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.