Skip to main content

Modes of Problem Solving with Multiple Objectives: Implications for Interpreting the Pareto Set and for Decision Making

  • Chapter
Multiobjective Problem Solving from Nature

Part of the book series: Natural Computing Series ((NCS))

Summary

This chapter identifies five distinct modes∈dexmodes of multiobjective optimization in which multiobjective optimization is used to solve practical optimization problems. Implications for the interpretation and analysis of the resulting Pareto front, and for decision making, are discussed, and each mode is illustrated using application examples taken from recent research.

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. P. Arabie, L. J. Hubert, and G. D. Soete. Clustering and Classification. World Scientific, New Jersey, NJ, 1996.

    Book  Google Scholar 

  2. S. Basu, A. Banerjee, and R. Mooney. Semi-supervised clustering by seeding. In Proceedings of the 19th International Conference on Machine Learning, pages 19–26. ACM Press, New York, NY, 2002.

    Google Scholar 

  3. R. Bellman. Adaptive Control Processes: A Guided Tour. Princeton University Press, Princeton, NJ, 1961.

    Book  Google Scholar 

  4. A. Blum and T. Mitchell. Combining labeled and unlabeled data with co-training. In Proceedings of the Conference on Computational Learning Theory. ACM Press, New York, NY, 1998.

    Google Scholar 

  5. J. Branke, K. Deb, H. Dierolf, and M. Osswald. Finding knees in multi-objective optimization. In Proceedings of the Eighth International Conference on Parallel Problem Solving from Nature, pages 722–731. Springer-Verlag, Berlin, Germany, 2004.

    Google Scholar 

  6. O. Chapelle, V. Vapnik, and J. Weston. Transductive inference for estimating values of functions. In S. A. Solla, T. K. Leen, and K.-R. Mddotuller, editors, Neural Information Processing Systems (NIPS), pages 421–427. The MIT Press, 1999.

    Google Scholar 

  7. D. W. Corne, N. R. Jerram, J. D. Knowles, and M. J. Oates. PESA-II: region-based selection in evolutionary multiobjective optimization. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 283–290. ACM Press, New York, NJ, 2001.

    Google Scholar 

  8. I. Das. On characterizing the ‘knee’ of the Pareto curve based on normal-boundary intersection. Structural Optimization, 18:107–115, 1999.

    Article  Google Scholar 

  9. M. Dash and H. Liu. Handling large unsupervised data via dimensionality reduction. In Proceedings of the ACM SIGMOD Workshop on Research Numbers in Data Mining and Knowledge Discovery, 1999. http://www.almaden.ibm.com/cs/dmkd/.

    Google Scholar 

  10. R. O. Duda, P. E. Hart, and D. G. Stork. Pattern Classification, second edition. John Wiley and Son Ltd, London, UK, 2001.

    MATH  Google Scholar 

  11. J. G. Dy and C. E. Brodley. Feature selection for unsupervised learning. Journal of Machine Learning Research, 5(5):845–889, 2004.

    MathSciNet  MATH  Google Scholar 

  12. M. Ehrgott. Multicriteria Optimization. Springer-Verlag, Berlin, Germany, 2000.

    Book  Google Scholar 

  13. M. Ehrgott and R. Johnston. Optimisation of beam directions in intensity modulated radiation therapy planning. OR Spectrum, 25(2):251–264, 2003.

    Article  Google Scholar 

  14. B. S. Everitt. Cluster Analysis. Edward Arnold, London, UK, 1993.

    MATH  Google Scholar 

  15. A. Ferligoj and V. Batagelj. Direct multicriterion clustering. Journal of Classification, 9:43–61, 1992.

    Article  MathSciNet  Google Scholar 

  16. R. Fletcher and S. Leyffer. Nonlinear programming without a penalty function. Mathematical Programming, 91(2):239–269, 2002.

    Article  MathSciNet  Google Scholar 

  17. D. Guo, M. Gahegan, D. Peuquet, and A. MacEachren. Breaking down dimensionality: an effective feature selection method for high-dimensional clustering. In Proceedings of the Third SIAM International Conference on Data Mining, pages 29–42. SIAM Press, San Francisco, CA, 2003.

