4OR

, Volume 4, Issue 4, pp 263–296

Ejection chain and filter-and-fan methods in combinatorial optimization

Invited survey

Abstract

The design of effective neighborhood structures is fundamental to the performance of local search and metaheuristic algorithms for combinatorial optimization. Significant efforts have been made in the creation of larger and more powerful neighborhoods that are able to explore the solution space more extensively and effectively while keeping computation complexity within acceptable levels. The most important advances in this domain derive from dynamic and adaptive neighborhood constructions originating in ejection chain methods and a special form of a candidate list design that constitutes the core of the filter-and-fan method. The objective of this paper is to lay out the general framework of the ejection chain and filter-and-fan methods and present applications to a number of important combinatorial optimization problems. The features of the methods that make them effective in these applications is expected to provide insights into solving challenging problems in other settings.

Keywords

Combinatorial optimization Metaheuristics Tabu search Local search Neighborhood structures Ejection chains Filter-and-fan 

MSC classification

90C59 90C27 90C06 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aarts EHL, Van Laarhoven PJM, Lenstra JK, Ulder NLJ (1994) A computational study of local search algorithms for job shop scheduling. ORSA J Comput 6(2):118–125Google Scholar
  2. Adams J, Balas E, Zawack D (1988) The shifting bottleneck procedure for job shop scheduling. Manage Sci 34 (3):391–401Google Scholar
  3. Ahuja RK, Orlin JB, Sharma D (2001) Multi-exchange neighborhood search structures for the capacitated minimum spanning tree problem. Math Program 91:71–97Google Scholar
  4. Ahuja RK, Orlin JB, Sharma D (2002) Very large-scale neighborhood search for the quadratic assignment problem. submitted to INFORMS J ComputGoogle Scholar
  5. Ahuja RK, Orlin JB, Sharma D (2003) A composite very large-scale neighborhood structure for the capacitated minimum spanning tree problem. Operat Res Lett 31:185–194CrossRefGoogle Scholar
  6. Amberg A, Domschke W, Voß S (1996) Capacitated minimum spanning trees: algorithms using intelligent search. Comb Opt Theory Practice 1:9–39Google Scholar
  7. Applegate D, Cook W, Rohe A (2003) Chained Lin-Kernighan for large traveling salesman problems. INFORMS J Comput 15:82–92CrossRefGoogle Scholar
  8. Balas E, Vazacopoulos A (1998) Guided local search with shifting bottleneck for job shop scheduling. Manage Sci 44(2):262–275Google Scholar
  9. Cavique L, Rego C, Themido I (1999) Subgraph ejection chains and tabu search for the crew scheduling problem. J Operat Res Soci 50:608–616CrossRefGoogle Scholar
  10. Cao B, Glover F (1997) Tabu search and ejection chains: application to a node weighted version of the cardinality-constrained TSP. Manage Sci 43(7):908–921Google Scholar
  11. Cela E (1998) The quadratic assignment problem: theory and algorithms. Kluwer, BostonGoogle Scholar
  12. Chan HS, Dill KA (1993) The protein folding problem. Phys Today 46(2):24–32Google Scholar
  13. Chrobak M, Szymacha T, Krawczyk A (1990) A data structure useful for finding hamiltonian cycles. Theoret Comput Sci 71:419–424CrossRefGoogle Scholar
  14. Christofides N, Mingozzi A, Toth P (1979) The vehicle routing problem. In: Mingozzi A, Toth P, Sandi C (eds) Combinatorial optimisation. Wiley, Chichester, pp 315–338Google Scholar
  15. Cirasella J, Johnson DS, McGeoch LA, Zhang W (2001) The asymmetric traveling salesman problem: algorithms, instance generators and tests. In: Proceedings of the algorithm engineering and experimentation, third international workshop, ALENEX 2001, pp 32–59Google Scholar
  16. Cornuéjols G, Nemhauser GH, Wolsey L (1990) “The uncapacitated facility location problem. In: Mirchandani P, Francis R (eds) Discrete location theory. J Wiley, New York, pp 119–171Google Scholar
  17. Dill KA (1985) “Theory for the folding and stability of globular proteins,”. Biochemistry 24(6): 1501-1509CrossRefGoogle Scholar
  18. Dorndorf U, Pesch E (1994) Fast clustering algorithms. ORSA J Comput 6:141–153Google Scholar
  19. Fisher ML (1994) Optimal solution of vehicle routing problems using minimum k-trees. Operat Res 42(4):626–642Google Scholar
  20. Fredman ML, Johnson DS, McGeoch LA, Ostheimer G (1995) Data structures for traveling salesmen. J Algorithms 18:432–479CrossRefGoogle Scholar
  21. Funke B, Grünert T, Irnich S (2005) A note on single alternating cycle neighborhoods for the TSP. J Heuristics, 11:135–146CrossRefGoogle Scholar
  22. Gamboa D, Rego C, Glover F (2005) Data structures and ejection chains for solving large-scale traveling salesman problems. Eur J Operat Res 160:154–171CrossRefGoogle Scholar
  23. Gamboa D, Rego C, Glover F (2006a) Implementation analysis of efficient heuristic algorithms for the traveling salesman problem. Comput Operat Res 33:1161–1179CrossRefGoogle Scholar
  24. Gamboa D, Rego C, Glover F, Osterman C (2006b) An experimental evaluation of ejection chain algorithms for the traveling salesman problem. School of Business Administration, University of Mississippi, MSGoogle Scholar
  25. Gao LL, Robinson EP (1994) Uncapacitated facility location: general solution procedures and computational experience. Eur J Operat Res 76:410–427CrossRefGoogle Scholar
  26. Gavish B (1982) Topological design of centralized computer networks: formulations and algorithms. Networks 12:355–377Google Scholar
  27. Gavish B (1991) Topological design telecommunications networks—local access design methods. Ann Operat Res 33:17–71CrossRefGoogle Scholar
  28. Glover F (1991) Multilevel tabu search and embedded search neighborhoods for the traveling salesman problem. Leeds School of Business, University of Colorado, BoulderGoogle Scholar
  29. Glover F (1992) New ejection chain and alternating path methods for traveling salesman problems. Comput Sci Operat Res 449–509Google Scholar
  30. Glover F (1996) Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Appli Math 65:223–253CrossRefGoogle Scholar
  31. Glover F (1998) A template for scatter search and path relinking. In: Hao J-K, Lutton E, Ronald E, Schoenauer M, Snyers D (eds) Artificial evolution. Lecture notes in computer science, vol. 1363. Springer, Berlin Heidelberg New York, pp 3–51Google Scholar
  32. Glover F, Laguna M (1997) Tabu Search. Kluwer, BostonGoogle Scholar
  33. Gonçalves JF, Mendes JJM, Resende MGC (2005) A hybrid genetic algorithm for the job shop scheduling problem. Eur J Operat Res 167:77–95CrossRefGoogle Scholar
  34. Grabowski J, Wodecki M (2005) A very fast tabu search algorithm for job shop problem. In: Rego C, Alidaee B (eds) Metaheuristic optimization via memory and evolution: tabu search and scatter search. Kluwer, Boston, pp 191–211Google Scholar
  35. Greistorfer P, Rego C (2006) A simple filter-and-fan approach to the facility location problem. Comput Operat Res 33(9):2590–2601CrossRefGoogle Scholar
  36. Helsgaun K (2000) An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur J Operat Res 126:106–130CrossRefGoogle Scholar
  37. Johnson DS, McGeoch LA (1997) The traveling salesman problem: a case study in local optimization. In: Local search in combinatorial optimization: Aarts EHL, Lenstra JK (eds) J Wiley, 215–310Google Scholar
  38. Johnson DS, McGeoch LA, Glover F, Rego C (2000) 8th DIMACS implementation challenge: the traveling salesman problem. http://www.research. att.com/~dsj/chtsp/Google Scholar
  39. Kanellakis PC, Papadimitriou CH (1980) Local search for the asymmetric traveling salesman problem. Operat Res 28:1086–1099Google Scholar
  40. Lengauer T (1993) Algorithmic research problems in molecular bioinformatics. In: Proceedings of the second israel symposium on theory of computing systems, ISTCS 1993, Natanya, Israel, 177–192Google Scholar
