Article Outline
Introduction
Background
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
Applications
References
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References
Aouchiche M, Caporossi G, Hansen P, Laffay M (2005) AutoGraphiX: A Survey. Electron Notes Discret Math 22:515–520
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):695–702
Andreatta A, Ribeiro C (2002) Heuristics for the phylogeny problem. J Heuristics 8(4):429–447
Archetti C, Hertz A, Speranza MG (2007) Metaheuristics for the team orienteering problem. J Heuristics 13(1):49–76
Audet C, Brimberg J, Hansen P, Mladenović N (2004) Pooling problem: alternate formulation and solution methods. Manag Sci 50:761–776
Avanthay C, Hertz A, Zufferey N (2003) A variable neighborhood search for graph coloring. Eur J Oper Res 151(2):379–388
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 53–58
Belacel N, Cuperlovic-Culf M, Ouellette R (2004) Fuzzy J‑Means and VNS methods for clustering genes from microarray data. Bioinformatics 20(11):1690–1701
Belacel N, Hansen P, Mladenović N (2002) Fuzzy J-Means: a new heuristic for fuzzy clustering. Pattern Recognit 35(10):2193–2200
Benati S, Hansen P (2002) The maximum capture problem with random utilities: Problem formulation and algorithms. Eur J Oper Res 143(3):518–530
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)
Braysy O (2003) A reactive variable neighborhood search for the vehicle routing problem with time windows. INFORMS J Comput 15(4):347–368
Brimberg J, Hansen P, Lih KW, Mladenović N, Breton M (2003) An oil pipeline design problem. Oper Res 51(2):228–239
Brimberg J, Hansen P, Mladenović N, Taillard É (2000) Improvements and comparison of heuristics for solving the Multisource Weber problem. Oper Res 48(3):444–460
Brimberg J, Mladenović N (1996) A variable neighborhood algorithm for solving the continuous location-allocation problem. Stud Locat Anal 10:1–12
Brimberg J, Urosević D, Mladenović N (2006) Variable neighborhood search for the vertex weighted k‑cardinality tree problem. Eur J Oper Res 171(1):74–84
Burke E, Kendall G (2005) Search Methodologies. Introductory tutorials in optimization and decision support techniques. Springer, Berlin
Canuto S, Resende M, Ribeiro C (2001) Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 31(3):201–206
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)
Caporossi G, Hansen P (2000) Variable neighborhood search for extremal graphs. 1. The AutoGraphiX system. Discret Math 212:29–44
Caporossi G, Hansen P (2004) Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures. Discret Math 276(1–3):81–94
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 39:984–996
Caporossi G, Gutman I, Hansen P (1999) Variable neighborhood search for extremal graphs. IV: Chemical trees with extremal connectivity index. Comput Chem 23(5):469–477
Costa MC, Monclar FR, Zrikem M (2002) Variable neighborhood decomposition search for the optimization of power plant cable layout. J Intell Manuf 13(5):353–365
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 3616:294–312
Crainic T, Gendreau M, Hansen P, Mladenović N (2004) Cooperative parallel variable neighborhood search for the p-median. J Heuristics 10:289–310
Davidović T (2000) Scheduling heuristic for dense task graphs. Yugoslav J Oper Res 10:113–136
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):297–326
Degila JR, Sansò B (2004) Topological design optimization of a Yottabit-per-second lattice network. IEEE J Sel Areas Commun 22(9):1613–1625
Desrosiers J, Mladenović N, Villeneuve D (2005) Design of balanced MBA student teams. J Oper Res Soc 56(1):60–66
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 4007:24–35
Dominguez-Marin P, Nickel S, Hansen P, Mladenović N (2005) Heuristic procedures for solving the Discret Ordered Median Problem. Annals Oper Res 136(1):145–173
Drezner Z (2005) The extended concentric tabu for the quadratic assignment problem. Eur J Oper Res 160(2):416–422
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):65–94
du Merle O, Hansen P, Jaumard B, Mladenović N (2000) An interior point algorithm for Minimum sum-of-squares clustering. SIAM J Sci Comput 21:1485–1505
du Merle O, Villeneuve D, Desrosiers J et al (1999) Stabilized column generation. Discret Math 194(1–3):229–237
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):440–462
Festa P, Pardalos PM, Resende MGC, Ribeiro CC (2002) Randomized heuristics for the MAX-CUT problem. Optim Methods Softw 17(6):1033–1058
Fischetti M, Lodi A (2003) Local branching. Math Program 98(1–3):23–47
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):61–72
Fleszar K, Hindi KS (2004) Solving the resource-constrained project scheduling problem by a variable neighborhood search. Eur J Oper Res 155(2):402–413
Fleszar K, Hindi KS (2002) New heuristics for one-dimensional bin-packing. Comput Oper Res 29:821–839
Fletcher R, Powell MJD (1963) Rapidly convergence method for minimization. Comput J 6:163–168
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):375–388
Garcia CG, Perez-Brito D, Campos V, Marti R (2006) Variable neighborhood search for the linear ordering problem. Comput Oper Res 33(12):3549–3565
Garey MR, Johnson DS (1978) Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York
Gendreau M, Potvin JY (2005) Metaheuristics in combinatorial optimization. Annals Oper Res 140(1):189–213
Gill P, Murray W, Wright M (1981) Practical optimization. Academic Press, London
Glover F, Kochenberger G (eds) (2003) Handbook of Metaheuristics. Kluwer, Boston
Griffith RE, Stewart RA (1961) A nonlinear programming technique for the optimization of continuous processing systems. Manag Sci 7:379–392
Gupta SR, Smith JS (2006) Algorithms for single machine total tardiness scheduling with sequence dependent setups. Eur J Oper Res 175(2):722–739
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
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, Canada
Hansen P, Mladenović N (1997) Variable neighborhood search for the p-median. Locat Sci 5:207–226
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 433–458
Hansen P, Mladenović N (2001) Variable neighborhood search: Principles and applications. Eur J Oper Res 130:449–467
Hansen P, Mladenović N (2001) J-Means: A new local search heuristic for minimum sum-of-squares clustering. Pattern Recognit 34:405–413
Hansen P, Mladenović N (2001) Developments of variable neighborhood search. In: Ribeiro C, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer, Boston, pp 415–440
Hansen P, Mladenović N (2003) Variable Neighborhood Search. In: Glover F, Kochenberger G (eds) Handbook of Metaheuristics. Kluwer, Boston, pp 145–184
Hansen P, Mladenović N, Perez-Brito D (2001) Variable neighborhood decomposition search. J Heuristics 7(4):335–350
Hansen P, Mladenović N, Urosević D (2006) Variable neighborhood search and local branching. Comput Oper Res 33(10):3034–3045
Hansen P, Mladenović N, Urosević D (2004) Variable neighborhood search for the maximum clique. Discret Appl Math 145(1):117–125
Hertz A, Mittaz M (2001) A variable neighborhood descent algorithm for the undirected capacitated arc routing problem. Transp Sci 35(4):425–434
Hertz A, Plumettaz M, Zufferey N (2006) Variable space search for graph coloring. Les Cahiers du GERAD G–2006–81. Res Report, HEC Montréal, Canada
Hindi KS, Fleszar K, Charalambous C (2003) An effective heuristic for the CLSP with setup times. J Oper Res Soc 54(5):490–498
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):2743–2757
Lapierre SD, Ruiz AB, Soriano P (2004) Designing distribution networks: Formulations and solution heuristic. Transp Sci 38(2):174–187
Lejeune MA (2006) A variable neighborhood decomposition search method for supply chain management planning problems. Eur J Oper Res 175(2):959–976
Liang YC, Chen YC (2007) Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm. Reliab Eng System Saf 92(3):323–331
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 4247:197–204
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):375–388
Melechovsky J, Prins C, Calvo R (2005) A metaheuristic to solve a location-routing problem with non-linear costs. J Heuristics 11(5–6):375–391
Melian B (2006) Using memory to improve the VNS metaheuristic for the design of SDH/WDM networks. Hybrid Metaheuristics, Proc Lect Notes Comput Sci 4030:82–93
Mladenović N (1995) A variable neighborhood algorithm – a new metaheuristic for combinatorial optimization. In: Abstracts of papers presented at Optimization Days. GERAD, Montréal, p 112
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 3
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):927–939
Mladenović N, Labbé M, Hansen P (2003) Solving the p-center problem by Tabu search and Variable Neighborhood Search. Networks 42:48–64
Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24:1097–1100
Mladenović N, Moreno JP, Moreno-Vega J (1996) A Chain‐interchange heuristic method. Yugoslav J Oper Res 6:41–54
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 151:389–399
Mladenović N, Plastria F, Urošević D (2005) Reformulation descent applied to circle packing problems. Comput Oper Res 32:2419–2434
Nuortio T, Kytojoki J, Niska H, Braysy O (2006) Improved route planning and scheduling of waste collection and transport. Expert Syst Appl 30(2):223–232
Ochi LS, Silva MB, Drummond L (2001) Metaheuristics based on GRASP and VNS for solving Traveling purchaser problem. MIC'2001. Porto University, pp 489–494
Plastria F, Mladenović N, Urošević D (2005) Variable neighborhood formulation space search for circle packing. In: 18th Mini Euro Conference VNS, Tenerife, Spain, pp 137–141
Papadimitriou C (1994) Computational Complexity. Addison Wesley, New Jersey
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):365–378
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):823–837
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):613–627
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 3906:195–208
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 345:1125–1136
Reeves CR (ed)(1992) Modern heuristic techniques for combinatorial problems. Blackwell Scientific Press, Oxford
Reinelt G (1991) TSLIB – A Traveling salesman library. ORSA J Comput 3:376–384
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 4030:124–138
Ribeiro CC, Souza MC (2002) Variable neighborhood search for the degree-constrained minimum spanning tree problem. Discret Appl Math 118(1–2):43–54
Ribeiro CC, Martins SL, Rosseti I (2007) Metaheuristics for optimization problems in computer communications. Comput Commun 30(4):656–669
Ribeiro CC, Uchoa E, Werneck R (2002) A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J Comput 14(3):228–246
Rousseau LM, Gendreau M, Pesant G (2002) Using constraint-based operators to solve the vehicle routing problem with time windows. J Heuristics 8(1):43–58
Sevkli M, Aydin ME (2006) A variable neighbourhood search algorithm for job shop scheduling problems. Lect Notes Comput Sci 3906:261–271
Stummeer C, Sun MH (2005) New multiobjective metaheuristic solution procedures for capital investment planning. J Heuristics 11(3):183–199
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):45–54
Toksari AD, Guner E (2007) Solving the unconstrained optimization problem by a variable neighborhood search. J Math Anal Appl 328(2):1178–1187
Urosević D, Brimberg J, Mladenović N (2004) Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem. Comput Oper Res 31(8):1205–1213
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 3906:284–292
Whittaker R (1983) A fast algorithm for the greedy interchange for large-scale clustering and median location problems. INFOR 21:95–108
Yepes V, Medina J (2006) Economic heuristic optimization for heterogeneous fleet VRPHESTW. J Transp engineering-Asce 132(4):303–311
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 3684:81–88
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Hansen, P., Mladenović, N. (2008). Variable Neighborhood Search Methods . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_694
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