An Effective Hybrid Memetic Algorithm for the Minimum Weight Dominating Set Problem

The minimum weight-dominating set (MWDS) problem is NP-hard and has a lot of applications in the real world. Several metaheuristic methods have been developed for solving the problem effectively, but suffering from high CPU time on large-scale instances. In this paper, we design an effective hybrid memetic algorithm (HMA) for the MWDS problem. First, the MWDS problem is formulated as a constrained 0-1 programming problem and is converted to an equivalent unconstrained 0-1 problem using an adaptive penalty function. Then, we develop a memetic algorithm for the resulting problem, which contains a greedy randomized adaptive construction procedure, a tabu local search procedure, a crossover operator, a population-updating method, and a path-relinking procedure. These strategies make a good tradeoff between intensification and diversification. A number of experiments were carried out on three types of instances from the literature. Compared with existing algorithms, HMA is able to find high-quality solutions in much less CPU time. Specifically, HMA is at least six times faster than existing algorithms on the tested instances. With increasing instance size, the CPU time required by HMA increases much more slowly than required by existing algorithms.

[1]  Wei Wang,et al.  PTAS for the minimum weighted dominating set in growth bounded graphs , 2012, J. Glob. Optim..

[2]  Ruhul A. Sarker,et al.  A genetic algorithm for solving economic lot size scheduling problem , 2002 .

[3]  K. Sörensen,et al.  Memetic algorithms with population management , 2006 .

[4]  Erwin Pesch,et al.  A branch-and-bound algorithm for the acyclic partitioning problem , 2014, Comput. Oper. Res..

[5]  Reuven Bar-Yehuda,et al.  On approximation problems related to the independent set and vertex cover problems , 1984, Discret. Appl. Math..

[6]  Jin-Kao Hao,et al.  A Multilevel Memetic Approach for Improving Graph k-Partitions , 2011, IEEE Transactions on Evolutionary Computation.

[7]  Zhi-Gang Ren,et al.  New ideas for applying ant colony optimization to the set covering problem , 2010, Comput. Ind. Eng..

[8]  Chellapilla Patvardhan,et al.  Solving the 0-1 Quadratic Knapsack Problem with a competitive Quantum Inspired Evolutionary Algorithm , 2015, J. Comput. Appl. Math..

[9]  Xin Yao,et al.  An Evolutionary Approach to the Multidepot Capacitated Arc Routing Problem , 2010, IEEE Transactions on Evolutionary Computation.

[10]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

[11]  Ram Dantu,et al.  An Impatient Evolutionary Algorithm With Probabilistic Tabu Search for Unified Solution of Some NP-Hard Problems in Graph and Set Theory via Clique Finding , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  M. M. Ali,et al.  A penalty function-based differential evolution algorithm for constrained global optimization , 2012, Computational Optimization and Applications.

[13]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[14]  Jin-Kao Hao,et al.  General swap-based multiple neighborhood tabu search for the maximum independent set problem , 2015, Eng. Appl. Artif. Intell..

[15]  Carlos Cotta,et al.  Memetic algorithms and memetic computing optimization: A literature review , 2012, Swarm Evol. Comput..

[16]  Alain Bretto,et al.  A reductive approach to hypergraph clustering: An application to image segmentation , 2012, Pattern Recognit..

[17]  Abraham Duarte,et al.  Advanced Scatter Search for the Max-Cut Problem , 2009, INFORMS J. Comput..

[18]  M. Tuba,et al.  Ant colony optimization applied to minimum weight dominating set problem , 2010 .

[19]  F. Glover,et al.  Fundamentals of Scatter Search and Path Relinking , 2000 .

[20]  Graham Kendall,et al.  A Hybrid Evolutionary Approach to the Nurse Rostering Problem , 2010, IEEE Transactions on Evolutionary Computation.

[21]  Gary G. Yen,et al.  An Adaptive Penalty Formulation for Constrained Evolutionary Optimization , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[22]  Alok Singh,et al.  Hybrid metaheuristic algorithms for minimum weight dominating set , 2013, Appl. Soft Comput..

