Skip to main content
SpringerLink
Log in

Fuzzy Optimality and Evolutionary Multiobjective Optimization

  • Conference paper
  • First Online:
Book cover Evolutionary Multi-Criterion Optimization (EMO 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2632))

Included in the following conference series:

Abstract

Pareto optimality is someway ineffective for optimization problems with several (more than three) objectives. In fact the Pareto optimal set tends to become a wide portion of the whole design domain search space with the increasing of the numbers of objectives. Consequently, little or no help is given to the human decision maker. Here we use fuzzy logic to give two new definitions of optimality that extend the notion of Pareto optimality. Our aim is to identify, inside the set of Pareto optimal solutions, different “degrees of optimality” such that only a few solutions have the highest degree of optimality; even in problems with a big number of objectives. Then we demonstrate (on simple analytical test cases) the coherence of these definitions and their reduction to Pareto optimality in some special subcases. At last we introduce a first extension of (1+1)ES mutation operator able to approximate the set of solutions with a given degree of optimality, and test it on analytical test cases.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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. P. Alotto, A. V. Kuntsevitch, Ch. Magele, C. Paul G. Molinari, K. Preis, M. Repetto, and K. R. Richter. Multiobjective optimization in magnetostatics: A proposal for benchmark problems. Technical report, Institut für Grundlagen und Theorie Electrotechnik, Technische Universität Graz, Graz, Austria, http://www-igte.tu-graz.ac.at/team/berl01.htm, 1996.

    Google Scholar 

  2. P. Amato and C. Manara. Relating the theory of partitions in mv-logic to the design of interpretable fuzzy systems. In J. Casillas, O. Cordón, F. Herrera, and L. Magdalena, editors, Trade-off between Accuracy and Interpretability in Fuzzy Rule-Based Modeling. Springer-Verlag, Berlin, to be published.

    Google Scholar 

  3. P. Di Barba and M. Farina. Multiobjective shape optimisation of air cored solenoids. COMPEL International Journal for computation and mathematics in Electrical and Electronic Engineering, 21(1):45–57, 2002. in press.

    Article  MATH  Google Scholar 

  4. P. Di Barba, M. Farina, and A. Savini. Multiobjective Design Optimization of Real-Life Devices in Electrical Engineering: A Cost-Effective Evolutionary Approach. In Eckart Zitzler, Kalyanmoy Deb, Lothar Thiele, Carlos A. Coello Coello, and David Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, pages 560–573. Springer-Verlag. Lecture Notes in Computer Science No. 1993, 2001.

    Google Scholar 

  5. C. Carlsson and R. Fuller. Multiobjective optimization with linguistic variables. Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT98, Aachen, 1998, Verlag Mainz, Aachen,, 2:1038–1042, 1998.

    Google Scholar 

  6. Lino Costa and Pedro Oliveira. An Evolution Strategy for Multiobjective Optimization. In Congress on Evolutionary Computation (CEC’ 2002), volume 1, pages 97–102, Piscataway, New Jersey, May 2002. IEEE Service Center.

    Article  Google Scholar 

  7. Masashi Morikawa Daisuke Sasaki, Shigeru Obayashi, and Kazuhiro Nakahashi. Constrained Test Problems for Multi-objective Evolutionary Optimization. In Eckart Zitzler, Kalyanmoy Deb, Lothar Thiele, Carlos A. Coello Coello, and David Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, pages 639–652. Springer-Verlag. Lecture Notes in Computer Science No. 1993, 2001.

    Google Scholar 

  8. M. Farina and P. Amato. A fuzzy definition of “optimality” for many-criteria decision-making and optimization problems. submitted to IEEE Trans. on Sys. Man and Cybern., 2002.

    Google Scholar 

  9. T. Hanne. Intelligent strategies for meta multiple criteria decision making. Kluwer Academic Publishers, Dordrecht, THE NETHERLANDS, 2001.

    MATH  Google Scholar 

  10. Ryoji Homma. Combustion process optimization by genetic algorithms — reduction of co emission via optimal post-flame process. Energy and Environmental Technology Laboratory, Tokyo Gas Co., Ltd., 9, 1999.

    Google Scholar 

  11. P. Tarvainen J. Hamalainee, R.A.E Makinen. Optimal design of paper machine headboxes. International Journal of Numerical Methods in Fluids, 34:685–700, 2000.

    Article  MATH  Google Scholar 

  12. G. J. Klir and Bo Yuan editors. Fuzzy Sets, Fuzzy Logic and Fussy Systems, selected papers by L.A. Zadeh, volume 6 of Advances in Fuzzy Systems — Applications and Theory. World Scientific, Singapore, 1996.

    Google Scholar 

  13. M. Farina and P. Amato. On the optimal solution definition for many-criteria optimization problems. In Proceedings of the NAFIPS-FLINT International Conference2002, New Orleans, June, 2002, pages 233–238. IEEE Service Center, June 2002.

    Google Scholar 

  14. K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Dordrecht, THE NETHERLANDS, 1999.

    MATH  Google Scholar 

  15. P.P. Chakrabarti P. Dasgupta and S. C. DeSarkar. Multiobjective Heuristic Search. Vieweg, 1999.

    Google Scholar 

  16. N. Srinivas and Kalyanmoy Deb. Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3):221–248, Fall 1994.

    Article  Google Scholar 

  17. http://energy.bmstu.ru/e02/diesel/d11eng.htm.

Download references

Author information

Authors and Affiliations

  1. STMicroelectronics Srl, Via C. Olivetti, 2, 20041, Agrate (MI), Italy

    M. Farina & P. Amato

Authors
  1. M. Farina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Amato
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Sciences and Technology, Centre for Intelligent Systems, University of the Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Carlos M. Fonseca

  2. Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    Peter J. Fleming

  3. Department of Electrical Engineering, Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology, Gloriastraße 35, 8092, Zürich, Switzerland

    Eckart Zitzler  & Lothar Thiele  & 

  4. Department of Mechanical Engineering, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, UP, 208 016, India

    Kalyanmoy Deb

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Farina, M., Amato, P. (2003). Fuzzy Optimality and Evolutionary Multiobjective Optimization. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-36970-8_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-01869-8

  • Online ISBN: 978-3-540-36970-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation