Encyclopedia of Optimization

2009 Edition
| Editors: Christodoulos A. Floudas, Panos M. Pardalos

Variable Neighborhood Search Methods

  • Pierre Hansen
  • Nenad Mladenović
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-74759-0_694

Article Outline



  Variable Metric Method

  Local Search

Basic Schemes

  Variable Neighborhood Descent

  Reduced VNS

  Basic VNS

  General VNS

  Skewed VNS

  Some Extensions of Basic VNS

  Variable Neighborhood Decomposition Search

  Parallel VNS

  Primal–Dual VNS

  Variable Neighborhood Formulation Space Search



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  1. 1.
    Aouchiche M, Caporossi G, Hansen P, Laffay M (2005) AutoGraphiX: A Survey. Electron Notes Discret Math 22:515–520Google Scholar
  2. 2.
    Aloise DJ, Aloise D, Rocha CTM, Ribeiro CC, Ribeiro JC, Moura LSS (2006) Scheduling workover rigs for onshore oil production. Discret Appl Math 154(5):695–702MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Andreatta A, Ribeiro C (2002) Heuristics for the phylogeny problem. J Heuristics 8(4):429–447MATHCrossRefGoogle Scholar
  4. 4.
    Archetti C, Hertz A, Speranza MG (2007) Metaheuristics for the team orienteering problem. J Heuristics 13(1):49–76Google Scholar
  5. 5.
    Audet C, Brimberg J, Hansen P, Mladenović N (2004) Pooling problem: alternate formulation and solution methods. Manag Sci 50:761–776CrossRefGoogle Scholar
  6. 6.
    Avanthay C, Hertz A, Zufferey N (2003) A variable neighborhood search for graph coloring. Eur J Oper Res 151(2):379–388Google Scholar
  7. 7.
    Baum EB (1987) Toward practical ‘neural’ computation for combinatorial optimization problems. In: AIP Conference Proceedings 151 on Neural Networks for Computing, Snowbird, USA, March 1987, pp 53–58Google Scholar
  8. 8.
    Belacel N, Cuperlovic-Culf M, Ouellette R (2004) Fuzzy J‑Means and VNS methods for clustering genes from microarray data. Bioinformatics 20(11):1690–1701CrossRefGoogle Scholar
  9. 9.
    Belacel N, Hansen P, Mladenović N (2002) Fuzzy J-Means: a new heuristic for fuzzy clustering. Pattern Recognit 35(10):2193–2200MATHCrossRefGoogle Scholar
  10. 10.
    Benati S, Hansen P (2002) The maximum capture problem with random utilities: Problem formulation and algorithms. Eur J Oper Res 143(3):518–530MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Blazewicz J, Pesch E, Sterna M, Werner F (2005) Metaheuristics for late work minimization in two-machine flow shop with common due date. KI2005: Advances in Artificial Intelligence, Proceedings Lecture Notes in Artificial Intelligence 3698:222–234 (2005)Google Scholar
  12. 12.
    Braysy O (2003) A reactive variable neighborhood search for the vehicle routing problem with time windows. INFORMS J Comput 15(4):347–368MathSciNetCrossRefGoogle Scholar
  13. 13.
    Brimberg J, Hansen P, Lih KW, Mladenović N, Breton M (2003) An oil pipeline design problem. Oper Res 51(2):228–239MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Brimberg J, Hansen P, Mladenović N, Taillard É (2000) Improvements and comparison of heuristics for solving the Multisource Weber problem. Oper Res 48(3):444–460Google Scholar
  15. 15.
    Brimberg J, Mladenović N (1996) A variable neighborhood algorithm for solving the continuous location-allocation problem. Stud Locat Anal 10:1–12MATHGoogle Scholar
  16. 16.
    Brimberg J, Urosević D, Mladenović N (2006) Variable neighborhood search for the vertex weighted k‑cardinality tree problem. Eur J Oper Res 171(1):74–84MATHCrossRefGoogle Scholar
  17. 17.
    Burke E, Kendall G (2005) Search Methodologies. Introductory tutorials in optimization and decision support techniques. Springer, BerlinMATHGoogle Scholar
  18. 18.
    Canuto S, Resende M, Ribeiro C (2001) Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 31(3):201–206MathSciNetGoogle Scholar
  19. 19.
    Caporossi G, Alamargot D, Chesnet D (2004) Using the computer to study the dynamics of the handwriting processes. Discov Sci, Proc Lect Notes Comp Sci 3245:242–254 (2004)Google Scholar
