General swap-based multiple neighborhood adaptive search for the maximum balanced biclique problem

Abstract The maximum balanced biclique problem (MBBP) is to find the largest complete bipartite subgraph induced by two equal-sized subsets of vertices in a bipartite graph. MBBP is an NP-hard problem with a number of relevant applications. In this work, we propose a general swap-based multiple neighborhood adaptive search (SBMNAS) for MBBP. This algorithm combines a general k-SWAP operator which is used in local searches for MBBP for the first time, an adaptive rule for neighborhood exploration and a frequency-based perturbation strategy to ensure a global diversification. SBMNAS is evaluated on 60 random dense instances and 25 real-life large sparse instances from the popular Koblenz Network Collection (KONECT). Computational results show that our proposed algorithm attains all but one best-known solutions, and finds improved best-known results for 19 instances (new lower bounds).

[1]  Chengqi Zhang,et al.  Rating Knowledge Sharing in Cross-Domain Collaborative Filtering , 2015, IEEE Transactions on Cybernetics.

[2]  Philip S. Yu,et al.  Enhanced biclustering on expression data , 2003, Third IEEE Symposium on Bioinformatics and Bioengineering, 2003. Proceedings..

[3]  Jin-Kao Hao,et al.  Tabu search with feasible and infeasible searches for equitable coloring , 2018, Eng. Appl. Artif. Intell..

[4]  Bo Yuan,et al.  A low time complexity defect-tolerance algorithm for nanoelectronic crossbar , 2011, International Conference on Information Science and Technology.

[5]  Jérôme Kunegis,et al.  KONECT: the Koblenz network collection , 2013, WWW.

[6]  Bin Li,et al.  A New Evolutionary Algorithm with Structure Mutation for the Maximum Balanced Biclique Problem , 2015, IEEE Transactions on Cybernetics.

[7]  S. S. Ravi,et al.  The Complexity of Near-Optimal Programmable Logic Array Folding , 1988, SIAM J. Comput..

[8]  David S. Johnson,et al.  The NP-Completeness Column: An Ongoing Guide , 1982, J. Algorithms.

[9]  Dhiraj K. Pradhan,et al.  A Defect Tolerance Scheme for Nanotechnology Circuits , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Fred W. Glover,et al.  Multi-neighborhood tabu search for the maximum weight clique problem , 2012, Annals of Operations Research.

[11]  Manuel Laguna,et al.  Tabu Search , 1997 .

[12]  Yi Zhou,et al.  PUSH: A generalized operator for the Maximum Vertex Weight Clique Problem , 2017, Eur. J. Oper. Res..

[13]  Bin Li,et al.  A Fast Extraction Algorithm for Defect-Free Subcrossbar in Nanoelectronic Crossbar , 2014, ACM J. Emerg. Technol. Comput. Syst..

[14]  Jin-Kao Hao,et al.  A clique-based exact method for optimal winner determination in combinatorial auctions , 2016, Inf. Sci..

[15]  Minghao Yin,et al.  New heuristic approaches for maximum balanced biclique problem , 2018, Inf. Sci..

[16]  George M. Church,et al.  Biclustering of Expression Data , 2000, ISMB.

[17]  T. Neumann.  Computers And Intractability A Guide To The Theory Of Np Completeness , 2016 .

[18]  Thomas Stützle,et al.  A Racing Algorithm for Configuring Metaheuristics , 2002, GECCO.

[19]  Leslie Pérez Cáceres,et al.  The irace package: Iterated racing for automatic algorithm configuration , 2016 .

[20]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[21]  Jin-Kao Hao,et al.  Tabu search with graph reduction for finding maximum balanced bicliques in bipartite graphs , 2019, Eng. Appl. Artif. Intell..

[22]  Thomas Stützle,et al.  Improvement Strategies for the F-Race Algorithm: Sampling Design and Iterative Refinement , 2007, Hybrid Metaheuristics.

[23]  Yi Zhou,et al.  Towards effective exact methods for the Maximum Balanced Biclique Problem in bipartite graphs , 2018, Eur. J. Oper. Res..

[24]  Mehdi Baradaran Tahoori,et al.  Application-independent defect tolerance of reconfigurable nanoarchitectures , 2006, JETC.

[25]  Abraham Duarte,et al.  Finding Balanced Bicliques in Bipartite Graphs Using Variable Neighborhood Search , 2018, ICVNS.

[26]  Qinghua Wu,et al.  A review on algorithms for maximum clique problems , 2015, Eur. J. Oper. Res..

[27]  Jin-Kao Hao,et al.  Adaptive feasible and infeasible tabu search for weighted vertex coloring , 2018, Inf. Sci..