Abstract
This paper describes and demonstrates a new and highly innovative technique that identifies an approximation of the entire bounding surface of the feasible objective region directly, including deep concavities, disconnected regions and the edges of interior holes in the feasible areas. The Pareto front is a subset of the surface of the objective boundary and can be extracted easily. Importantly, if the entire objective boundary is known, breaks and discontinuities in the Pareto front may be identified using automated methods; even with high objective dimensionality. This paper describes a proof-of-principle evolutionary algorithm that implements the new and unique Direct Objective Boundary Identification (DOBI) method.
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.
References
Hughes, E.J.: Radar waveform optimisation as a many-objective application benchmark. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 700–714. Springer, Heidelberg (2007)
Hughes, E.J.: MSOPS-II: A general-purpose many-objective optimiser. In: Congress on Evolutionary Computation CEC 2007, Singapore, pp. 3944–3951. IEEE, Los Alamitos (2007)
Purshouse, R.C.: On the Evolutionary Optimisation of Many Objectives. PhD thesis, Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, UK (September 2003)
Hughes, E.J.: Evolutionary many-objective optimisation: Many once or one many? In: IEEE Congress on Evolutionary Computation, vol. 1, pp. 222–227. IEEE, Los Alamitos (2005)
Knowles, C., Deb, K. (eds.): Multiobjective Problem Solving from Nature: From Concepts to Applications. Natural Computing Series. Springer, Berlin (2008)
Zhao, H., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM 2001) (July 2001)
Jiřina, M.: Nearest neighbour distance statistics estimation. Technical report, Institute of Computer Science: Academy of Sciences of the Czech Republic (October 2002), ftp://ftp.cs.cas.cz/pub/reports/v878-02.pdf
Muller, M.E.: A note on a method for generating points uniformly on n-dimensional spheres. Communications of the ACM 2, 19–20 (1959)
Hicks, J.S., Wheeling, R.F.: An efficient method for generating uniformly distributed points on the surface of an n-dimensional sphere. Communications of the ACM 2, 17–19 (1959)
Rose, C., Smith, M.D.: Mathematical Statistics with Mathematica. Springer, Heidelberg (2002)
Hughes, E.J.: Software resources, http://code.evanhughes.org
Jacquelin, J.: Le problème de l’hyperchèvre. Quadrature (49), 6–12 (July- September 2003), http://www.maths-express.com/articles/hyperchevre.pdf ISSN 1142-2785
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hughes, E.J. (2008). Many Objective Optimisation: Direct Objective Boundary Identification. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_73
Download citation
DOI: https://doi.org/10.1007/978-3-540-87700-4_73
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87699-1
Online ISBN: 978-3-540-87700-4
eBook Packages: Computer ScienceComputer Science (R0)