Differential Evolution Applied to Large Scale Parametric Interval Linear Systems

  • Jerzy Duda
  • Iwona Skalna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)


Differential evolution (DE) is regarded to be a very effective optimisation method for continuous problems in terms of both good optimal solution approximation and short computation time. The authors applied DE method to the problem of solving large scale interval linear systems. Different variants of DE were compared and different strategies were used to ensure that candidate solutions generated in the process of recombination mechanism were always feasible. For the large scale problems the method occurred to be very sensitive to the constraint handling strategy used, so finding an appropriate strategy was very important to achieve good solutions in a reasonable time. Real world large optimisation problems coming from structural engineering were used as the test problems. Additionally DE performance was compared with evolutionary optimisation method presented in [10].


Test Problem Outer Solution Graphical Processor Unit Interval Linear System Evolutionary Optimisation Method 
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  1. 1.
    Alefeld, G., Kreinovich, V., Mayer, G.: The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients. Mathematische Nachrichten 192(1), 23–36 (2006)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Dréo, J., Pétrowski, A., Siarry, P., Taillard, E.: Metaheuristics for Hard Optimization. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  3. 3.
    Feoktistov, V.: Differential Evolution in Search of Solutions. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  4. 4.
    Neumaier, A., Pownuk, A.: Linear Systems with Large Uncertainties with Applications to Truss Structures. Reliable Computing 13(2), 149–172 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Popova, E., Iankov, R., Bonev, Z.: Bounding the Response of Mechanical Structures with Uncertainties in all the Parameters. In: Muhannah, R.L., Mullen, R.L. (eds.) Proceedings of the NSF Workshop on Reliable Engineering Computing (REC), Savannah, Georgia, USA, pp. 245–265 (2006)Google Scholar
  6. 6.
    Pownuk, A.: Efficient Method of Solution of Large Scale Engineering Problems with Interval Parameters Based on Sensitivity Analysis. In: Muhanna, R.L., Mullen, R.L. (eds.) Proc. NSF Workshop Reliable Engineering Computing, Savannah, Georgia, USA, pp. 305–316 (2004)Google Scholar
  7. 7.
    Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution. A Practical Approach to Global Optimization. Springer, Berlin (2005)zbMATHGoogle Scholar
  8. 8.
    Rao, S.S., Berke, L.: Analysis of uncertain structural systems using interval analysis. AIAA Journal 35, 727–735 (1997)zbMATHCrossRefGoogle Scholar
  9. 9.
    Rohn, J., Kreinovich, V.: Computing exact componentwise bounds on solutions of linear systems with interval data is NP-hard. SIAM Journal on Matrix Analysis and Applications (SIMAX) 16, 415–420 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Skalna, I.: Evolutionary Optimization Method for Approximating the Solution Set Hull of Parametric Linear Systems. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds.) NMA 2006. LNCS, vol. 4310, pp. 361–368. Springer, Heidelberg (2007)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jerzy Duda
    • 1
  • Iwona Skalna
    • 1
  1. 1.AGH University of Science and TechnologyKrakowPoland

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