Authors: Urošević, Dragan 
Alghoul, Yiad Ibrahim Yousef
Amirgaliyeva, Zhazira
Mladenović, Nenad 
Title: Less is more: Tabu search for bipartite quadratic programming problem
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 11548 LNCS
First page: 390
Last page: 401
Conference: 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019; Ekaterinburg; Russian Federation
Issue Date: 1-Jan-2019
Rank: M33
ISBN: 978-3-030-22628-2
ISSN: 0302-9743
DOI: 10.1007/978-3-030-22629-9_27
Having defined a complete bipartite graph G, with weights associated with both vertices and edges, the Bipartite Quadratic Programming problem (BQP) consists in selecting a subgraph that maximizes the sum of the weights associated with the chosen vertices and the edges that connect them. Applications of the BQP arise in mining discrete patterns from binary data, approximation of matrices by rank-one binary matrices, computation of the cut-norm of a matrix, etc. In addition, BQP is also known in the literature under different names such as maximum weighted induced subgraph, maximum weight bi-clique and maximum cut on bipartite graphs. Since the problem is NP-hard, many heuristic methods have been proposed in the literature to solve it. In this paper, we apply the recent Less is more approach, whose basic idea is to design a heuristic as simple as possible, i.e., a method that uses a minimum number of ingredients but provides solutions of better quality than the current state-of-the-art. To reach that goal, we propose a simple hybrid heuristic based on Tabu search, that uses two neighborhood structures and relatively simple rule for implementation of short-term memory operation. In addition, a simple rule for calculation of tabu list length is introduced. Computational results were compared favorably with the current state-of-the-art heuristics. Despite its simplicity, our heuristic was able to find 6 new best known solutions on very well studied test instances.
Keywords: Bipartite quadratic programming | Discrete optimization | Graphs | Tabu search | Variable neighborhood search
Publisher: Springer Link
Project: 174010
Grant Number BR05236839 “Development of information technologies and systems for stimulation of personality’s sustainable development as one of the bases of development of digital Kazakhstan”
Ministry of Education and Science, Republic of Kazakhstan, project no. AP05133090

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