Mechanical engineering problem optimization by SOMA

  • Ivan Zelinka
  • Jouni Lampinen
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 141)


To discover the effectiveness of the techniques just proposed in Chapter 7, three numerical examples were optimized using SOMA (Table 26.1). These non-linear, engineering design optimization problems with discrete, integer and continuous variables were first investigated by Eric Sandgren [1] and subsequently by many other researchers [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and [12] who applied a variety of optimization techniques (Table 26.2). These problems represent optimization situations involving discrete, integer and continuous variables that are similar to those encountered in everyday mechanical engineering design tasks. Because the problems are clearly defined and relatively easy to understand, they form a suitable basis for comparing alternative optimization methods


Pressure Vessel Type Item Gear Ratio Boundary Constraint Gear Train 
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  1. [1]
    Sandgren, E. (1990). Nonlinear integer and discrete programming in mechanical design optimization Transactions of the ASME, Journal of Mechanical Design, 112(2):223–229, June 1990. ISSN 0738–0666Google Scholar
  2. [2]
    Fu, J.-F., Fenton, R. G. and Cleghorn, W. L. (1991). A mixed integerdiscrete-continuous programming method and its application to engineering design optimization. Engineering Optimization, 17(4):263–280, 1991. ISSN 0305–2154Google Scholar
  3. [3]
    Loh, Han Tong and Papalambros, P. Y. (1991). A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems Transactions of the ASME, Journal of Mechanical Design, 113(3):325–334, September 1991.Google Scholar
  4. [4]
    Loh, Han Tong and Papalambros, P. Y. (1991). Computational implementation and tests of a sequential linearization algorithm for mixed-discrete nonlinear design optimization. Transactions of the ASME, Journal of Mechanical Design, 113 (3): 335–345, September 1991.CrossRefGoogle Scholar
  5. [5]
    Zhang, Chun and Wang, Hsu-Pin (1993). Mixed-discrete nonlinear optimization with simulated annealing Engineering Optimization, 21(4):277291, 1993. ISSN 0305–215XGoogle Scholar
  6. [6]
    Chen, J. L. and Tsao, Y. C. (1993). Optimal design of machine elements using genetic algorithms. Journal of the Chinese Society of Mechanical Engineers, 14 (2): 193–199, 1993.Google Scholar
  7. [7]
    Li, H.-L. and Chou, C.-T. (1994). A global approach for nonlinear mixed discrete programming in design optimization. Engineering Optimization, 220: 109–122, 1994.Google Scholar
  8. [8]
    Wu, S.-J. and Chow, P.-T. (1995). Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization Engineering Optimization, 24(2):137–159, 1995. ISSN 0305–215XGoogle Scholar
  9. [9]
    Lin, Shui-Shun, Zhang, Chun and Wang, Hsu-Pin (1993). On mixed-discrete nonlinear optimization problems: A comparative study Engineering Optimization, 23(4):287–300, 1995. ISSN 0305–215XGoogle Scholar
  10. [10]
    Thierauf, G. and Cai, J. (1997). Evolution strategies — parallelisation and application in engineering optimization In B.H.V. Topping (ed.) (1997). Parallel and distributed processing for computational mechanics SaxeCoburg Publications, Edinburgh (Scotland). ISBN 1–874672–03–2Google Scholar
  11. [11]
    Cao, Y. J. and Wu, Q. H. (1997). Mechanical design optimization by mixed-variable evolutionary programming Proceedings of the 1997 IEEE Conference on Evolutionary Computation, IEEE Press, pp. 443–446.Google Scholar
  12. [12]
    Lampinen Jouni, ZELINKA, Ivan. New Ideas in Optimization–Mechanical Engineering Design Optimization by Differential Evolution. Volume 1. London: McGraw–Hill, 1999. 20 p. ISBN 007–709506–5.Google Scholar
  13. [13]
    Siddall, James N. (1982). Optimal engineering design: principles and applications Mechanical engineering series/14. Marcel Dekker Inc. ISBN 08247–1633–7Google Scholar
  14. [14]
    Articles about SOMA algorithm (source codes, graphics animated gallery, bibliography, see

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© Springer-Verlag Berlin Heidelberg 2004

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  • Ivan Zelinka
  • Jouni Lampinen

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