KSII Transactions on Internet and Information Systems (TIIS)

Korean Society for Internet Information (한국인터넷정보학회)
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Optimization by Simulated Catalytic Reaction: Application to Graph Bisection

  • Received : 2017.10.27
  • Accepted : 2017.12.22
  • Published : 2018.05.31
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Abstract

Chemical reactions have an intricate relationship with the search for better-quality neighborhood solutions to optimization problems. A catalytic reaction for chemical reactions provides a clue and a framework to solve complicated optimization problems. The application of a catalytic reaction reveals new information hidden in the optimization problem and provides a non-intuitive perspective. This paper proposes a new simulated catalytic reaction method for search in optimization problems. In the experiments using this method, significantly improved results are obtained in almost all graphs tested by applying to a graph bisection problem, which is a representative problem of combinatorial optimization problems.

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References

  1. Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P. "Optimization by simulated annealing," Science 220(4598), pp. 671-680, 1983. https://doi.org/10.1126/science.220.4598.671
  2. Hong, I., Kahng, A.B., Moon, B.-R. "Improved Large-Step Markov Chain Variants for the Symmetric TSP," Journal of Heuristics, vol. 3, no. 1, pp. 63-81, 1997. https://doi.org/10.1023/A:1009624916728
  3. Goldberg, D. Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, 1989.
  4. Garey, M., Johnson, D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
  5. Bui, T.N., Moon, B.-R. "Genetic algorithm and graph partitioning," IEEE Transactions on Computers, vol. 45, no. 7, pp. 841-855, 1996. https://doi.org/10.1109/12.508322
  6. Kim, Y.-H., Moon, B.-R. "Lock-gain based graph partitioning," Journal of Heuristics, vol. 10, no. 1, pp. 37-57, 2004. https://doi.org/10.1023/B:HEUR.0000019985.94952.eb
  7. Hwang, I., Kim, Y.-H., Yoon, Y. "Moving clusters within a memetic algorithm for graph partitioning," Mathematical Problems in Engineering, Vol. 2015, Article ID 238529, 2015.
  8. Battiti, R., Bertossi, A. "Greedy, prohibition, and reactive heuristics for graph partitioning," IEEE Transactions on Computers, vol. 48, no. 4, pp. 361-385, 1999. https://doi.org/10.1109/12.762522
  9. Kalayci, T.E., Battiti, R. "A reactive self-tuning scheme for multilevel graph partitioning," Applied Mathematics and Computation, vol. 318, pp. 227-244, 2018. https://doi.org/10.1016/j.amc.2017.08.031
  10. Kim, J., Hwang, I., Kim, Y.-H., Moon, B.-R. "Genetic approaches for graph partitioning: a survey," in Proc. of of the Genetic and Evolutionary Computation Conference, pp. 473-480, 2011.
  11. Hwang, I., Kim, Y.-H., Moon, B.-R. "Multi-attractor gene reordering for graph bisection," in Proc. of the Eighth Annual Conference on Genetic and Evolutionary Computation, pp. 1209-1216, 2006.
  12. Johnson, D.S., Aragon, C., McGeoch, L., Schevon, C. "Optimization by simulated annealing: An experimental evaluation, Part 1, graph partitioning," Operations Research, vol. 37, pp. 865-892, 1989. https://doi.org/10.1287/opre.37.6.865
  13. Kim, Y.-H., Moon, B.-R. "Investigation of the fitness landscapes in graph bipartitioning: An empirical study," Journal of Heuristics, vol. 10, no. 2, pp. 111-133, 2004. https://doi.org/10.1023/B:HEUR.0000026263.43711.44
  14. Merz, P., Freisleben, B. "Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning," Evolutionary Computation, vol. 8, no. 1, pp. 61-91, 2000. https://doi.org/10.1162/106365600568103