    Google Scholar 

  18. I. Guyon and A. Elisseeff. An introduction to variable and feature selection. Journal of Machine Learning Research, 3(3):1157–1182, 2002.

    MATH  Google Scholar 

  19. J. Handl and J. Knowles. Exploiting the Trade-Off—The Benefits of Multiple Objectives in Data Clustering. In C. A. Coello Coello, A. Hernández Aguirre, and E. Zitzler, editors, Evolutionary Multi-Criterion Optimization. Third International Conference, EMO 2005, pages 547–560, Guanajuato, México, Mar. 2005. Springer. Lecture Notes in Computer Science Vol. 3410.

    Google Scholar 

  20. J. Handl and J. Knowles. Multiobjective clustering around medoids. In D. Corne, Z. Michalewicz, B. McKay, G. Eiben, D. Fogel, C. Fonseca, G. Greenwood, G. Raidl, K. C. Tan, and A. Zalzala, editors, Proceedings of the 2005 IEEE Congress on Evolutionary Computation, volume 1, pages 632–639, Edinburgh, Scotland, UK, 2-5 Sept. 2005. IEEE Press. ISBN 0-7803-9363-5. URL http://ieeexplore.ieee.org/servlet/opac?punumber=10417&isvol=1.

    Google Scholar 

  21. J. Handl and J. Knowles. Feature subset selection in unsupervised learning via multiobjective optimization. International Journal on Computational Intelligence Research, 2(3):217–238, 2006.

    Article  MathSciNet  Google Scholar 

  22. J. Handl and J. Knowles. On semi-supervised clustering via multiobjective optimization. Technical Report TR-COMPSYSBIO-2006-02, Manchester Interdisciplinary Biocentre, University of Manchester, UK, 2006. http://dbk.ch.umist.ac.uk/handl/publications.html.

    Google Scholar 

  23. J. Handl and J. Knowles. Semi-supervised feature selection via multiobjective optimization. Technical Report TR-COMPSYSBIO-2006-03, Manchester Interdisciplinary Biocentre, University of Manchester, UK, 2006. http://dbk.ch.umist.ac.uk/handl/publications.html.

    Google Scholar 

  24. J. Handl and J. Knowles. An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation, 11(1):56–76, 2007.

    Article  Google Scholar 

  25. J. Handl and J. Knowles. Multiobjective optimization in bioinformatics and computational biology. IEEE/ACM Transactions on Computational Biology, 4(2), 2007.

    Google Scholar 

  26. D. Hanisch, A. Zien, R. Zimmer, and T. Lengauer. Co-clustering of biological networks and gene expression data. Bioinformatics, 18:145–154, 2002.

    Article  Google Scholar 

  27. G. G. Harrigan and R. Goodacre. Metabolic Profiling: Its Role in Biomarker Discovery and Gene Function Analysis. Kluwer Academic Publishers, London, UK, 2003.

    Book  Google Scholar 

  28. L. Hubert and P. Arabie. Comparing partitions. Journal of Classification, 2:193–218, 1985.

    Article  Google Scholar 

  29. A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

  30. M. T. Jensen. Guiding single-objective optimization using multi-objective methods. In Applications of Evolutionary Computation, pages 268–279. Springer-Verlag, Berlin, Germany, 2003.

    MATH  Google Scholar 

  31. T. Joachims. Transductive inference for text classification using support vector machines. In Proceedings of 16th International Conference on Machine Learning, pages 200–209. Morgan Kaufmann Publishers, San Francisco, CA, 1999.

    Google Scholar 

  32. D. Kim. Structural risk minimization on decision trees using an evolutionary multiobjective optimization. In Proceedings of the Seventh European Conference on Genetic Programming, pages 338–348. Springer-Verlag, Berlin, Germany, 2004.

    Google Scholar 

  33. J. D. Knowles, R. A. Watson, and D. W. Corne. Reducing local optima in single-objective problems by multi-objectivization. In Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization, pages 269–283. Springer-Verlag, Berlin, Germany, 2001.

