Multiobjective evolutionary optimization of quadratic Takagi-Sugeno fuzzy rules for remote bathymetry estimation

In this work we tackle the problem of bathymetry estimation using: i) a multispectral optical image of the region of interest, and ii) a set of in situ measurements. The idea is to learn the relation that between the reflectances and the depth using a supervised learning approach. In particular, quadratic Takagi-Sugeno fuzzy rules are used to model this relation. The rule base is optimized by means of a multiobjective evolutionary algorithm. To the best of our knowledge this work represents the first use of a quadratic Takagi-Sugeno fuzzy system optimized by a multiobjective evolutionary algorithm with bounded complexity, i.e., able to control the complexity of the consequent part of second-order fuzzy rules. This model has an outstanding modeling power, without inheriting the drawback of complexity due to the use of quadratic functions (which have complexity that scales quadratically with the number of inputs). This opens the way to the use of the proposed approach even for medium/high dimensional problems, like in the case of hyper-spectral images

On Reducing Computational Overhead in Multi-Objective Genetic Takagi-Sugeno Fuzzy Systems

The use of multi-objective evolutionary algorithms (MOEAs) to generate a set of fuzzy rule-based systems (FRBSs) with different trade-offs between complexity and accuracy has gained more and more interest in the scientific community. The evolutionary process requires, however, a large number of FRBS generations and evaluations. When we deal with high dimensional datasets, these tasks can be very time-consuming, especially when we generate Takagi-Sugeno FRBSs, thus making a satisfactory exploration of the search space very awkward. In this paper, we first analyze the time complexity for both the generation and the evaluation of Takagi-Sugeno FRBSs. Then we introduce a simple but effective technique for speeding up the identification of the rule consequent parameters, one of the most time-consuming phases in Takagi-Sugeno FRBS generation. Finally, we highlight how the application of this technique produces as a side-effect a decoupling of the rules. This decoupling allows us to avoid re-computing consequent parameters of rules which are not directly modified during the evolutionary process, thus saving a considerable amount of time. In the experimental part we first test the correctness of the predicted asymptotical time complexity. Then we show the benefits in terms of computing time saving and improved search space exploration through an example of multi-objective genetic learning of Takagi-Sugeno FRBSs in the regression domain