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Variable neighborhood search: Principles and applications. (English) Zbl 0981.90063

Summary: Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called Variable Neighborhood Search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a two-level VNS, called Variable Neighborhood Decomposition Search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear to have been applied before.

MSC:

90C59 Approximation methods and heuristics in mathematical programming
90C26 Nonconvex programming, global optimization
90C27 Combinatorial optimization
90B36 Stochastic scheduling theory in operations research
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