Skip to main content
Log in

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

  • Invited survey
  • Published:
4OR Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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):118–125

    Google Scholar 

  • Adams J, Balas E, Zawack D (1988) The shifting bottleneck procedure for job shop scheduling. Manage Sci 34 (3):391–401

    Google Scholar 

  • Ahuja RK, Orlin JB, Sharma D (2001) Multi-exchange neighborhood search structures for the capacitated minimum spanning tree problem. Math Program 91:71–97

    Google Scholar 

  • Ahuja RK, Orlin JB, Sharma D (2002) Very large-scale neighborhood search for the quadratic assignment problem. submitted to INFORMS J Comput

  • Ahuja RK, Orlin JB, Sharma D (2003) A composite very large-scale neighborhood structure for the capacitated minimum spanning tree problem. Operat Res Lett 31:185–194

    Article  Google Scholar 

  • Amberg A, Domschke W, Voß S (1996) Capacitated minimum spanning trees: algorithms using intelligent search. Comb Opt Theory Practice 1:9–39

    Google Scholar 

  • Applegate D, Cook W, Rohe A (2003) Chained Lin-Kernighan for large traveling salesman problems. INFORMS J Comput 15:82–92

    Article  Google Scholar 

  • Balas E, Vazacopoulos A (1998) Guided local search with shifting bottleneck for job shop scheduling. Manage Sci 44(2):262–275

    Google Scholar 

  • Cavique L, Rego C, Themido I (1999) Subgraph ejection chains and tabu search for the crew scheduling problem. J Operat Res Soci 50:608–616

    Article  Google Scholar 

  • 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):908–921

    Google Scholar 

  • Cela E (1998) The quadratic assignment problem: theory and algorithms. Kluwer, Boston

    Google Scholar 

  • Chan HS, Dill KA (1993) The protein folding problem. Phys Today 46(2):24–32

    Google Scholar 

  • Chrobak M, Szymacha T, Krawczyk A (1990) A data structure useful for finding hamiltonian cycles. Theoret Comput Sci 71:419–424

    Article  Google Scholar 

  • Christofides N, Mingozzi A, Toth P (1979) The vehicle routing problem. In: Mingozzi A, Toth P, Sandi C (eds) Combinatorial optimisation. Wiley, Chichester, pp 315–338

    Google Scholar 

  • 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 32–59

  • 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 119–171

    Google Scholar 

  • Dill KA (1985) “Theory for the folding and stability of globular proteins,”. Biochemistry 24(6): 1501-1509

    Article  Google Scholar 

  • Dorndorf U, Pesch E (1994) Fast clustering algorithms. ORSA J Comput 6:141–153

    Google Scholar 

  • Fisher ML (1994) Optimal solution of vehicle routing problems using minimum k-trees. Operat Res 42(4):626–642

    Google Scholar 

  • Fredman ML, Johnson DS, McGeoch LA, Ostheimer G (1995) Data structures for traveling salesmen. J Algorithms 18:432–479

    Article  Google Scholar 

  • Funke B, Grünert T, Irnich S (2005) A note on single alternating cycle neighborhoods for the TSP. J Heuristics, 11:135–146

    Article  Google Scholar 

  • Gamboa D, Rego C, Glover F (2005) Data structures and ejection chains for solving large-scale traveling salesman problems. Eur J Operat Res 160:154–171

    Article  Google Scholar 

  • Gamboa D, Rego C, Glover F (2006a) Implementation analysis of efficient heuristic algorithms for the traveling salesman problem. Comput Operat Res 33:1161–1179

    Article  Google Scholar 

  • 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, MS

  • Gao LL, Robinson EP (1994) Uncapacitated facility location: general solution procedures and computational experience. Eur J Operat Res 76:410–427

    Article  Google Scholar 

  • Gavish B (1982) Topological design of centralized computer networks: formulations and algorithms. Networks 12:355–377

    Google Scholar 

  • Gavish B (1991) Topological design telecommunications networks—local access design methods. Ann Operat Res 33:17–71

    Article  Google Scholar 

  • Glover F (1991) Multilevel tabu search and embedded search neighborhoods for the traveling salesman problem. Leeds School of Business, University of Colorado, Boulder