  15. Moraglio, A., Kim, Y.-H., Yoon, Y., Moon, B.-R. "Geometric crossovers for multiway graph partitioning," Evolutionary Computation, vol. 15, no. 4, pp. 445-474, 2007. https://doi.org/10.1162/evco.2007.15.4.445
  16. Yoon, Y., Kim, Y.-H. "New bucket managements in iterative improvement partitioning algorithms," Applied Mathematics & Information Sciences, vol. 7, no. 2, pp. 529-532, 2013. https://doi.org/10.12785/amis/070214
  17. Seo, K., Hyun, S., Kim, Y.-H. "An edge-set representation based on spanning tree for searching cut space," IEEE Transactions on Evolutionary Computation, vol. 19, no. 4, pp. 465-473, 2015. https://doi.org/10.1109/TEVC.2014.2338076
  18. Fiduccia, C., Mattheyses, R. "A linear time heuristic for improving network partitions," in Proc. of Proceedings of the 19th ACM/IEEE Design Automation Conference, pp. 175-181, 1982.
  19. Alpert, C., Kahng, A.B. "A general framework for vertex orderings, with applications to netlist clustering," in Proc. of Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, pp. 63-67, 1994.
  20. Bui, T.N., Heigham, C., Jones, C., Leighton, T. "Improving the performance of the Kernighan-Lin and simulated annealing graph bisection algorithms," in Proc. of Proceedings of the 26th ACM/IEEE Design Automation Conference, pp. 775-778, 1989.
  21. Yoon, Y., Kim, Y.-H. "Vertex ordering, clustering, and their application to graph partitioning," Applied Mathematics & Information Sciences, vol. 8, no. 1, pp. 135-138, 2014. https://doi.org/10.12785/amis/080116
  22. Kim, Y.-H. "An enzyme-inspired approach to surmount barriers in graph bisection," in Proc. of Proceedings of the International Conference on Computational Science and Its Applications - Lecture Notes in Computer Science 5072, pp. 841-851, 2008.
  23. Kernighan, B., Lin, S. "An efficient heuristic procedure for partitioning graphs," Bell Systems Technical Journal 49, pp. 291-307, 1970. https://doi.org/10.1002/j.1538-7305.1970.tb01770.x
  24. Alpert, C.J., Kahng, A.B. "Recent directions in netlist partitioning: a survey," Integration, the VLSI Journal, vol. 19, no. 1-2, pp. 1-81, 1995. https://doi.org/10.1016/0167-9260(95)00008-4
  25. Choe, T.-Y., Park, C.-I. "A k-way graph partitioning algorithm based on clustering by eigenvector," in Proc. of Proceedings of the Fourth International Conference on Computational Science, pp. 598-601, 2004.
  26. Cong, J., Lim, S.K. "Edge separability-based circuit clustering with application to multilevel circuit partitioning," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 23, no. 3, pp. 346-357, 2004. https://doi.org/10.1109/TCAD.2004.823353
  27. Dhillon, I., Guan, Y., Kulis, B. "A fast kernel-based multilevel algorithm for graph clustering," in Proc. of Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge discovery in data mining, pp. 629-634, 2005.
  28. Huang, M.L., Nguyen, Q.V. "A fast algorithm for balanced graph clustering" in Proc. of Proceedings of the Eleventh International Conference on Information Visualization, pp. 46-52, 2007.
  29. Saha, B., Mitra, P. "Dynamic algorithm for graph clustering using minimum cut tree," in Proc. of Proceedings of the Sixth IEEE International Conference on Data Mining Workshops, pp. 667-671, 2006.
  30. Schaeffer, S.E. "Graph clustering," Computer Science Review, vol. 1, no. 1, pp. 27-64, 2007. https://doi.org/10.1016/j.cosrev.2007.05.001
  31. Wang, J., Peng, H., Hu, J., Yang, C. "A graph clustering algorithm based on minimum and normalized cut," in Proc. of Proceedings of the Seventh International Conference on Computational Science, pp. 497-504, 2007.