  41. Lesh N, Mitzenmacher M, Whitesides S (2003) A complete and effective move set for simple protein folding. In: Proceedings of the 7th annual international conference on research in computational molecular biology (RECOMB), ACM Press, New York, pp 188–195Google Scholar
  42. Lin S, Kernighan B (1973) An effective heuristic algorithm for the traveling salesman problem. Operat Res 21:498–516CrossRefGoogle Scholar
  43. Mathew F, Rego C (2006) Recent advances in heuristic algorithms for the capacitated minimum spanning tree problem. In: Proceedings of the 37th annual meeting of decision sciences institute (DSI). 31021–31026Google Scholar
  44. Mathew F, Rego C, Glover F (2006) A filter-and-fan algorithm for the capacitated minimum spanning tree. School of Business Administration, University of Mississippi, MSGoogle Scholar
  45. Nowichi E, Smutnicki C (1996) A fast taboo search algorithm for the job shop problem. Manage Sci 42(6):797–813Google Scholar
  46. Osterman C, Rego C (2003) The satellite list and new data structures for symmetric traveling salesman problems. School of Business Administration, University of Mississippi, MSGoogle Scholar
  47. Patterson R, Pirkul H, Rolland E (1999) Memory adaptive reasoning for solving the capacitated minimum spanning tree problem. J Heuristics 5:159–180CrossRefGoogle Scholar
  48. Pinedo ML (2006) Planning and scheduling in manufacturing and services. Series in operations research and financial engineering. Springer, Berlin Heidelberg New YorkGoogle Scholar
  49. Rego C (1998a) Relaxed tours and path ejections for the traveling salesman problem. Eur J Operat Res 106:522–538CrossRefGoogle Scholar
  50. Rego C (1998b) A subpath ejection method for the vehicle routing problem. Manage Sci 44(10):1447–1459Google Scholar
  51. Rego C (2001) Node ejection chains for the vehicle routing problem: sequential and parallel algorithms. Parallel Comput 27:201–222CrossRefGoogle Scholar
  52. Rego C, Duarte R (2006) A filter and fan approach for the job shop scheduling problem. School of Business Administration, University of Mississippi, MSGoogle Scholar
  53. Rego C, Glover F (2002) Local search and metaheuristics for the traveling salesman problem. In: Gutin G, Punnen A (eds) The traveling salesman problem and its variations. Kluwer, Boston, pp 309–368Google Scholar
  54. Rego C, Glover F, Gamboa D, Osterman C (2006a) A doubly-rooted stem-and-cycle ejection chain algorithm for asymmetric traveling salesman problems. School of Business Administration, University of Mississippi, MSGoogle Scholar
  55. Rego C, Li H, Glover F (2006b) A filter-and-fan approach to the 2D HP model of the protein folding problem. School of Business Administration, University of Mississippi, MSGoogle Scholar
  56. Rego C, James T, Glover F (2006c) “An ejection chain algorithm for the quadratic assignment problem,” School of Business Ad on, University of Mississippi, MSGoogle Scholar
  57. Richards FM (1991) The protein folding problem. Sci Am 264(1):54–7, 60–3Google Scholar
  58. Rochat Y, Taillard E (1995) Probabilistic intensification and diversification in local search for vehicle routing. J Heuristics. 1:147–167CrossRefGoogle Scholar
  59. Sabuncuoglu I, Bayiz M (1999) Job shop scheduling with beam search. Eur J Operat Res 118: 390–412CrossRefGoogle Scholar
  60. Sharaiha YM, Gendreau M, Laporte G, Osman IH (1997) A tabu search algorithm for the capacitated shortest spanning tree problem. Networks 29:161–171CrossRefGoogle Scholar
  61. Taillard E (1993) Parallel iterative search methods for vehicle routing problems. Networks 23: 661–673Google Scholar
  62. Yagiura M, Ibaraki T, Glover F (2004) “An ejection chain approach for the generalized assignment problem”. INFORMS J Comput, 16:133–151CrossRefGoogle Scholar

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  1. 1.University of ColoradoBoulderUSA
  2. 2.School of Business AdministrationUniversity of MississippiUniversityUSA

Personalised recommendations