On some variants of the bandwidth minimization problem
SIAM Journal on Computing
Tabu Search
A survey of graph layout problems
ACM Computing Surveys (CSUR)
The Obnoxious Center Problem on a Tree
SIAM Journal on Discrete Mathematics
Probability Distribution of Solution Time in GRASP: An Experimental Investigation
Journal of Heuristics
A Survey on Obnoxious Facility Location Problems
A Survey on Obnoxious Facility Location Problems
An effective two-stage simulated annealing algorithm for the minimum linear arrangement problem
Computers and Operations Research
Note: On explicit formulas for bandwidth and antibandwidth of hypercubes
Discrete Applied Mathematics
Advanced Scatter Search for the Max-Cut Problem
INFORMS Journal on Computing
GRASP and path relinking for the max-min diversity problem
Computers and Operations Research
Memetic algorithm for the antibandwidth maximization problem
Journal of Heuristics
Variable neighborhood search for the Vertex Separation Problem
Computers and Operations Research
Antibandwidth and cyclic antibandwidth of Hamming graphs
Discrete Applied Mathematics
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In this paper, we address the optimization problem arising in some practical applications in which we want to maximize the minimum difference between the labels of adjacent elements. For example, in the context of location models, the elements can represent sensitive facilities or chemicals and their labels locations, and the objective is to locate (label) them in a way that avoids placing some of them too close together (since it can be risky). This optimization problem is referred to as the antibandwidth maximization problem (AMP) and, modeled in terms of graphs, consists of labeling the vertices with different integers or labels such that the minimum difference between the labels of adjacent vertices is maximized. This optimization problem is the dual of the well-known bandwidth problem and it is also known as the separation problem or directly as the dual bandwidth problem. In this paper, we first review the previous methods for the AMP and then propose a heuristic algorithm based on the variable neighborhood search methodology to obtain high quality solutions. One of our neighborhoods implements ejection chains which have been successfully applied in the context of tabu search. Our extensive experimentation with 236 previously reported instances shows that the proposed procedure outperforms existing methods in terms of solution quality.