Multi-Objective Genetic Algorithms

Multi-Objective Genetic Algorithms (MOGAs) are an extension of the classical single objective Genetic Algorithms (GAs). MOGAs are used to solve multi-objective optimization problems in which the objectives are in competition among them: in this case it could be useful to find a collection of solutions with a good trade-off between all the objectives.

The trade-off surface is called Pareto Front, and it is composed by non-dominated solutions (a solution s1 dominates a solution s2 if s1 is not worse than s2 on all the objectives and better than s2 in at least one objective). Using a MOGA to find a good approximation of the Pareto Front, a fitness vector is associated to each element (chromosome) of the actual population, in order to evaluate its level of goodness, instead of a single fitness value such as in the classical GAs.

The research focuses on:

In the last year, we studied how to use a MOGA to identify the rule base of a Mamdani type Fuzzy System, from numerical data, with application to regression, functions approximation and time series forecasting problems. Usually, during the identification process of a Fuzzy System, only the maximization of the accuracy of the system is considered, but we also tried to minimize the complexity. These two objectives are in competition and a good trade-off between the accuracy and the complexity should be found.

We used the Pareto Archived Evolutionary Strategy (PAES) to identify a set of non dominated rule bases, for a Mamdani System in which the fuzzy partitions of input and output variables have pre-determined numbers of fuzzy sets and uniformly distributed membership functions.

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