Abstract
In this article we investigate a new variant of Variable Neighborhood Search (VNS): Relaxation Guided Variable Neighborhood Search. It is based on the general VNS scheme and a new Variable Neighborhood Descent (VND) algorithm. The ordering of the neighborhood structures in this VND is determined dynamically by solving relaxations of them. The objective values of these relaxations are used as indicators for the potential gains of searching the corresponding neighborhoods. We tested this new approach on the well-studied multidimensional knapsack problem. Computational experiments show that our approach is beneficial to the search, improving the obtained results. The concept is, in principle, more generally applicable and seems to be promising for many other combinatorial optimization problems approached by VNS.
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NICTA is funded by the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council.The Institute of Computer Graphics and Algorithms is supported by the European RTN ADONET under grant 504438.
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Puchinger, J., Raidl, G.R. Bringing order into the neighborhoods: relaxation guided variable neighborhood search. J Heuristics 14, 457–472 (2008). https://doi.org/10.1007/s10732-007-9048-9
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DOI: https://doi.org/10.1007/s10732-007-9048-9