A novel local search algorithm with configuration checking and scoring mechanism for the set k-covering problem

The set k-covering problem, an extension of the classical set covering problem, is an important NP-hard combinatorial optimization problem with extensive applications, including computational biology and wireless network. The aim of this paper is to design a new local search algorithm to solve this problem. First, to overcome the cycling problem in local search, the set k-covering configuration checking (SKCC) strategy is proposed. Second, we use the cost scheme of elements to define the scoring mechanism so that our algorithm can find different possible good-quality solutions. Having combined the SKCC strategy with the scoring mechanism, a subset selection strategy is designed to decide which subset should be selected as a candidate solution component. After that, a novel local search framework, as we call DLLccsm (diversion local search based on configuration checking and scoring mechanism), is proposed. DLLccsm is evaluated against two state-of-the-art algorithms. The experimental results show that DLLccsm performs better than its competitors in terms of solution quality in most classical instances.

[1]  Mauricio G. C. Resende,et al.  AN OPTIMIZER IN THE TELECOMMUNICATIONS INDUSTRY , 2007 .

[2]  Wei-Tek Tsai,et al.  Software-as-a-service (SaaS): perspectives and challenges , 2013, Science China Information Sciences.

[3]  S. Safra,et al.  On the hardness of approximating minimum vertex cover , 2005 .

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

[5]  Wei Wu,et al.  Double Configuration Checking in Stochastic Local Search for Satisfiability , 2014, AAAI.

[6]  Kun-Mao Chao,et al.  A greedier approach for finding tag SNPs , 2006, Bioinform..

[7]  Celso C. Ribeiro,et al.  TTT plots: a perl program to create time-to-target plots , 2007, Optim. Lett..

[8]  Minghao Yin,et al.  Two Efficient Local Search Algorithms for Maximum Weight Clique Problem , 2016, AAAI.

[9]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[10]  Kaile Su,et al.  Tailoring Local Search for Partial MaxSAT , 2014, AAAI.

[11]  Russell Schwartz,et al.  Haplotypes and informative SNP selection algorithms: don't block out information , 2003, RECOMB '03.

[12]  Giorgio Ausiello,et al.  Structure Preserving Reductions among Convex Optimization Problems , 1980, J. Comput. Syst. Sci..

[13]  Ting Chen,et al.  Selecting additional tag SNPs for tolerating missing data in genotyping , 2005, BMC Bioinformatics.

[14]  Wei Wu,et al.  Clause States Based Configuration Checking in Local Search for Satisfiability , 2015, IEEE Transactions on Cybernetics.

[15]  Dorit S. Hochbaum,et al.  The multicovering problem , 1992 .

[16]  Lei Zhang,et al.  Robust low-rank tensor factorization by cyclic weighted median , 2014, Science China Information Sciences.

[17]  Claudio Arbib,et al.  One-dimensional cutting stock with a limited number of open stacks: bounds and solutions from a new integer linear programming model , 2016, Int. Trans. Oper. Res..

[18]  Kaile Su,et al.  Local search for Boolean Satisfiability with configuration checking and subscore , 2013, Artif. Intell..

[19]  Francis C. M. Lau,et al.  Set multi-covering via inclusion-exclusion , 2009, Theor. Comput. Sci..

[20]  Krishnendu Chakrabarty,et al.  Accepted for Publication in Ieee Transactions on Computer-aided Design of Integrated Circuits and Systems Test Scheduling for Core-based Systems Using Mixed-integer Linear Programming , 2000 .

[21]  Francis C. M. Lau,et al.  Dynamic programming based algorithms for set multicover and multiset multicover problems , 2010, Theor. Comput. Sci..

[22]  Minghao Yin,et al.  A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity , 2017, Science China Information Sciences.

[23]  Bart Selman,et al.  Noise Strategies for Improving Local Search , 1994, AAAI.

[24]  Abdul Sattar,et al.  NuMVC: An Efficient Local Search Algorithm for Minimum Vertex Cover , 2014, J. Artif. Intell. Res..

[25]  Emile H. L. Aarts,et al.  Theoretical aspects of local search , 2006, Monographs in Theoretical Computer Science. An EATCS Series.

[26]  Vittorio Maniezzo,et al.  A set covering based matheuristic for a real-world city logistics problem , 2015, Int. Trans. Oper. Res..

[27]  René van Bevern.  Towards Optimal and Expressive Kernelization for d-Hitting Set , 2011, Algorithmica.

[28]  Ping Huang,et al.  An upper (lower) bound for Max (Min) CSP , 2013, Science China Information Sciences.

[29]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[30]  Celso C. Ribeiro,et al.  A hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering , 2013, Comput. Oper. Res..

[31]  Minghao Yin,et al.  Experimental analyses on phase transitions in compiling satisfiability problems , 2014, Science China Information Sciences.

[32]  Yang Gao,et al.  Joint number and DOA estimation via the eigen-beam mCapon method for closely spaced sources , 2015, Science China Information Sciences.

[33]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[34]  Kaile Su,et al.  Two Weighting Local Search for Minimum Vertex Cover , 2015, AAAI.