  • Glover F (1992) New ejection chain and alternating path methods for traveling salesman problems. Comput Sci Operat Res 449–509

  • Glover F (1996) Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discrete Appli Math 65:223–253

    Article  Google Scholar 

  • 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 3–51

    Google Scholar 

  • Glover F, Laguna M (1997) Tabu Search. Kluwer, Boston

    Google Scholar 

  • Gonçalves JF, Mendes JJM, Resende MGC (2005) A hybrid genetic algorithm for the job shop scheduling problem. Eur J Operat Res 167:77–95

    Article  Google Scholar 

  • 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 191–211

    Google Scholar 

  • Greistorfer P, Rego C (2006) A simple filter-and-fan approach to the facility location problem. Comput Operat Res 33(9):2590–2601

    Article  Google Scholar 

  • Helsgaun K (2000) An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur J Operat Res 126:106–130

    Article  Google Scholar 

  • 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, 215–310

  • Johnson DS, McGeoch LA, Glover F, Rego C (2000) 8th DIMACS implementation challenge: the traveling salesman problem. http://www.research. att.com/~dsj/chtsp/

  • Kanellakis PC, Papadimitriou CH (1980) Local search for the asymmetric traveling salesman problem. Operat Res 28:1086–1099

    Google Scholar 

  • 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, 177–192

  • 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 188–195

  • Lin S, Kernighan B (1973) An effective heuristic algorithm for the traveling salesman problem. Operat Res 21:498–516

    Article  Google Scholar 

  • 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). 31021–31026

  • 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, MS

  • Nowichi E, Smutnicki C (1996) A fast taboo search algorithm for the job shop problem. Manage Sci 42(6):797–813

    Google Scholar 

  • Osterman C, Rego C (2003) The satellite list and new data structures for symmetric traveling salesman problems. School of Business Administration, University of Mississippi, MS

  • Patterson R, Pirkul H, Rolland E (1999) Memory adaptive reasoning for solving the capacitated minimum spanning tree problem. J Heuristics 5:159–180

    Article  Google Scholar 

  • Pinedo ML (2006) Planning and scheduling in manufacturing and services. Series in operations research and financial engineering. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Rego C (1998a) Relaxed tours and path ejections for the traveling salesman problem. Eur J Operat Res 106:522–538

    Article  Google Scholar 

  • Rego C (1998b) A subpath ejection method for the vehicle routing problem. Manage Sci 44(10):1447–1459

    Google Scholar 

  • Rego C (2001) Node ejection chains for the vehicle routing problem: sequential and parallel algorithms. Parallel Comput 27:201–222

    Article  Google Scholar 

  • Rego C, Duarte R (2006) A filter and fan approach for the job shop scheduling problem. School of Business Administration, University of Mississippi, MS

  • 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 309–368

    Google Scholar 

  • 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, MS

  • 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, MS

  • Rego C, James T, Glover F (2006c) “An ejection chain algorithm for the quadratic assignment problem,” School of Business Ad on, University of Mississippi, MS

  • Richards FM (1991) The protein folding problem. Sci Am 264(1):54–7, 60–3

    Google Scholar 

  • Rochat Y, Taillard E (1995) Probabilistic intensification and diversification in local search for vehicle routing. J Heuristics. 1:147–167

    Article  Google Scholar 

  • Sabuncuoglu I, Bayiz M (1999) Job shop scheduling with beam search. Eur J Operat Res 118: 390–412

    Article  Google Scholar 

  • Sharaiha YM, Gendreau M, Laporte G, Osman IH (1997) A tabu search algorithm for the capacitated shortest spanning tree problem. Networks 29:161–171

    Article  Google Scholar 

  • Taillard E (1993) Parallel iterative search methods for vehicle routing problems. Networks 23: 661–673

    Google Scholar 

  • Yagiura M, Ibaraki T, Glover F (2004) “An ejection chain approach for the generalized assignment problem”. INFORMS J Comput, 16:133–151

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fred Glover.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glover, F., Rego, C. Ejection chain and filter-and-fan methods in combinatorial optimization. 4OR 4, 263–296 (2006). https://doi.org/10.1007/s10288-006-0029-x

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10288-006-0029-x

Keywords

MSC classification

Navigation