Abstract
Most of the available multiobjective evolutionary algorithms (MOEA) for approximating the Pareto set have been designed for and tested on low dimensional problems (≤3 objectives). However, it is known that problems with a high number of objectives cause additional difficulties in terms of the quality of the Pareto set approximation and running time. Furthermore, the decision making process becomes the harder the more objectives are involved. In this context, the question arises whether all objectives are necessary to preserve the problem characteristics. One may also ask under which conditions such an objective reduction is feasible, and how a minimum set of objectives can be computed. In this paper, we propose a general mathematical framework, suited to answer these three questions, and corresponding algorithms, exact and heuristic ones. The heuristic variants are geared towards direct integration into the evolutionary search process. Moreover, extensive experiments for four well-known test problems show that substantial dimensionality reductions are possible on the basis of the proposed methodology.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York (2002)
Paechter, B., Rankin, R.C., Cumming, A., Fogarty, T.C.: Timetabling the classes of an entire university with an evolutionary algorithm. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 865–874. Springer, Heidelberg (1998)
Coello Coello, C.A., Hernández Aguirre, A.: Design of Combinational Logic Circuits through an Evolutionary Multiobjective Optimization Approach. Artificial Intelligence for Engineering, Design, Analysis and Manufacture 16(1), 39–53 (2002)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. In: Abraham, A., Jain, R., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, pp. 105–145. Springer, Heidelberg (2005)
Emmerich, M., Beume, N., Naujoks, B.: An emo algorithm using the hypervolume measure as selection criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005)
Knowles, J., Corne, D.: Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation 7(2), 100–116 (2003)
While, L.: A new analysis of the lebmeasure algorithm for calculating hypervolume. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 326–340. Springer, Heidelberg (2005)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)
Purshouse, R.C., Fleming, P.J.: Conflict, harmony, and independence: Relationships in evolutionary multi-criterion optimisation. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 16–30. Springer, Heidelberg (2003)
Tan, K.C., Khor, E.F., Lee, T.H.: Multiobjective Evolutionary Algorithms and Applications. Springer, London (2005)
Deb, K., Saxena, D.K.: On finding pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. Kangal report no. 2005011, Kanpur Genetic Algorithms Laboratory (KanGAL) (2005)
Brockhoff, D., Zitzler, E.: On Objective Conflicts and Objective Reduction in Multiple Criteria Optimization. TIK Report 243, ETH Zurich, Zurich, Switzerland (2006); Operations Research 2006 (submitted)
Zitzler, E., Thiele, L., Laumanns, M., Foneseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Brockhoff, D., Zitzler, E.: Dimensionality Reduction in Multiobjective Optimization with (Partial) Dominance Structure Preservation: Generalized Minimum Objective Subset Problems. TIK Report 247, ETH Zurich, Zurich, Switzerland (2006)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brockhoff, D., Zitzler, E. (2006). Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_54
Download citation
DOI: https://doi.org/10.1007/11844297_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38990-3
Online ISBN: 978-3-540-38991-0
eBook Packages: Computer ScienceComputer Science (R0)