A Random-Search Approach to Multicriterion Discrete Optimization

  • Andrzej Osyczka
  • Jerzy Montusiewicz
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


In the paper the random search method is used for generating a set of feasible solutions for general nonlinear programming models with discrete decision variables. From this set all Pareto optimal solutions are selected using the algorithm based on contact theorem. For most engineering design problems the set of Pareto optimal solutions obtained in this way is large and it is difficult and tiresome to make the right decision while looking through all of them. Thus a method for selecting a preferred subset of Pareto optimal solutions is proposed. The computer program for this method has been developed. The program has an interactive character and all optional parts of the method are run on the basis of a dialogue with the computer. Finally the real - life application example dealing with an optimum design of a gear set is discussed.


Multicriteria optimization random search Pareto optimal set discrete model gear design 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Paczkowski, W. M.: OPTIM — Nonlinear Discrete Optimization Program, 10th Conference on Computer Methods in Mechanics, Swinoujscie 1991, PolandGoogle Scholar
  2. 2.
    Hajela P., Shih C. J.: Multiobjective Design in Mixed Integer and Discrete Design Variable Problems, Proceeding AIAA/ASME/AHS/ASC 30th Struct. Dynamics and Materials Conference, Mibile, Alabama, April 3–5, 1989Google Scholar
  3. 3.
    Sobieski-SobieszaAski J.: Optimization by Decomposition in Structural and Multidisciplinaiy Applications, In: Optimization of Large Structural Systems NATO/DFG ASI Conference Berctesgaden, 1991, GermanyGoogle Scholar
  4. 4.
    Rosenman M. A., Gero J. S.: Reducing the Pareto Optimal Set in Multicriteria Optimization, Eng. Opt., vol. 8, 1985, pp. 189–206CrossRefGoogle Scholar
  5. 5.
    Osyczka A.: Multicriterion Optimization in Engineering with FORTRAN Programs, John Wiley and Sons, Chichester, 1984Google Scholar
  6. 6.
    Osyczka A.: Computer Aided Multicriterion Optimization System (CAMOS) -Software Package in FORTRAN, International Software Publishers, Cracow, 1992Google Scholar
  7. 7.
    Thwberge Y.,Cardou A., Cloutier L.: Parallel Axes Gear Set Optimization in Two-Parameter Space, MPT91 JSME Int. Conf. on Motion and Power Trans., Nov. 23–26, 1991, HiroshimaGoogle Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1994

Authors and Affiliations

  • Andrzej Osyczka
    • 1
  • Jerzy Montusiewicz
    • 2
  1. 1.Department of Mechanical EngineeringTechnical University of CracowCracowPoland
  2. 2.Department of Technology FoundationTechnical University of LublinLublinPoland

Personalised recommendations