Coevolution and Encoding of Fuzzy Systems, and Multiobjective Optimisation


This thesis covers several topics relevant to the design of fuzzy systems using evolutionary algorithms (EAs), with application to control problems and constrained multiobjective problems. Encoding is a fundamental part of any EA. The solution encoding, and its interactions with the EA's operators, should be designed to minimise arbitrary search bias. A multidimensional encoding suitable for fully specified fuzzy logic rulebases is investigated, and is shown to have better convergence than traditional single-dimensional encoding. By comparison with 2-point and uniform crossover, the improvement is attributed to the elimination of dimensional encoding bias. The "curse of dimensionality" is the exponential growth of the search space as the number of decision variables increases. In particular, encoding a fully specified fuzzy logic rulebase can result in a prohibitively large search space. Cooperative coevolution and hierarchical fuzzy rulebases both mitigate the curse of dimensionality through modularity, for evolutionary algorithms and fuzzy systems respectively, and these techniques are shown to be highly compatible with one another. The evolutionary convergence, hierarchical design, and opportunity for parallel computation are analysed for the combined techniques. Most real-world problems are characterised by multiple, conflicting objectives, and are subject to multiple constraints. Multiobjective optimisation, particularly constrained multiobjective optimisation, is investigated using control and function optimisation benchmark problems. Two multiobjective diversity measures, hypervolume and distance-to-neighbours, are quantitatively analysed: hypervolume is found to more accurately identify the Pareto front, and distance-to-neighbours is found to distribute solutions more uniformly. The inverted pendulum is used as a case study to qualitatively investigate multiobjective design and optimisation of a control problem. This thesis presents the reconciliation of objective optimisation and constraint satisfaction as the main challenge facing any constrained multiobjective optimisation algorithm, and identifies and investigates two strategies for reconciliation: extended dominance, and blended space. A novel blended space algorithm – the Blended Rank Evolutionary Algorithm (BREA) – is proposed. BREA dynamically maintains trade-offs between objective optimisation, constraint satisfaction, and population diversity, in order to better identify the Pareto optimal set of solutions in difficult problems. BREA is very favourably compared to the extended dominance algorithm NSGA-II on the nonlinear crop-rotation problem, improving both solution quality and reliability.