%0 Journal Article
%T Application of DEO Method to Solving Fuzzy Multiobjective Optimal Control Problem
%A Latafat A. Gardashova
%J Applied Computational Intelligence and Soft Computing
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/971894
%X In the present paper a problem of optimal control for a single-product dynamical macroeconomic model is considered. In this model gross domestic product is divided into productive consumption, gross investment, and nonproductive consumption. The model is described by a fuzzy differential equation (FDE) to take into account imprecision inherent in the dynamics that may be naturally conditioned by influence of various external factors, unforeseen contingencies of future, and so forth. The considered problems are characterized by four criteria and by several important aspects. On one hand, the problem is complicated by the presence of fuzzy uncertainty as a result of a natural imprecision inherent in information about dynamics of real-world systems. On the other hand, the number of the criteria is not small and most of them are integral criteria. Due to the above mentioned aspects, solving the considered problem by using convolution of criteria into one criterion would lead to loss of information and also would be counterintuitive and complex. We applied DEO (differential evolution optimization) method to solve the considered problem. 1. Introduction The studies devoted to solving optimal control problems for dynamic economic models have a long history. The models of economic growth attracted a large interest in the area of mathematical economics [1¨C3]. Recently, intensive revisiting of the growth models took place [4, 5] as a result of the improvements in existing models and progress in development of the associated analytical techniques [6¨C8]. The intensive research in this direction was also conditioned by the support of the developed countries as the latter were interested in construction of accurate economic growth models to improve their economic development [9¨C11]. A lot of various mathematical methods of measuring the effectiveness of economic growth were suggested. In [12] for describing the change of production and accumulated R&D investment in a firm, a nonlinear control model is considered and analyzed. They provide a solution of an optimal control problem with R&D investment rate as a control parameter. They also analyze an optimal dynamics of economic growth of a firm versus the current cost of innovation. The results of analytical investigation showed that the optimal control can be of the two types depending on the model parameters: (a) piecewise constant with at most two switchings and (b) piecewise constant with two switchings and containing a singular arc. In [13] the authors provide results of comparison of solution methods for dynamic
%U http://www.hindawi.com/journals/acisc/2014/971894/