As many-objective optimisation problems become more prevalent, evolutionary algorithms that are based on Pareto dominance relations are slowly becoming less popular due to severe limitations that such an approach has for this class of problems. At the same time decomposition-based methods, which have been employed traditionally in mathematical programming, are consistently increasing in popularity. These developments have been led by recent research studies that show that decomposition-based algorithms have very good convergence properties compared to Pareto-based algorithms. Decomposition-based methods use a scalarising function to decompose a problem with multiple objectives into several single objective subproblems. The subproblems are defined with the help of weighting vectors. The location on the Pareto front that each subproblem tends to converge, strongly depends on the choice of weighting vectors and the scalarising function. Therefore, the selection of an appropriate set of weighting vectors to decompose the multi-objective problem, determines the distribution of the final Pareto set approximation along the Pareto front. Currently a limiting factor in decomposition-based methods is that the distribution of Pareto optimal points cannot be directly controlled, at least not to a satisfactory degree. Generalised Decomposition is introduced in this thesis as a way to optimally solve this problem and enable the analyst and the decision maker define and obtain the desired distribution of Pareto optimal solutions. Furthermore, many algorithms generate a set of Pareto optimal solutions. An interesting question is whether such a set can be used to generate more solutions in specific locations of the Pareto front. Pareto Estimation - a method introduced in this thesis - answers this question quite positively. The decision maker, using the Pareto Estimation method can request a set of solutions in a particular region on the Pareto front, and although not guaranteed to be generated in the exact location, it is shown that the spatial accuracy of the produced solutions is very high. Also the cost of generating these solutions is several orders of magnitude lower compared with the alternative to restart the optimisation.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:568121 |
| Date | January 2012 |
| Creators | Giagkiozis, Ioannis |
| Contributors | Fleming, Peter J. |
| Publisher | University of Sheffield |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.whiterose.ac.uk/3683/ |
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