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Volume 3, Number 1, 2001

A Special Issue on Evolutionary Multicriteria Optimization


A Multi-Objective Genetic Algorithm Approach to Feature Selection in Neural and Fuzzy Modeling 1
Abstract :A large number of techniques, such a neural networks and neurofuzzy systems, are used to produce empirical models based in part or in whole on observed data. A key stage in the modelling process is the selection of features. Irrelevant or noisy features increase the complexity of the modelling problem, may introduce additional costs in gathering unneeded data, and frequently degrade modelling performance. Often it is acceptable to trade off some decrease in performance against a reduction in complexity (number of input features), although we rarely know a priori what an acceptable trade-off is. In this paper, feature selection is posed as a multiobjective optimisation problem, as in the simplest case it involves feature subset size minimisation and performance maximisation. We propose multiobjective genetic algorithms as an effective means of evolving a population of alternative feature subsets with various modelling accuracy/complexity trade-offs, based on the concept of dominance. We discuss methods to reduce the computational costs of the technique, including the use of special forms of neural network and neurofuzzy models. The major contributions of this paper are: the formulation of feature selection as a multiobjective optimisation problem; the use of multiobjective evolutionary algorithms, based on the concept of dominance, for multiobjective feature subset selection; and the application of the multiobjective genetic algorithm feature selection on a number of neural and fuzzy models together with fast subset evaluation techniques. By considering both neural networks and neurofuzzy models, we show that our approach can be generically applied to different modelling techniques. The proposed method is applied on two small and high dimensional regression problems.  
Keywords: Multi-objective evolutionary algorithms, Feature Selection, Neurofuzzy modelling, Neural Networks  
Selection and Mutation Strategies in Evolutionary Algorithms for Global Multiobjective Optimization 27
Thomas HANNE  
Abstract :This paper serves the discussion of some questions concerning the application of evolutionary algorithms to multiobjective optimization problems with continuous variables. A main question of transforming evolutionary algorithms for scalar optimization into those for multiobjective optimization concerns the modification of the selection step. In earlier work we have analyzed specific properties of selection rules called efficiency preservation and negative efficiency preservation. In this article , we discuss the use of these properties by applying an accordingly modified selection rule to some test problems. The number of efficient alternatives of a population for different test problems provides a better understanding of the change of data during the evolutionary process. Also effects of the number of objective functions are treated. We also analyze the influence of the number of objectives and the relevance of these results in the context of the 1/5 rule, a mutation control concept for scalar evolutionary algorithms which cannot easily be transformed into the multiobjective case.  
Keywords :Evolutionary Algorithms, Multicriteria Optimization, Stochastic Search, Selection Mechanism, Step Sizes, 1/5 Rule.  
A Minimal Cost Hybrid Strategy for Pareto Optimal Front Approximation 41
Marco FARINA  
Abstract :A strategy is proposed for coarse grained Pareto Optimal Front approximation. It is devoted to industrial design optimization problems when the number of objective function calls that can be afforded in a practical time is much lower than the number required for convergence of available and powerful MOEAs. An hybrid evolutionary-deterministic and global-local search is applied on a movable preference function derived from L8 norm in objective domain. Both convergence and diversity of solution is tested on several analytical functions.  
Keywords :Pareto Optimal Front, Industrial Design, L8 Norm.  
Design By Sourav Kundu