Multicriteria identification sets method

G. K. Kamenev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 11, pp. 1872-1888

Résumé

A multicriteria identification and prediction method for mathematical models of simulation type in the case of several identification criteria (error functions) is proposed. The necessity of the multicriteria formulation arises, for example, when one needs to take into account errors of completely different origins (not reducible to a single characteristic) or when there is no information on the class of noise in the data to be analyzed. An identification sets method is described based on the approximation and visualization of the multidimensional graph of the identification error function and sets of suboptimal parameters. This method allows for additional advantages of the multicriteria approach, namely, the construction and visual analysis of the frontier and the effective identification set (frontier and the Pareto set for identification criteria), various representations of the sets of Pareto effective and subeffective parameter combinations, and the corresponding predictive trajectory tubes. The approximation is based on the deep holes method, which yields metric ε-coverings with nearly optimal properties, and on multiphase approximation methods for the Edgeworth-Pareto hull. The visualization relies on the approach of interactive decision maps. With the use of the multicriteria method, multiple-choice solutions of identification and prediction problems can be produced and justified by analyzing the stability of the optimal solution not only with respect to the parameters (robustness with respect to data) but also with respect to the chosen set of identification criteria (robustness with respect to the given collection of functionals).

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