    Google Scholar 

  34. J. D. Knowles, R. A. Watson, and D. W. Corne. Reducing Local Optima in Single-Objective Problems by Multi-objectivization. In E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, pages 268–282. Springer-Verlag. Lecture Notes in Computer Science No. 1993, 2001.

    Google Scholar 

  35. K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, 1999.

    Google Scholar 

  36. G. W. Milligan. Clustering validation: results and implications for applied analyses. In Clustering and Classification, chapter 10, pages 341–367. World Scientific, New Jersey, NJ, 1996.

    MATH  Google Scholar 

  37. S. Mitra. Computational intelligence in bioinformatics. Transactions on Rough Sets, pages 134–152, 2005.

    Google Scholar 

  38. M. Morita, R. Sabourin, F. Bortolozzi, and C. Y. Suen. Unsupervised feature selection using multi-objective genetic algorithms for handwritten word recognition. In Proceedings of the Seventh International Conference on Document Analysis and Recognition, pages 666–671. IEEE Press, New York, NY, 2003.

    Google Scholar 

  39. S. O’Hagan, W. B. Dunn, D. Broadhurst, R. Williams, J. Ashworth, M. Cameron, J. Knowles, and D. B. Kell. Closed-loop, multi-objective optimisation of two-dimensional gas chromatography (gcxgc-tof-ms) for serum metabolomics. Analytical Chemistry, 79:464–476, 2007.

    Article  Google Scholar 

  40. S. O’Hagan, W. B. Dunn, M. Brown, J. D. Knowles, and D. B. Kell. Closed-loop, multiobjective optimization of analytical instrumentation: gas chromatography/time-of-flight mass spectrometry of the metabolomes of human serum and of yeast fermentations. Analytical Chemistry, 77(1):290–303, 2005.

    Article  Google Scholar 

  41. J. M. Pena, J. A. Lozano, P. Larranaga, and I. Inza. Dimensionality reduction in unsupervised learning of conditional Gaussian networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6):590–603, 2001.

    Article  Google Scholar 

  42. P. J. Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20:53–65, 1987.

    Article  Google Scholar 

  43. E. Schreibmann, M. Lahanas, L. Xing, and D. Baltas. Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy. Physics in Medicine and Biology, 49(5):747–770, 2004.

    Article  Google Scholar 

  44. Y. Siskos and A. Spyridakos. Intelligent multicriteria decision support: Overview and perspectives. European Journal of Operational Research, 113 (2):236–246, 1999.

    Article  Google Scholar 

  45. N. Sondberg-Madsen, C. Thomsen, and J. M. Pena. Unsupervised feature subset selection. In Proceedings of the Workshop on Probabilistic Graphical Models for Classification, pages 71–82, 2003. http://www.sc.ehu.es/ccwbayes/ecml-pkdd-03-workshop/call.htm.

    Google Scholar 

  46. A. Strehl and J. Ghosh. Cluster ensembles — a knowledge reuse framework for combining multiple partitions. Journal on Machine Learning Research, 3:583–617, 2002.

    MathSciNet  MATH  Google Scholar 

  47. L. Talavera. Feature selection as a preprocessing step for hierarchical clustering. In Proceedings of the Sixteenth International Conference on Machine Learning, pages 389–39. Morgan Kaufmann, San Francisco, CA, 1999.

    Google Scholar 

  48. A. Topchy, A. K. Jain, and W. Punch. A mixture model for clustering ensembles. In Proceedings of the SIAM International Conference on Data Mining, pages 379–390. SIAM, Lake Buena Vista, FL, 2004.

    Google Scholar 

  49. P. Vincke. Multicriteria decision-aid. Wiley New York, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Handl, J., Knowles, J. (2008). Modes of Problem Solving with Multiple Objectives: Implications for Interpreting the Pareto Set and for Decision Making. In: Knowles, J., Corne, D., Deb, K. (eds) Multiobjective Problem Solving from Nature. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72964-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72964-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72963-1

  • Online ISBN: 978-3-540-72964-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics