Abstract
Very Large-Scale Neighborhood Search is not an algorithm or a class of algorithms, but rather a conceptual framework which can be used for solving combinatorial optimization problems. The approach “concentrates on neighborhood search algorithms where the size of the neighborhood is ‘very large’ with respect to the size of the input data.” Typically, the searched neighborhoods are exponentially large, but the term has come to be used more generally to describe algorithms working on neighborhoods that are too large to explicitly search in practice. The search of the large neighborhood has often been made by dedicated mathematical programming modules, deriving from different techniques. This chapter reports on the rich literature following this approach and proposes a possible implementation for the GAP.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahuja RK, Magnanti TL, Orlin J (1993) Network flows: Theory, algorithms, and applications. Prentice-Hall, Upper Saddle River, NJ, USA
Ahuja RK, Orlin JB, Sharma D (1999) New neighborhood search structures for the capacitated minimum spanning tree problem. Technical Report 99-2, Department of Industrial and Systems Engineering, University of Florida
Ahuja RK, Orlin JB, Sharma D (2000) Very large-scale neighborhood search. Int Trans Oper Res 7(4-5):301–317
Ahuja RK, Ergun O, Orlin JB, Punnen APA (2002) Survey of very large-scale neighborhood search techniques. Discrete Appl Math 123:75–102
Ahuja RK, Orlin JB, Pallottino S, Scaparra MP, Scutella MG (2004) A multi-exchange heuristic for the single source capacitated facility location. Management Science 50:749–760
Ahuja RK, Ergun O, Orlin JB, Punnen AP (2007) Very large-scale neighborhood search. In: Gonzalez TF (ed) Approximation algorithms and metaheuristics. Chapman & Hall, pp 20–1–20–12
Altner DS (2017) Very large-scale neighborhood search. In: Handbook of discrete and combinatorial mathematics. Chapman and Hall/CRC
Altner DS, Ahuja RK, Ergun O, Orlin JB (2014) Very large-scale neighborhood search. In: Burke E, Kendall G (eds) Search methodologies. Springer, Boston, MA
Brueggemann T, Hurink JL (2007) Two exponential neighborhoods for single machine scheduling. OR Spectrum 29:513–533
Brueggemann T, Hurink JL (2011) Matching based very large-scale neighborhoods for parallel machine scheduling. J Heuristics 17(6):637–658
Chiarandini M, Dumitrescu I, Stützle T (2008) Very large-scale neighborhood search: Overview and case studies on coloring problems. In: Blum C, Blesa MJ, Roli A, Sampels M (eds) Hybrid metaheuristics, vol. 114. Studies in computational intelligence. Springer, pp 117–150
Congram RK (2000) Polynomially searchable exponential neighbourhoods for sequencing problems in combinatorial optimization. Ph.D. thesis, Southampton University, Faculty of Mathematical Studies, Southampton, UK
Congram RK, Potts CN, van de Velde S (2002) An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS J Comput 14(1):52–67
Copado-Méndez P, Blum C, Guillén-Gosálbez G, Jiménez L (2013) Large neighbourhood search applied to the efficient solution of spatially explicit strategic supply chain management problems. Comput Chem Eng 49:114–126
Cunha CB, Ahuja RK (2005) Very large scale neighborhood search for the k-constrained multiple knapsack problem. J Heuristics 11:465–481
De Franceschi R, Fischetti M, Toth P (2006) A new ILP-based refinement heuristic for vehicle routing problems. Mathematical Programming 105(2-3):471–499
Dror M, Levy L (1986) A vehicle routing improvement algorithm comparison of a “greedy” and a “matching” implementation for inventory routing. Comput Oper Res 13:33–45
Ergun O, Orlin JB, Steele-Feldman A (2006) Creating very large scale neighborhoods out of smaller ones by compounding moves. J Heuristics 12(1-2):115–140
