Discrete Applied Mathematics 123 (2002) 75 – 102
A survey of very large-scale neighborhood search
Ravindra K. Ahuja
, James B. Orlin
Abraham P. Punnen
Department of Industrial & Systems Engineering, University of Florida, P.O. Box 116595, Gainesville,
FL 32611, USA
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta,
GA 30332, USA
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Department of Mathematics, Statistics and Computer Science, University of New Brunswick,
Saint John, N.B., Canada E2L 4L5
Received 9 September 1999; received inrevised form 3 November 2000; accepted 8 January 2001
Many optimization problems of practical interest are computationally intractable. Therefore,
a practical approach for solving such problems is to employ heuristic (approximation) algo-
rithms that can ÿnd nearly optimal solutions within a reasonable amount of computation time.
An improvement algorithm is a heuristic algorithm that generally starts with a feasible solution
and iteratively tries to obtain a better solution. Neighborhood search algorithms (alternatively
called local search algorithms) are a wide class of improvement algorithms where at each iter-
ation an improving solution is found by searching the “neighborhood” of the current solution.
A critical issue inthe designof a neighborhood search algorithm is the choice of the neighbor-
hood structure, that is, the manner in which the neighborhood is deÿned. As a rule of thumb,
the larger the neighborhood, the better is the quality of the locally optimal solutions, and the
greater is the accuracy of the ÿnal solution that is obtained. At the same time, the larger the
neighborhood, the longer it takes to search the neighborhood at each iteration. For this reason,
a larger neighborhood does not necessarily produce a more eective heuristic unless one can
search the larger neighborhood in a very ecient manner. This paper concentrates on neigh-
borhood search algorithms where the size of the neighborhood is “very large” with respect to
the size of the input data and in which the neighborhood is searched in an ecient manner.
We survey three broad classes of very large-scale neighborhood search (VLSN) algorithms: (1)
variable-depth methods in which large neighborhoods are searched heuristically, (2) large neigh-
borhoods in which the neighborhoods are searched using network ow techniques or dynamic
E-mail addresses: firstname.lastname@example.org (R.K. Ahuja), email@example.com (
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(J.B. Orlin), email@example.com (A.P. Punnen).
0166-218X/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved.