Abstract
The minimum feedback vertex set in a directed graph is a NP-hard problem i.e., it is very unlikely that a polynomial algorithm can be found to solve any instances of it. Solutions of the minimum feedback vertex set can find several real world applications. For this reason, it is useful to investigate heuristics that might give near-optimal solutions. Here we present an enhanced genetic algorithm with an ad hoc local search improvement strategy that finds good solutions for any given instance. To prove the effectiveness of the algorithm, we provide an implementation tested against a large variety of test cases. The results we obtain are compared to the results obtained by greedy and randomized algorithms for finding approximate solutions to the problem.
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References
Becker, A., Bar-Yehuda, R.: Randomized algorithms for the loop cutset problem. J. Artif. Intell. Res. 12, 219–234 (2000)
Becker, A., Geiger, D.: Optimization of pearl’s method of conditioning and greedy like approximation algorithms for the vertex feedback set problem. Artif. Intell. 83, 167–188 (1996)
Bonsma, P., Lokshtanov, D.: Feedback vertex set in mixed graphs. Lect. Notes Comput. Sci. 6844, 122–133 (2011)
Cai, M.C., Deng, X., Zang, W.: An approximation algorithm for feedback vertex sets in tournaments. SIAM J. Comput. 30(6), 1993–2007 (2001)
Even, G., Naor, S., Schieber, B., Sudan, M.: Approximating minimum feedback sets and multicuts in directed graphs. Algorithmica 20, 151–174 (1998)
Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Global Opt. 6, 109–133 (1995)
Festa, P., Pardalos, P.M., Resende, M.G.C.: Feedback set problems. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, Supplement, vol. A, pp. 209–259. Kluwer Academic Publishers, Dordrecht (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability - A guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco (1979)
Goldberg, D.E.: A comparative analysis of selection schemes used in genetic algorithms. Morgan Kaufmann Publishers, gregory rawlins (edn) (1991)
Hockbaum, D.S.: Approximating covering and packing problems: set cover, vertex cover, indipendent set, and related problems. In: Hockbaum, D.S. (ed.) Approximation Algorithms for NP-Hard Problems, pp. 94–143. PWS Publishing Company, Boston (1997)
Kann, V.: On the Approximability of NP-complete Optimization Problems. Ph.D. thesis, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm (1992)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)
Khanna, S., Motwani, R., Sudan, M., Vazirani, U.: On syntactic versus computational views of approximability. SIAM J. Comp. 28, 164–191 (1999)
Lin, H.M., Jou, J.Y.: Computing minimum feedback vertex sets by contraction operations and its applications on cad. In: International Conference on Computer Design, (ICCD 1999). pp. 364–369 (10–13 October 1999)
Lin, H.M., Jou, J.Y.: On computing the minimum feedback vertex set of a directed graph by contraction operations. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 19(3), 295–307 (2000)
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. System Sci 43, 425–440 (1991)
Pappalardo, F.: Using Viruses to Improve GAs. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 161–170. Springer, Heidelberg (2005)
Pardalos, P.M., Qian, T., Resende, M.G.C.: A greedy randomized adaptive search procedure for feedback vertex set. J. Comb. Opt. 2, 399–412 (1999)
Pop, M., Kosack, D., Salzberg, S.: Hierarchical scaffolding with bambus. Genome Res. 14(1), 149–159 (2004)
Seymour, P.: Packing directed circuits fractionally. Combinatorica 15, 281–288 (1995)
Shamir, A.: A linear time algorithm for finding cutsets in reduced graphs. J. Comput. 8, 645–655 (1979)
Soranzo, N., Ramezani, F., Iacono, G., Altafini, C.: Decompositions of large-scale biological systems based on dynamical properties. Bioinform. 28(1), 76–83 (2012)
Speckenmeyer, E.: On feedback problems in digraphs. Graph-Theoretic Concepts in Computer Science. Lecture Notes in Computer Science, vol. 411, pp. 218–231. Springer-Verlag, Berlin (1989)
Taoka, S., Watanabe, T.: Performance comparison of approximation algorithms for the minimum weight vertex cover problem. In: SCAS 2012 - 2012 IEEE International Symposium on Circuits and Systems, vol. 6272111, pp. 632–635 (2012)
Wang, C., Lloyd, E., Soffa, M.: Feedbackvertexsetsandcyclicallyreduciblegraphs. J. ACM 32, 296–313 (1985)
Yannakakis, M.: Node and edge-delition np-complete problems. In: Proceedings of the 10-th Annual ACM Symposium on Theory of Computing. pp. 253–264 (1978)
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Cutello, V., Pappalardo, F. (2015). Targeting the Minimum Vertex Set Problem with an Enhanced Genetic Algorithm Improved with Local Search Strategies. In: Huang, DS., Bevilacqua, V., Premaratne, P. (eds) Intelligent Computing Theories and Methodologies. ICIC 2015. Lecture Notes in Computer Science(), vol 9225. Springer, Cham. https://doi.org/10.1007/978-3-319-22180-9_18
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