Abstract
The maximum min-sum dispersion problem (Max-Minsum DP for short) is a representative binary optimization problem that is proved to be NP-hard and has a number of real-world or potential applications. In this paper, to solve efficiently this computationally challenging problem, we propose a tabu search algorithm with a dynamical neighborhood size (TSDNS) by integrating a solution-based tabu strategy, three new hash functions, and a mechanism of adjusting adaptively the size of neighborhood exploited by the algorithm. The performance of the proposed TSDNS algorithm is assessed through extensive experiments on 160 benchmark instances widely used in the literature, and the experimental results show that the proposed algorithm is very competitive compared with the state-of-the-art algorithms in the literature especially for the large scale instances, and that the best known results are improved for a number of benchmark instances. Analysis experiments show that the new hash functions used in the tabu strategy are more efficient than those from the literature for the large scale instances, and that the mechanism of controlling adaptively neighborhood size plays a key role for the high performance of proposed algorithm.
Highlights
Given a set V = {1, 2, . . . , n} of n elements, the distance matrix [dij]n×n between the elements, a dispersion problem is to select a subset M from V, such that some dispersion criterion defined on the subset M is maximized or minimized
This paper proposes a kind of new hash functions for the solution-based tabu algorithms of solving binary optimization problems, and the experimental analysis shows that these hash functions are efficient in determining the tabu status of neighbor solutions for the large scale instances
EXPERIMENTAL RESULTS AND COMPARISON we carried out extensive experiments based on a number of benchmark instances widely used in the literature to assess the performance of the proposed algorithm
Summary
Fu: Tabu Search Approach With Dynamical Neighborhood Size for Solving the Max-Minsum DP These dispersion problems have been proved to be NP-hard [18], [28], and there does not exist a polynomial time algorithm to solve them unless P = NP. To overcome the above drawback of the existing algorithms in the literature, we propose a tabu search algorithm with a dynamical neighborhood size (TSDNS) for the Max-Minsum DP. This paper proposes a kind of new hash functions for the solution-based tabu algorithms of solving binary optimization problems, and the experimental analysis shows that these hash functions are efficient in determining the tabu status of neighbor solutions for the large scale instances.
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