optimisation by simulated annealing: An experimental evaluation, Part II: Graph colouring and number partitioning, ” Operations Research, vol. 39, pp. 378–406, 1991.

    Google Scholar 

  34. T. Kampke, “Simulated annealing: Use of a new tool in bin packing, ” Annals of Operations Research, vol. 16, pp. 327–332, 1988.

    Google Scholar 

  35. S. Kirpatrick, D. Gelatt, and M. Vecchi, “Optimization by simulated annealing, ” Science, vol. 220, pp. 671–680, 1983.

    Google Scholar 

  36. P. Kouvelis and W. Chiang, “A simulated annealing procedure for single row layout problems in flexible manufacturing systems, ” International Journal of Production Research, vol. 30, pp. 717–732, 1992.

    Google Scholar 

  37. J. Lauriere, “A language and a program for stating and solving combinatorial problems, ” Artificial Intelligence, vol. 10, pp. 29–127, 1978.

    Google Scholar 

  38. E. Lawler, J. Lenstra, A. Rinnoy Kan, and D. Shmoys, The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley: Chichester, 1985.

    Google Scholar 

  39. S. Lin and B. Kernighan, “An effective heuristic algorithm for the traveling salesman problem, ” Operations Research, vol. 21, pp. 498–516, 1973.

    Google Scholar 

  40. J. Little and K. Darby-Dowman, “The significance of constraint logic programming to operational research, ” in Operational Research Tutorial Papers, M. Lawrence and C. Wilsdon (Eds.), Operational Research Society: Birmingham, 1995.

    Google Scholar 

  41. C. Nugent, T. Vollman, and J. Runl, “An experimental comparison of techniques for the assignment of facilities to locations, ” Operations Research, vol. 16, pp. 150–173, 1968.

    Google Scholar 

  42. I. Osman, “Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem, ” Annals of Operations Research, vol. 41, pp. 421–451, 1993.

    Google Scholar 

  43. I. Osman, “Heuristics for the Generalised Assignment Problem: Simulated Annealing and Tabu Search Approaches, ” Operations Research Spektrum, vol. 17, pp. 211–225, 1995.

    Google Scholar 

  44. I. Osman and J. Kelly, Metaheuristics: Theory and Applications, Kluwer Academic Publishers: Norwell MA, 1996.

    Google Scholar 

  45. C. Petersen, “Computational experience with variants of the Balas algorithm applied to the selection of R&D projects, ” Management Science, vol. 13, pp. 736–750, 1967.

    Google Scholar 

  46. M. Randall, “A general modelling systems and meta-heuristic based solver for combinatorial optimisation problems, ” Ph.D. Thesis, Faculty of Environmental Science, Griffith University, 1999. On line at http//www.it.bond.edu.au/randall/general.pdf

  47. M. Randall and D. Abramson, “A general parallel tabu search algorithm for combinatorial optimisation problems, ” Part' 99: Proceedings of the 6th Australasian Conference on Parallel and Real Time Systems, W. Cheng and A. Sajeev (Eds.), Springer-Verlag, Singapore, 1999, pp. 68–79.

    Google Scholar 

  48. G. Reinelt, “The linear ordering problem: Algorithms and applications, research and exposition, ” in Research in Exposition and Mathematics, vol. 8, Heldermann Verlag: Berlin, 1985.

    Google Scholar 

  49. G. Reinelt, “TSPLIB–A traveling salesman problem library, ” ORSA Journal on Computing, vol. 3, pp. 376–384, 1991.

    Google Scholar 

  50. K. Smith, M. Palaniswami, and M. Krishnamoorthy, “Traditional heuristic versus Hopfield neural network approaches to a car sequencing Problem, ” European Journal of Operational Research, vol. 93, pp. 300–316, 1996.

    Google Scholar 

  51. S. Sofianopoulou, “The process allocation problem: A survey of the application of graph-theoretic and integer programming approaches, ” Journal of the Operational Research Society, vol. 43, pp. 407–413, 1992.

    Google Scholar 

  52. R. Sosic and J. Gu, “Fast search algorithms for the N-queens problem, ” IEEE Transactions on Systems, Man and Cybernetics, vol. 21, pp. 1572–1576, 1991.

    Google Scholar 

  53. H. Taha, Operations Research: An Introduction, 5th ed., Macmillan Publishing Company: New York, 1992.

    Google Scholar 

  54. E. Taillard, “Robust taboo search for the quadratic assignment problem, ” Parallel Computing, vol. 17, pp. 443–455, 1991.

    Google Scholar 

  55. E. Taillard, P. Badeau, M. Gendreau, F. Guertin, and J. Potvin, “A tabu search for the vehicle routing problem with soft time windows, ” Transportation Science, vol. 31, pp. 170–186, 1997.

    Google Scholar 

  56. D. Tank and J. Hopfield, “'Neural' computation of decisions in optimization problems, ” Biological Cybernetics, vol. 52, pp. 141–152, 1985.

    Google Scholar 

  57. P. van Hentenryck, Constraint Satisfaction in Logic Programming, The MIT Press: Cambridge, MA, 1989.

    Google Scholar 

  58. L. van Laarhoven and E. Aarts, Simulated Annealing: Theory and Applications, D. Reidel Publishing Company: Dordecht, 1987.

    Google Scholar 

  59. D. Woodruff and E. Zemel, “Hashing vectors for tabu search, ” Annals of Operations Research, vol. 41, pp. 123–137, 1993.

    Google Scholar 

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Randall, M., Abramson, D. A General Meta-Heuristic Based Solver for Combinatorial Optimisation Problems. Computational Optimization and Applications 20, 185–210 (2001). https://doi.org/10.1023/A:1011211220465

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