Fischetti M, Lodi A, Salvagnin D (2009) Just MIP it! In: Maniezzo V, Stützle T, Voß S (eds) Matheuristics: Hybridizing metaheuristics and mathematical programming. Annals of information systems, vol 10. Springer, pp 39–70
Frangioni A, Necciari E, Scutellá MG (2004) A multi-exchange neighborhood for minimum makespan parallel machine scheduling problems. J Comb Optim 8(2):195–220
Gendreau M, Guertin F, Potvin JY, Seguin R (2006) Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries. Transp Res C Emerg Technol 14:157–174
Hewitt M, Nemhauser GL, Savelsbergh MWP (2010) Combining exact and heuristic approaches for the capacitated fixed-charge network flow problem. INFORMS J Comput 22(2):314–325
Lin S, Kernighan B (1973) An effective heuristic algorithm for the traveling salesman problem. Operations Research 21:498–516
Meyers C, Orlin JB (2006) Very large-scale neighborhood search techniques in timetabling problems. In: Burke EK, Rudová H (eds) Proceedings of the 6th international conference on practice and theory of automated timetabling VI (PATAT’06). Springer, Berlin, Heidelberg, pp 24–39
Mitrović-Minić S, Punnen AP (2008) Very large-scale variable neighborhood search for the generalized assignment problem. J Interdisciplinary Math 11(5):653–670
Mitrović-Minić S, Punnen AP (2009) Variable intensity local search. In: Maniezzo V, Stützle T, Voß S (eds) Matheuristics: Hybridizing metaheuristics and mathematical programming. Annals of information systems, vol 10. Springer US, Boston, MA, pp 245–252
Nishi T, Okura T, Lalla-Ruiz E, Voß S (2020) A dynamic programming-based matheuristic for the dynamic berth allocation problem. Ann Oper Res 286:391–410
Pisinger D, Ropke S (2010) Large neighborhood search. In: Gendreau M, Potvin J (eds) Handbook of metaheuristics. International series in operations research & management science, vol 146. Springer, Boston, MA, pp 399–419
Roli A, Benedettini S, Stützle T, Blum C (2012) Large neighbourhood search algorithms for the founder sequence reconstruction problem. Comput Oper Res 39:213–224
Ropke S, Pisinger D (2006) An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science 40(4):455–472
Salari M, Toth P, Tramontani A (2010) An ILP improvement procedure for the open vehicle routing problem. Comput Oper Res 37(12):2106–2120
Sarvanov VI, Doroshko NN (1981) Approximate solution of the traveling salesman problem by a local algorithm with scanning neighborhoods of factorial cardinality in cubic time. Software: Algorithms and Programs, Mathematics Institute of the Belorussia Academy of Science, Minsk, vol 31, pp 11–13
Schmid V, Doerner KF, Hartl RF, Salazar-González JJ (2010) Hybridization of very large neighborhood search for ready-mixed concrete delivery problems. Comput Oper Res 37(3):559–574
Shaw P (1998) Using constraint programming and local search methods to solve vehicle routing problems. In: CP-98 (Fourth international conference on principles and practice of constraint programming). Lecture notes in computer science, vol 1520. Springer, pp 417-431
Sourd F (2006) Dynasearch neighborhood for the earliness-tardiness scheduling problem with release dates and setup constraints. Oper Res Lett 34(5):591–598
Thompson PM, Psaraftis HN (1993) Cyclic transfer algorithms for multivehicle routing and scheduling problems. Operations Research 41:935–946
Yagiura M, Yamaguchi T, Ibaraki T (1998) A variable depth search algorithm with branching search for the generalized assignment problem. Optim Methods Softw 10:419–441
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Maniezzo, V., Boschetti, M.A., Stützle, T. (2021). Very Large-Scale Neighborhood Search. In: Matheuristics. EURO Advanced Tutorials on Operational Research. Springer, Cham. https://doi.org/10.1007/978-3-030-70277-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-70277-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-70276-2
Online ISBN: 978-3-030-70277-9
eBook Packages: Business and ManagementBusiness and Management (R0)