Abstract
This paper proposes a new relation-based genetic algorithm named relational genetic algorithm (RGA) for solving partitioning problems. In our RGA, a relation-oriented representation (or relational encoding) is adopted and corresponding genetic operators are redesigned. The relational encoding is represented by the equivalence relation matrix which has a 1-1 and onto correspondence with the class of all possible partitions. It eliminates the redundancy of previous GA representations and improves the performance of genetic search. The generalized problem-independent operators we redesigned manipulate the genes without requiring specific heuristics in the process of evolution. In addition, our RGA also supports a variable number of subsets. It works without requiring a fixed number of subsets in advance. Experiments for solving some well-known classic partitioning problems by RGA and GGA with and without heuristics are performed. Experimental results show that our RGA is significantly better than GGA in all cases with larger problem sizes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Appel, K., Haaken, W.: Every map is four-colourable I: discharging. Illinois J. Math 21, 429–490 (1997)
Brown, E.C., Sumichrast, R.T.: Evaluating performance advantages of grouping genetic algorithms. Engineering Applications of Artificial Intelligence 18, 1–12 (2005)
Chen, J.S., Lin, Y.T.: A Partitioned Portfolio Insurance Strategy by Relational Genetic Algorithm. In: Sattar, A., Kang, B.-H. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 857–866. Springer, Heidelberg (2006)
Chiang, W-C., Kouvelis, P.: An improved tabu search heuristic for solving facility layout design problem. International Journal of Production Research 34(9), 2565–2585 (1996)
Eiben, A.E., van der Hauw, J.K., van Hemert, J.I.: Graph coloring with adaptive evolutionary algorithms. J. Heuristics 4(1), 25–46 (1998)
Falkenauer, E.: The Grouping Genetic Algorithms – Widening The Scope of The GAs. JORBEL?Belgian Journal of Operations Research, Statistics and Computer Science 33(1,2), 79–102 (1992)
Garey, M. R., Johnson, D.S.: Computers and Intractability – A Guide to the Theory of NP-completeness, W.H. Freeman, San Francisco, USA (1979)
Johnson, D., Aragon, C., McGeoch, L., Schevon, C.: Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning. Operations Research 39(3), 378–406 (1991)
Jones, D.R., Beltramo, M.A.: Solving partitioning problems with genetic algorithms. In: Belew, K.R., Booker, L.B. (eds.) Proc. 4th Intnl. Conf. on Genetic Algorithms, pp. 442–449. Morgan Kaufmann, San Francisco (1991)
Smith, D.: Bin Packing with Adaptive Search. In: Proceeding of an International Conference on Genetic Algorithms and Their Application, pp. 202–206 (1985)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Chen, JS., Lin, YT., Chen, LY. (2007). A Relation-Based Genetic Algorithm for Partitioning Problems with Applications. In: Okuno, H.G., Ali, M. (eds) New Trends in Applied Artificial Intelligence. IEA/AIE 2007. Lecture Notes in Computer Science(), vol 4570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73325-6_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-73325-6_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73322-5
Online ISBN: 978-3-540-73325-6
eBook Packages: Computer ScienceComputer Science (R0)