Multi-objective Optimization of Graph Partitioning using Genetic Algorithm

Authors: M. Farshbaf, M. R. Feizi-Derakhshi

Abstract:

Graph partitioning is a NP-hard problem with multiple conflicting objectives. The graph partitioning should minimize the inter-partition relationship while maximizing the intra-partition relationship. Furthermore, the partition load should be evenly distributed over the respective partitions. Therefore this is a multiobjective optimization problem (MOO). One of the approaches to MOO is Pareto optimization which has been used in this paper. The proposed methods of this paper used to improve the performance are injecting best solutions of previous runs into the first generation of next runs and also storing the non-dominated set of previous generations to combine with later generation's non-dominated set. These improvements prevent the GA from getting stuck in the local optima and increase the probability of finding more optimal solutions. Finally, a simulation research is carried out to investigate the effectiveness of the proposed algorithm. The simulation results confirm the effectiveness of the proposed method.

Keywords: Graph partitioning, Genetic algorithm, Multiobjective optimization, Pareto front.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077068

References:

[1] Nguyen Thang, Ro Moon Byung, "Genetic Algorithm and Graph Partitioning", IEEE Transaction on Computers 1996.
[2] E. Zitzler, K. Deb, and L. Thiele, "Comparison of multiobjective evolutionary algorithms: Empirical results.,"Evolutionary Computation, vol. 8, pp. 173-195, 2000.
[3] Coello Coello, Carlos A. A Comprehensive Survey of Evolutionary- Based Multiobjective Optimization Techniques, Knowledge and Information Systems, Vol. 1, No. 3, pp. 269-308, August 1999.
[4] D.Goldberg. Genetic Algorithms in search, optimization and machine learning. Reading, Mass., Addison-Wesley, 1989.
[5] K. Deb, S. Agrawal, A. Pratab, and T. Meyarivan, "A Fast Elitist Non- Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II," presented at Parallel Problem Solving from Nature VI Conference, Paris, France, 2000.
[6] Songerwala, M., 1994. Efficient solutions to the network division problem. Ph.D. Thesis, Department of Computer Science, Curtin University of Technology.
[7] Holland, J. H. 1975. Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press.
[8] K.Bryant, Genetic Algorithms and the Traveling Salesman Problem, Thesis, Harvey Mudd College, Dept. of Mathematics, 2000.
[9] E. Cantu-Paz, A Survey of Parallel Genetic Algorithms, IlliGAL Report No. 97003, May 1997.
[10] Philipp Limbourg and Daniel E. Salazar Aponte. An Optimization Algorithm for Imprecise Multi-Objective Problem Functions, IEEE Congress on Evolutionary Computation, CEC2005, 2005.
[11] Krommenacker, N.; Rondeau, E.; Divoux, T.Factory Communication Systems, 2002. 4th IEEE International Workshop on Volume, Issue, 2002 Page(s): 149 - 156.
[12] Salcedo-Sanz, S.; Xin Yao Systems, Man, and Cybernetics, Part B, IEEE Transactions on Volume 34, Issue 6, Dec. 2004 Page(s):2343 - 2353.