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This work presents and formalizes an explicit multi-objective evolutionary approach for the segmentation issue according to Piecewise Linear Representation, which consists in the approximation of a given digital curve by a set of linear models minimizing the representation error and the number of such models required. Available techniques are focused on the minimization of the quality of the obtained approximation, being the cost of that approximation considered, in general, only for certain comparison purposes. The multi-objective nature of the problem is analysed and its treatment in available works reviewed, presenting an a posteriori approach based on an evolutionary algorithm. Three representative curves are included in the data set, comparing the proposed technique to nine different techniques. The performance of the presented approach is tested according to single and multiobjective perspectives. The statistical tests carried out show that the experimental results are, in general, significantly better than available approaches from both perspectives.
polygonal approximation; time series; piecewise linear representation; multi-objective optimization; evolutionary algorithms