[23]  Kay Chen Tan,et al.  A Multi-Facet Survey on Memetic Computation , 2011, IEEE Transactions on Evolutionary Computation.

[24]  Christine Solnon,et al.  A study of ACO capabilities for solving the maximum clique problem , 2006, J. Heuristics.

[25]  Oliviu Matei,et al.  A memetic algorithm approach for solving the multidimensional multi-way number partitioning problem , 2013 .

[26]  Pablo Moscato,et al.  On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms , 1989 .

[27]  Steven Li,et al.  Solving large-scale multidimensional knapsack problems with a new binary harmony search algorithm , 2015, Comput. Oper. Res..

[28]  Marius Sinclair,et al.  An exact penalty function approach for nonlinear integer programming problems , 1986 .

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

[30]  Gregorio Toscano Pulido,et al.  Handling constraints in the HP model for protein structure prediction by multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[31]  Celina M. H. de Figueiredo,et al.  Efficient sub-5 approximations for minimum dominating sets in unit disk graphs , 2012, Theor. Comput. Sci..

[32]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..

[33]  Dario Floreano,et al.  Memetic Viability Evolution for Constrained Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[34]  Qingfu Zhang,et al.  An External Archive Guided Multiobjective Evolutionary Algorithm Based on Decomposition for Combinatorial Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[35]  Mhand Hifi,et al.  A genetic algorithm-based heuristic for solving the weighted maximum independent set and some equivalent problems , 1997 .

[36]  Rong Qu,et al.  A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems , 2010, Applied Intelligence.

[37]  Geng Lin,et al.  An Efficient Memetic Algorithm for theMax-Bisection Problem , 2013, IEEE Transactions on Computers.

[38]  Ivor W. Tsang,et al.  Memetic Search With Interdomain Learning: A Realization Between CVRP and CARP , 2015, IEEE Transactions on Evolutionary Computation.

[39]  Jozef Kratica,et al.  Two metaheuristic approaches for solving multidimensional two-way number partitioning problem , 2014, Comput. Oper. Res..

[40]  Bin Li,et al.  A New Memetic Algorithm With Fitness Approximation for the Defect-Tolerant Logic Mapping in Crossbar-Based Nanoarchitectures , 2014, IEEE Transactions on Evolutionary Computation.

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

[42]  Xavier Gandibleux,et al.  Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem , 2010, Eur. J. Oper. Res..

[43]  Chien-Chih Liao,et al.  A memetic algorithm for extending wireless sensor network lifetime , 2010, Inf. Sci..

[44]  Yiqiao Cai,et al.  Memetic clonal selection algorithm with EDA vaccination for unconstrained binary quadratic programming problems , 2011, Expert Syst. Appl..

[45]  Jin-Kao Hao,et al.  A memetic algorithm for graph coloring , 2010, Eur. J. Oper. Res..

[46]  Charles M. Fiduccia,et al.  A linear-time heuristic for improving network partitions , 1988, 25 years of DAC.

[47]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[48]  David W. Coit,et al.  Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems , 1996, INFORMS J. Comput..

[49]  Masha Sosonkina,et al.  Graph Partitioning Using Matrix Values for Preconditioning Symmetric Positive Definite Systems , 2011, SIAM J. Sci. Comput..

[50]  Xiang-Yang Li,et al.  Efficient distributed low-cost backbone formation for wireless networks , 2006, IEEE Transactions on Parallel and Distributed Systems.

[51]  Shiu Yin Yuen,et al.  A Multiobjective Evolutionary Algorithm That Diversifies Population by Its Density , 2012, IEEE Transactions on Evolutionary Computation.

[52]  Chee Keong Kwoh,et al.  Using classification for constrained memetic algorithm: A new paradigm , 2008, 2008 IEEE International Conference on Systems, Man and Cybernetics.

[53]  Kalyanmoy Deb,et al.  Optimization for Engineering Design: Algorithms and Examples , 2004 .

[54]  Marek Kubiak,et al.  Accelerating Local Search in a Memetic Algorithm for the Capacitated Vehicle Routing Problem , 2007, EvoCOP.