  20. 20.
    Caporossi G, Hansen P (2000) Variable neighborhood search for extremal graphs. 1. The AutoGraphiX system. Discret Math 212:29–44MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Caporossi G, Hansen P (2004) Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures. Discret Math 276(1–3):81–94MATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Caporossi G, Cvetković D, Gutman I, Hansen P (1999) Variable neighborhood search for extremal graphs. 2. Finding graphs with extremal energy. J Chem Inf Comput Sci 39:984–996CrossRefGoogle Scholar
  23. 23.
    Caporossi G, Gutman I, Hansen P (1999) Variable neighborhood search for extremal graphs. IV: Chemical trees with extremal connectivity index. Comput Chem 23(5):469–477CrossRefGoogle Scholar
  24. 24.
    Costa MC, Monclar FR, Zrikem M (2002) Variable neighborhood decomposition search for the optimization of power plant cable layout. J Intell Manuf 13(5):353–365CrossRefGoogle Scholar
  25. 25.
    Cote P, Wong T, Sabourin R (2005) A hybrid multi‐objective evolutionary algorithm for the uncapacitated exam proximity problem. Practice and Theory of Automated Timetabling V Lect Notes Comput Sci 3616:294–312Google Scholar
  26. 26.
    Crainic T, Gendreau M, Hansen P, Mladenović N (2004) Cooperative parallel variable neighborhood search for the p-median. J Heuristics 10:289–310Google Scholar
  27. 27.
    Davidović T (2000) Scheduling heuristic for dense task graphs. Yugoslav J Oper Res 10:113–136Google Scholar
  28. 28.
    Davidović T, Hansen P, Mladenović N (2005) Permutation-based genetic, tabu, and variable neighborhood search heuristics for multiprocessor scheduling with communication delays. Asia-Pacific J Oper Res 22(3):297–326MATHCrossRefGoogle Scholar
  29. 29.
    Degila JR, Sansò B (2004) Topological design optimization of a Yottabit-per-second lattice network. IEEE J Sel Areas Commun 22(9):1613–1625CrossRefGoogle Scholar
  30. 30.
    Desrosiers J, Mladenović N, Villeneuve D (2005) Design of balanced MBA student teams. J Oper Res Soc 56(1):60–66MATHCrossRefGoogle Scholar
  31. 31.
    Dias TCS, De Sousa GF, Macambira EM, Cabral LDAF, Fampa MHC (2006) An efficient heuristic for the ring star problem. Exp Alg, Proc Lect Notes Comput Sci 4007:24–35Google Scholar
  32. 32.
    Dominguez-Marin P, Nickel S, Hansen P, Mladenović N (2005) Heuristic procedures for solving the Discret Ordered Median Problem. Annals Oper Res 136(1):145–173MATHCrossRefGoogle Scholar
  33. 33.
    Drezner Z (2005) The extended concentric tabu for the quadratic assignment problem. Eur J Oper Res 160(2):416–422Google Scholar
  34. 34.
    Drezner Z, Hahn PM, Taillard ED (2005) Recent advances for the quadratic assignment problem with special emphasis on instances that are difficult for meta-heuristic methods. Annals Oper Res 139(1):65–94MATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    du Merle O, Hansen P, Jaumard B, Mladenović N (2000) An interior point algorithm for Minimum sum-of-squares clustering. SIAM J Sci Comput 21:1485–1505MATHCrossRefGoogle Scholar
  36. 36.
    du Merle O, Villeneuve D, Desrosiers J et al (1999) Stabilized column generation. Discret Math 194(1–3):229–237MATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Fathali J, Kakhki HT (2006) Solving the p-median problem with pos/neg weights by variable neighborhood search and some results for special cases. Eur J Oper Res 170(2):440–462MATHMathSciNetCrossRefGoogle Scholar
  38. 38.
    Festa P, Pardalos PM, Resende MGC, Ribeiro CC (2002) Randomized heuristics for the MAX-CUT problem. Optim Methods Softw 17(6):1033–1058MATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    Fischetti M, Lodi A (2003) Local branching. Math Program 98(1–3):23–47MATHMathSciNetCrossRefGoogle Scholar
  40. 40.
    Fischetti M, Polo C, Scantamburlo M (2004) A local branching heuristic for mixed-integer programs with 2‑level variables, with an application to a telecommunication network design problem. Networks 44(2):61–72MATHMathSciNetCrossRefGoogle Scholar
