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

Solving the ocean color inverse problem by using evolutionary multi-objective optimization of neuro-fuzzy systems

The ocean color inverse problem consists of determining the concentrations of optically active constituents, such as chlorophyll, suspended particulate matter and colored dissolved organic matter, from remotely sensed multispectral measurements of the reflected sunlight back-scattered by the water body. In this paper, we approach this regression problem by using an evolutionary multi-objective algorithm, namely the (2+2) Modified Pareto Archived Evolutionary Strategy ((2+2)M-PAES), to optimize Takagi-Sugeno type (TS-type) fuzzy rule-based systems (FRBSs). Accuracy and complexity are the two competitive objectives to be simultaneously optimized. TS-type FRBSs are implemented as an artificial neural network; by training the neural network, the parameters of the fuzzy model are adjusted. In this way, the evolutionary optimization coarsely identifies the structure of the TS-type FRBSs, while the corresponding neural networks finely tune their parameters. As a result, a set of TS-type FRBSs with different trade-offs between accuracy and complexity is provided at the end of the optimization process. We show the effectiveness of our approach by comparing our results with those obtained on the ocean color inverse problem by other techniques recently proposed in the literature

Solving the ocean color inverse problem by using evolutionary multi-objective optimization of neuro-fuzzy systems

The ocean color inverse problem consists of determining the concentrations of optically active constituents, such as chlorophyll, suspended particulate matter and colored dissolved organic matter, from remotely sensed multispectral measurements of the reflected sunlight back-scattered by the water body. In this paper, we approach this regression problem by using an evolutionary multi-objective algorithm, namely the (2+2) Modified Pareto Archived Evolutionary Strategy ((2+2)M-PAES), to optimize Takagi-Sugeno type (TS-type) fuzzy rule-based systems (FRBSs). Accuracy and complexity are the two competitive objectives to be simultaneously optimized. TS-type FRBSs are implemented as an artificial neural network; by training the neural network, the parameters of the fuzzy model are adjusted. In this way, the evolutionary optimization coarsely identifies the structure of the TS-type FRBSs, while the corresponding neural networks finely tune their parameters. As a result, a set of TS-type FRBSs with different trade-offs between accuracy and complexity is provided at the end of the optimization process. We show the effectiveness of our approach by comparing our results with those obtained on the ocean color inverse problem by other techniques recently proposed in the literature