Skip to main content

An Evolutionary Approach to Solve a Novel Mechatronic Multiobjective Optimization Problem

  • Chapter
Book cover Advances in Metaheuristics for Hard Optimization

Abstract

In this chapter, we present an evolutionary approach to solve a novelmechatronic design problemof a pinion-rack continuously variable transmission (CVT).This problem is stated as a multiobjective optimization problem, because we concurrently optimize the mechanical structure and the controller performance, in order to produce mechanical, electronic and control flexibility for the designed system. The problem is solved first with a mathematical programming technique called the goal attainment method. Based on some shortcomings found, we propose a differential evolution (DE)-based approach to solve the aforementioned problem. The performance of both approaches (goal attainment and the modified DE) are compared and discussed, based on quality, robustness, computational time and implementation complexity. We also highlight the interpretation of the solutions obtained in the context of the application.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Cervantes and L.T. Biegler. Large-scale DAE optimization using a simultaneous NLP formulation. AIChe Journal, 44:1038–1050, 1998

    Article  Google Scholar 

  2. J. Alvarez-Gallegos, C. Cruz-Villar, and E. Portilla-Flores. Parametric optimal design of a pinion-rack based continuously variable transmission. In Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pages 899–904, Monterey California, 2005

    Google Scholar 

  3. J. Alvarez-Gallegos, C. Alberto Cruz Villar, and E. Alfredo Portilla Flores. Evolutionary Dynamic Optimization of a Continuously Variable Transmission for Mechanical Efficiency Maximization. In A. Gelbukh, Álvaro de Albornoz and H. Terashima-Marín, editors, MICAI 2005: Advances in Artificial Intelligence, pages 1093–1102, Monterrey, México, November 2005. Springer. Lecture Notes in Artificial Intelligence Vol. 3789

    Google Scholar 

  4. J.T. Betts. Practical Methods for Optimal Control using Nonlinear Programming. SIAM, Philadelphia, USA, 2001

    MATH  Google Scholar 

  5. C. A. Coello Coello, D. A. Van Veldhuizen, and G. B. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York, June 2002. ISBN 0-3064-6762-3

    MATH  Google Scholar 

  6. I.L. Lopez Cruz, L.G. Van Willigenburg, and G. Van Straten. Parameter Control Strategy in Differential Evolution Algorithm for Optimal Control. In M.H. Hamza, editor, Proceedings of the IASTED International Conference Artificial Intelligence and Soft Computing (ASC 2001), pages 211–216. Cancun, México, ACTA Press, May 2001. ISBN 0-88986-283-4

    Google Scholar 

  7. K. Deb. An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2/4):311–338, 2000

    Article  MATH  Google Scholar 

  8. D. E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Co., Reading, Massachusetts, 1989

    MATH  Google Scholar 

  9. F. Jiménez and J. L. Verdegay. Evolutionary Techniques for Constrained Optimization Problems. In H.-J. Zimmermann, editor, 7th European Congress on Intelligent Techniques and Soft Computing (EUFIT’99), Aachen, Germany, 1999. Verlag Mainz. ISBN 3-89653-808-X

    Google Scholar 

  10. J. Lampinen. A Constraint Handling Approach for the Differential Evolution Algorithm. In Proceedings of the Congress on Evolutionary Computation 2002 (CEC’2002), volume 2, pages 1468–1473, Piscataway, New Jersey, May 2002. IEEE Service Center

    Google Scholar 

  11. G. P Liu, J. Yang, and J. Whidborne. Multiobjective Optimisation and Control. Research Studies Press, 2003

    Google Scholar 

  12. E. Mezura-Montes and C. A. Coello Coello. A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Transactions on Evolutionary Computation, 9(1):1–17, February 2005

    Article  Google Scholar 

  13. E. Mezura-Montes, J. Velázquez-Reyes, and C. A. Coello Coello. Promising Infeasibility and Multiple Offspring Incorporated to Differential Evolution for Constrained Optimization. In H.-G. Beyer and et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2005), volume 1, pages 225–232, New York, June 2005. ACM Press

    Google Scholar 

  14. R. Norton. Machine Design. An Integrated Approach. Prentice-Hall Inc., 1996

    Google Scholar 

  15. A. Osyczka. Multicriterion Optimization in Engineering. John Wiley and Sons, 1984

    Google Scholar 

  16. P. Papalambros and D. Wilde. Principles of Optimal Design. Modelling and Computation. Cambridge University Press, 2000

    Google Scholar 

  17. K. V. Price. An Introduction to Differential Evolution. In David Corne, Marco Dorigo, and Fred Glover, editors, New Ideas in Optimization, pages 79–108. Mc Graw-Hill, UK, 1999

    Google Scholar 

  18. H.-P. Schwefel, editor. Evolution and Optimization Seeking. John Wiley & Sons, New York, 1995

    Google Scholar 

  19. P. Setlur, J. Wagner, D. Dawson, and B. Samuels. Nonlinear control of a continuously variable transmission (cvt). In Transactions on Control Systems Technology, Vol 11, pp. 101–108. IEEE, 2003

    Google Scholar 

  20. E. Shafai, M. Simons, U. Neff, and H. Geering. Model of a continuously variable transmission. In First IFAC Workshop on Advances in Automotive Control, pp. 575–593, 1995

    Google Scholar 

  21. C. De Silva, M. Schultz, and E. Dolejsi. Kinematic analysis and design of a continuously variable transmission. Mechanism and Machine Theory, 29(1):149–167, 1994

    Article  Google Scholar 

  22. M. Spotts. Mechanical Design Analysis. Prentice Hall Inc, 1964

    Google Scholar 

  23. H. van Brussel, Németh I. Sas P, P.D. De Fonseca, and P. van den Braembussche. Towards a mechatronic compiler. IEEE/ASME Transactions on Mechatronics, 6(1):90–104, 2001

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mezura-Montes, E., Portilla-Flores, E., Coello Coello, C., Alvarez-Gallegos, J., Cruz-Villar, C. (2007). An Evolutionary Approach to Solve a Novel Mechatronic Multiobjective Optimization Problem. In: Siarry, P., Michalewicz, Z. (eds) Advances in Metaheuristics for Hard Optimization. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72960-0_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72960-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72959-4

  • Online ISBN: 978-3-540-72960-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics