A Meta-Heuristic Algorithm for Vertex Covering Problem Based on Gravity
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32771
A Meta-Heuristic Algorithm for Vertex Covering Problem Based on Gravity

Authors: S. Raja Balachandar, K.Kannan

Abstract:

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving vertex covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the vertex covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

Keywords: Vertex covering Problem, Velocity, Gravitational Force, Newton's Law, Meta Heuristic, Combinatorial optimization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076940

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1954

References:


[1] Bollobas. B : Random graphs (2nd Ed.). Cambridge, UK: Cambridge University press, 2001.
[2] Berman. P and Fujito. T: On approximation properties of the independent set problem for low degree graphs, Theory of Computing Syst., vol. 32, pp. 115 - 132, 1999.
[3] Chvatal, V. (1979). "A Greedy-Heuristic for the Set Cover Problem." Mathematics of Operations Research 4, 233-235.
[4] Clarkson, K.L (1983). "A Modification of the Greedy Algorithm for Vertex Cover." Information Processing Lettters 16, 23-25.
[5] Cormen. T. H, C. E. Leiserson, R. L. R., and Stein. C: Introduction to algorithms, 2nd ed., McGraw - Hill, New York , 2001.
[6] Dehne. F, et al.: Solving large FPT problems on coarse grained parallel machines, Available: http://www.scs.carleton.ca/fpt/papers/index.htm.
[7] Fellows. M. R: On the complexity of vertex cover problems, Technical report, Computer science department, University of New Mexico, 1988.
[8] Garey. M. R, Johnson. D. S: Computers and Intractability: A Guide to the theory NP - completeness. San Francisco: Freeman ,1979.
[9] Garey. M. R, Johnson. D. S, and Stock Meyer. L: Some simplified NP - complete graph problems, Theoretical computer science, Vol.1563, pp. 561 - 570, 1999.
[10] Glover. F: Tabu Search - Part I, ORSA journal of computing, vol. 1, No.3, (1989), pp. 190 - 206.
[11] Glover. F: Tabu search: A Tutorial, Interface 20, pp. 74 - 94, 1990.
[12] Gomes. F. C, Meneses. C. N, Pardalos. P. M and Viana. G. V. R: Experimental analysis of approximation algorithms for the vertex cover and set covering problems, Journal of computers and Operations Research, vol. 33, pp. 3520 - 3534, 2006.
[13] Hastad. J: Some Optimal Inapproximability Results., Journal of the ACM, vol. 48, No.4, pp. 798 - 859, 2001.
[14] Hochbaum. D. S: Approximation algorithm for the set covering and vertex cover problems, SIAM Journal on computing, 11(3), 555 - 6, 1982.
[15] D. Holliday, R. Resnick, J. Walker, Fundamentals of physics, John Wiley and Sons, 1993.
[16] Johnson. D.S, Approximation Algorithms for Combinatorial problems, J.Comput.System Sci.9(1974)256-278.
[17] Johnson, D.s., C.R Aragon, L.A. McGeoch, and C. Schevon. (1989). "Optimization by Simulated Anealing: An Experimental Evaluation, Part I: Graph Partitioning." Operations Research 37, 875-892.
[18] Johnson, D.S., C.R. Aragon, L.A. McGeoch, and C.Schevon. (1989b). "Optimization by Simulated Annealing: An Experimental Evaluation, part II: Graph Coloring and Number Partitioning." Operations Research 39, 378-406.
[19] Karp. R. M: Reducibility among combinatorial problems, Plenum Press, New York, pp. 85 - 103, 1972.
[20] I.R. Kenyon, General Relativity, Oxford University Press, 1990.
[21] Khuri S, Back Th. An Evolutionary heuristic for the minimum vertexcover problem. 18th Deutche Jahrestagung fur Kunstliche. Max-Planck Institut fur Informatik Journal 1994;MPI-I-94-241:86-90.
[22] Likas, A and Stafylopatis, A: A parallel algorithm for the minimum weighted vertex cover problem, Information Processing Letters, vol. 53, pp. 229 - 234, 1995.
[23] R. Mansouri, F. Nasseri, M. Khorrami, Effective time variation of G in a model universe with variable space dimension, Physics Letters 259 (1999) 194-200.
[24] Motwani, R. (1992). "Lecture Notes on Application. " Technical Report, STAN-CS-92-1435, Department of Computer Science, Stanford University.
[25] Motwani. R: Lecture Notes on Approximation Algorithms, Technical Report, STAN-CS-92-1435, Department of Computer Science, Stanford University, 1992.
[26] Neidermeier. R and Rossmanith. P: On efficient fixed-parameter algorithms for weighted vertex cover, Journal of Algorithms, vol. 47, pp. 63 - 77, 2003.
[27] Pitt. L: A Simple Probabilistic Approximation Algorithm for Vertex Cover, Technical Report, YaleU/DCS/TR-404, Department of Computer Science, Yale University, 1985.
[28] E. Rashedi, Gravitational Search Algorithm, M.Sc. Thesis, Shahid Bahonar University of Kerman, Kerman, Iran, 2007 (in Farsi).
[29] B. Schutz, Gravity from the Ground Up, Cambridge University Press, 2003.
[30] Monien. B and Speckenmeyer. E: Ramsey numbers and an approximation algorithm for the vertex cover problems, Acta Informatica, vol. 22, pp. 115 - 123, 1985.
[31] Shyu. S.J, Yin. P.Y and Lin. B.M.T: An ant colony optimization algorithm for the minimum weight vertex cover problem, Annals of Operations Research, Vol. 131, pp. 283 - 304, 2004.
[32] Weight. M and Hartmann. A. K: The number of guards needed by a museum - a phase transition in vertex covering of random graphs., Phys - Rev. Lett., 84, 6118, 2000b.
[33] Weight. M and Hartmann. A. K.: Minimal vertex covers on finite connectivity random graphs - A hard-sphere lattice-gas picture, Phys. Rev. E, 63, 056127.