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Generalized decomposition and cross entropy methods for many-objective optimization

Giagkiozis, I., Purshouse, R.C. and Fleming, P.J. (2012) Generalized decomposition and cross entropy methods for many-objective optimization. Research Report. ACSE Research Report no. 1029 . Automatic Control and Systems Engineering, University of Sheffield

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Abstract

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduce a novel concept which we call generalized decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying evolutionary algorithm toward specific regions of interest or the entire Pareto front with the desired distribution of Pareto optimal solutions. Additionally, it is shown that generalized decomposition simplifies many-objective problems by unifying the three performance objectives of multi-objective evolutionary algorithms – convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method (CE), is created to illustrate the benefits of the proposed concept for many objective problems. This choice of EDA also enables the test of the hypothesis that low-order statistics based EDAs can have comparable performance to more elaborate EDAs.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Keywords: Generalized decomposition, cross entropy method, MACE, many-objective optimization, multiobjective optimization, decomposition methods, scalarising functions.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
Depositing User: Miss Anthea Tucker
Date Deposited: 23 Nov 2012 14:38
Last Modified: 05 Jun 2014 08:33
Status: Published
Publisher: Automatic Control and Systems Engineering, University of Sheffield
URI: http://eprints.whiterose.ac.uk/id/eprint/74767

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