  41. 41.
    Fleszar K, Hindi KS (2004) Solving the resource-constrained project scheduling problem by a variable neighborhood search. Eur J Oper Res 155(2):402–413MATHMathSciNetCrossRefGoogle Scholar
  42. 42.
    Fleszar K, Hindi KS (2002) New heuristics for one-dimensional bin-packing. Comput Oper Res 29:821–839MATHCrossRefGoogle Scholar
  43. 43.
    Fletcher R, Powell MJD (1963) Rapidly convergence method for minimization. Comput J 6:163–168MATHMathSciNetGoogle Scholar
  44. 44.
    Garcia-Lopez F, Melian-Batista B, Moreno-Perez JA, Moreno-Vega JM (2002) The parallel variable neighborhood search for the p-median problem. J Heuristics 8(3):375–388MATHCrossRefGoogle Scholar
  45. 45.
    Garcia CG, Perez-Brito D, Campos V, Marti R (2006) Variable neighborhood search for the linear ordering problem. Comput Oper Res 33(12):3549–3565MATHCrossRefGoogle Scholar
  46. 46.
    Garey MR, Johnson DS (1978) Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New YorkGoogle Scholar
  47. 47.
    Gendreau M, Potvin JY (2005) Metaheuristics in combinatorial optimization. Annals Oper Res 140(1):189–213MATHMathSciNetCrossRefGoogle Scholar
  48. 48.
    Gill P, Murray W, Wright M (1981) Practical optimization. Academic Press, LondonMATHGoogle Scholar
  49. 49.
    Glover F, Kochenberger G (eds) (2003) Handbook of Metaheuristics. Kluwer, BostonMATHGoogle Scholar
  50. 50.
    Griffith RE, Stewart RA (1961) A nonlinear programming technique for the optimization of continuous processing systems. Manag Sci 7:379–392MATHMathSciNetGoogle Scholar
  51. 51.
    Gupta SR, Smith JS (2006) Algorithms for single machine total tardiness scheduling with sequence dependent setups. Eur J Oper Res 175(2):722–739MATHCrossRefGoogle Scholar
  52. 52.
    Hansen P, Brimberg J, Urosevic D, Mladenovic N (2007) Primal-Dual Variable Neighborhood Search for the Simple Plant Location Problem. INFORMS J Comput, doi:10.1287/ijoc.1060.0196
  53. 53.
    Hansen P, Jaumard B, Mladenović N, Parreira A (2000) Variable neighborhood search for Weighted maximum satisfiability problem. Les Cahiers du GERAD G–2000–62, HEC Montréal, CanadaGoogle Scholar
  54. 54.
    Hansen P, Mladenović N (1997) Variable neighborhood search for the p-median. Locat Sci 5:207–226MATHCrossRefGoogle Scholar
  55. 55.
    Hansen P, Mladenović N (1999) An introduction to variable neighborhood search. In: Voss S et al (eds) Metaheuristics, Advances and Trends in Local Search Paradigms for Optimization. Kluwer, Dordrecht, pp 433–458Google Scholar
  56. 56.
    Hansen P, Mladenović N (2001) Variable neighborhood search: Principles and applications. Eur J Oper Res 130:449–467MATHCrossRefGoogle Scholar
  57. 57.
    Hansen P, Mladenović N (2001) J-Means: A new local search heuristic for minimum sum-of-squares clustering. Pattern Recognit 34:405–413MATHCrossRefGoogle Scholar
  58. 58.
    Hansen P, Mladenović N (2001) Developments of variable neighborhood search. In: Ribeiro C, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer, Boston, pp 415–440Google Scholar
  59. 59.
    Hansen P, Mladenović N (2003) Variable Neighborhood Search. In: Glover F, Kochenberger G (eds) Handbook of Metaheuristics. Kluwer, Boston, pp 145–184CrossRefGoogle Scholar
  60. 60.
    Hansen P, Mladenović N, Perez-Brito D (2001) Variable neighborhood decomposition search. J Heuristics 7(4):335–350MATHCrossRefGoogle Scholar
  61. 61.
    Hansen P, Mladenović N, Urosević D (2006) Variable neighborhood search and local branching. Comput Oper Res 33(10):3034–3045MATHCrossRefGoogle Scholar
  62. 62.
    Hansen P, Mladenović N, Urosević D (2004) Variable neighborhood search for the maximum clique. Discret Appl Math 145(1):117–125MATHCrossRefGoogle Scholar
  63. 63.
    Hertz A, Mittaz M (2001) A variable neighborhood descent algorithm for the undirected capacitated arc routing problem. Transp Sci 35(4):425–434MATHCrossRefGoogle Scholar
  64. 64.
    Hertz A, Plumettaz M, Zufferey N (2006) Variable space search for graph coloring. Les Cahiers du GERAD G–2006–81. Res Report, HEC Montréal, CanadaGoogle Scholar
  65. 65.
    Hindi KS, Fleszar K, Charalambous C (2003) An effective heuristic for the CLSP with setup times. J Oper Res Soc 54(5):490–498MATHCrossRefGoogle Scholar
  66. 66.
    Kytojoki J, Nuortio T, Braysy O, Gendreau M (2007) An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Comput Oper Res 34(9):2743–2757CrossRefGoogle Scholar
  67. 67.
    Lapierre SD, Ruiz AB, Soriano P (2004) Designing distribution networks: Formulations and solution heuristic. Transp Sci 38(2):174–187CrossRefGoogle Scholar
  68. 68.
    Lejeune MA (2006) A variable neighborhood decomposition search method for supply chain management planning problems. Eur J Oper Res 175(2):959–976MATHCrossRefGoogle Scholar
  69. 69.
    Liang YC, Chen YC (2007) Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm. Reliab Eng System Saf 92(3):323–331CrossRefGoogle Scholar
  70. 70.
    Liu HB, Abraham A, Choi O, Moon SH (2006) Variable neighborhood particle swarm optimization for multi-objective flexible job-shop scheduling problems. Simulated Evolution and Learning, Proc Lect Notes Comput Sci 4247:197–204Google Scholar
  71. 71.
    Lopez FG, Batista BM, Moreno Pérez JA, Moreno Vega JM (2002) The parallel variable neighborhood search for the p-median problem. J Heuristic 8(3):375–388MATHCrossRefGoogle Scholar
  72. 72.
    Melechovsky J, Prins C, Calvo R (2005) A metaheuristic to solve a location-routing problem with non-linear costs. J Heuristics 11(5–6):375–391MATHCrossRefGoogle Scholar
  73. 73.
    Melian B (2006) Using memory to improve the VNS metaheuristic for the design of SDH/WDM networks. Hybrid Metaheuristics, Proc Lect Notes Comput Sci 4030:82–93Google Scholar
  74. 74.
    Mladenović N (1995) A variable neighborhood algorithm – a new metaheuristic for combinatorial optimization. In: Abstracts of papers presented at Optimization Days. GERAD, Montréal, p 112Google Scholar
  75. 75.
    Mladenović N (2005) Formulation space search – a new approach to optimization (plenary talk). In: Vuleta J (eds) Proceedings of XXXII SYMOPIS'05. Vrnjacka Banja, Serbia, p 3Google Scholar
  76. 76.
    Mladenović N, Brimberg J, Hansen P, Moreno Perez JA (2007) The p-median problem: A survey of metaheuristic approaches. Eur J Oper Res 179(3):927–939MATHCrossRefGoogle Scholar
  77. 77.
    Mladenović N, Labbé M, Hansen P (2003) Solving the p-center problem by Tabu search and Variable Neighborhood Search. Networks 42:48–64MATHMathSciNetCrossRefGoogle Scholar
  78. 78.
    Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24:1097–1100MATHMathSciNetCrossRefGoogle Scholar
  79. 79.
    Mladenović N, Moreno JP, Moreno-Vega J (1996) A Chain‐interchange heuristic method. Yugoslav J Oper Res 6:41–54Google Scholar
  80. 80.
    Mladenović N, Petrović J, Kovačević-Vujčić V, Čangalović M (2003) Solving Spread spectrum radar polyphase code design problem by Tabu search and Variable neighborhood search. Eur J Oper Res 151:389–399MATHCrossRefGoogle Scholar
  81. 81.
    Mladenović N, Plastria F, Urošević D (2005) Reformulation descent applied to circle packing problems. Comput Oper Res 32:2419–2434MATHCrossRefGoogle Scholar
  82. 82.
    Nuortio T, Kytojoki J, Niska H, Braysy O (2006) Improved route planning and scheduling of waste collection and transport. Expert Syst Appl 30(2):223–232CrossRefGoogle Scholar
  83. 83.
    Ochi LS, Silva MB, Drummond L (2001) Metaheuristics based on GRASP and VNS for solving Traveling purchaser problem. MIC'2001. Porto University, pp 489–494Google Scholar
  84. 84.
    Plastria F, Mladenović N, Urošević D (2005) Variable neighborhood formulation space search for circle packing. In: 18th Mini Euro Conference VNS, Tenerife, Spain, pp 137–141Google Scholar
  85. 85.
    Papadimitriou C (1994) Computational Complexity. Addison Wesley, New JerseyMATHGoogle Scholar
  86. 86.
    Perez JAM, Moreno-Vega JM, Martin IR (2003) Variable neighborhood tabu search and its application to the median cycle problem. Eur J Oper Res 151(2):365–378MATHCrossRefGoogle Scholar
