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Task Decomposition for Optimization Problem Solving

  • Ehab Z. Elfeky
  • Ruhul A. Sarker
  • Daryl L. Essam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5361)

Abstract

This paper examines a new way of dividing computational tasks into smaller interacting components, in order to effectively solve constrained optimization problems. In dividing the tasks, we propose problem decomposition, and the use of GAs as the solution approach. In this paper, we consider problems with block angular structures with or without overlapping variables. We decompose not only the problem but also appropriately the chromosome for different components of the problem. We also design a communication process for exchanging information between the components. The approach can be implemented for solving large scale optimization problems using parallel machines. A number of test problems have been solved to demonstrate the use of the proposed approach. The results are very encouraging.

Keywords

Test Problem Constrain Optimization Problem Computational Task Communication Topology Task Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Conn, A.R., Gould, N.I.M., Toint, P.L.: Large-scale nonlinear constrained optimization: a current survey. In: Shanno, D.F., Dixon, L., Spedicato, E. (eds.) Algorithms for continuous optimization: the state of the art, vol. 434, pp. 287–332. Kluwer Academic Publishers Group (1994)Google Scholar
  2. 2.
    Elfeky, E.Z., Sarker, R.A., Essam, D.L.: Analyzing the Simple Ranking and Selection Process for Constrained Evolutionary Optimization. Journal of Computer Science And Technology 23(1), 19–34 (2008)CrossRefGoogle Scholar
  3. 3.
    Martin, R.K.: Large Scale Linear and Integer Optimization: A Unified Approach. Springer, Heidelberg (1998)Google Scholar
  4. 4.
    Kato, K., Sakawa, M.: Genetic algorithms with decomposition procedures for multidimensional 0-1 knapsack problems with block angular structures. IEEE Transactions on Systems, Man, and Cybernetics, Part B 33(3), 410–419 (2003)CrossRefGoogle Scholar
  5. 5.
    Lin, S.-S., Chang, H.: A Decomposition-Technique-Based Algorithm for Nonlinear Large Scale Mesh-Interconnected System and Application. IEICE Trans. Fundamentals E89-A(10), 2847–2856 (2006)CrossRefGoogle Scholar
  6. 6.
    Benjamin, W.W., Yixin, C., Andrew, W.: Constrained Global Optimization by Constraint Partitioning and Simulated Annealing. In: Proceedings of the 18th IEEE International Conference on Tools with Artificial Intelligence. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  7. 7.
    Yang, Z., Tang, K., Yao, X.: Large scale evolutionary optimization using cooperative coevolution. Information Sciences 178(15), 2985–2999 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill, New York (1972)zbMATHGoogle Scholar
  9. 9.
    Dembo, R.S.: A set of geometric programming test problems and their solutions. Mathematical Programming 10(1), 192–213 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Floudas, C.A., Pardalos, P.M.: A Collection of Test Problems for Constrained Global Optimization Algorithms. LNCS, vol. 455. Springer, Heidelberg (1990)zbMATHGoogle Scholar
  11. 11.
    Koziel, S., Michalewicz, Z.: Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evolutionary Computation 7(1), 19–44 (1999)CrossRefGoogle Scholar
  12. 12.
    Hock, W., Schittkowski, K.: Text examples for nonlinear programming codes. Springer, New York (1981)CrossRefzbMATHGoogle Scholar
  13. 13.
    Elfeky Ehab, Z., Sarker Ruhul, A., Essam, D.L.: Analyzing the Simple Ranking and Selection Process for Constrained Evolutionary Optimization. Journal of Computer Science And Technology 23(1), 19–34 (2008)CrossRefGoogle Scholar
  14. 14.
    Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  15. 15.
    Elfeky, E.Z., Sarker, R.A., Essam, D.L.: A Simple Ranking and Selection for Constrained Evolutionary Optimization. In: Wang, T.-D., Li, X.-D., Chen, S.-H., Wang, X., Abbass, H.A., Iba, H., Chen, G.-L., Yao, X. (eds.) SEAL 2006. LNCS, vol. 4247, pp. 537–544. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ehab Z. Elfeky
    • 1
  • Ruhul A. Sarker
    • 1
  • Daryl L. Essam
    • 1
  1. 1.School of ITEEUniversity of New South Wales at ADFACanberraAustralia

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