  87. 87.
    Polacek M, Doerner KF, Hard RF, Kiechle G, Reimann M (2007) Scheduling periodic customer visits for a traveling salesperson. Eur J Oper Res 179(3):823–837MATHCrossRefGoogle Scholar
  88. 88.
    Polacek M, Hartl RF, Doemer K (2004) A variable neighborhood search for the multi depot vehicle routing problem with time windows. J Heuristics 10(6):613–627CrossRefGoogle Scholar
  89. 89.
    Puchinger J, Raidl GR, Pferschy U (2006) The core concept for the Multidimensional Knapsack Problem. Evolutionary Computation in Combinatorial Optimization, Proc Lect Notes Comput Sci 3906:195–208Google Scholar
  90. 90.
    Qian B, Wang L, Huang DX, Wang X (2006) Multi-objective flow shop scheduling using differential evolution. Intell Computing in Signal Processing and Pattern Recognition. Lect Notes Control Inf Scis 345:1125–1136CrossRefGoogle Scholar
  91. 91.
    Reeves CR (ed)(1992) Modern heuristic techniques for combinatorial problems. Blackwell Scientific Press, OxfordGoogle Scholar
  92. 92.
    Reinelt G (1991) TSLIB – A Traveling salesman library. ORSA J Comput 3:376–384MATHGoogle Scholar
  93. 93.
    Repoussis PP, Paraskevopoulos DC, Tarantilis CD, Ioannou G (2006) A reactive greedy randomized variable neighborhood Tabu search for the vehicle routing problem with time windows. Hybrid Metaheuristics, Proc Lect Notes Comput Sci 4030:124–138Google Scholar
  94. 94.
    Ribeiro CC, Souza MC (2002) Variable neighborhood search for the degree-constrained minimum spanning tree problem. Discret Appl Math 118(1–2):43–54MATHMathSciNetCrossRefGoogle Scholar
  95. 95.
    Ribeiro CC, Martins SL, Rosseti I (2007) Metaheuristics for optimization problems in computer communications. Comput Commun 30(4):656–669CrossRefGoogle Scholar
  96. 96.
    Ribeiro CC, Uchoa E, Werneck R (2002) A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J Comput 14(3):228–246Google Scholar
  97. 97.
    Rousseau LM, Gendreau M, Pesant G (2002) Using constraint-based operators to solve the vehicle routing problem with time windows. J Heuristics 8(1):43–58MATHCrossRefGoogle Scholar
  98. 98.
    Sevkli M, Aydin ME (2006) A variable neighbourhood search algorithm for job shop scheduling problems. Lect Notes Comput Sci 3906:261–271CrossRefGoogle Scholar
  99. 99.
    Stummeer C, Sun MH (2005) New multiobjective metaheuristic solution procedures for capital investment planning. J Heuristics 11(3):183–199CrossRefGoogle Scholar
  100. 100.
    Tagawa K, Ohtani T, Igaki T, Seki S, Inoue K (2007) Robust optimum design of SAW filters by the penalty function method. Electr Eng Japan 158(3):45–54CrossRefGoogle Scholar
  101. 101.
    Toksari AD, Guner E (2007) Solving the unconstrained optimization problem by a variable neighborhood search. J Math Anal Appl 328(2):1178–1187MATHMathSciNetCrossRefGoogle Scholar
  102. 102.
    Urosević D, Brimberg J, Mladenović N (2004) Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem. Comput Oper Res 31(8):1205–1213MATHMathSciNetCrossRefGoogle Scholar
  103. 103.
    Villa G, Lozano S, Racero J, Canca D (2006) A hybrid VNS/Tabu Search algorithm for apportioning the European Parliament. Evolutionary Computation in Combinatorial Optimization. Proc Lect Notes Comput Sci 3906:284–292Google Scholar
  104. 104.
    Whittaker R (1983) A fast algorithm for the greedy interchange for large-scale clustering and median location problems. INFOR 21:95–108Google Scholar
  105. 105.
    Yepes V, Medina J (2006) Economic heuristic optimization for heterogeneous fleet VRPHESTW. J Transp engineering-Asce 132(4):303–311Google Scholar
  106. 106.
    Zhang C, Lin ZG, Lin ZQ (2005) Variable neighborhood search with permutation distance for QAP. Knowledge-Based Intelligent Information and Engineering Systems, PT 4. Proc Lecture Notes Artif Intell 3684:81–88Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Pierre Hansen
    • 1
  • Nenad Mladenović
    • 2
  1. 1.GERAD and HEC MontréalMontrealCanada
  2. 2.GERAD and School of MathematicsBrunel UniversityUxbridgeUK