This grant provides funding for the exploratory research on the methods of measuring and utilizing information in optimization and decision making problems encountered in Engineering, Operations Research and Management Science. In particular, applications of the Maximum Entropy Principle based on general Renyi entropies will be studied. Ways of determining the suitable value of the Renyi parameter for different classes of optimization problems will be explored. New methods of measuring information content of optimization problems will be developed based on Renyi entropies and compared to existing concepts such as Kolmogorov complexity. These methods then will be applied to study the relation between the information content of the problem input data and the corresponding solution set, and principles of information conservation (or non-increase) will be formulated. These principles will be applied to optimization problems of practical interest including problems with high uncertainty.
If successful, the results of this research will lead to a formulation of a new framework for the analysis of the information content of optimization and decision making problems of practical significance. This, in particular, will allow for the development of a consistent method for evaluating the additional benefit provided by new (more precise) input data. This will also provide a mathematically sound method for treating decision making problems with high uncertainty. In particular, it will be possible to determine the decision set that can be singled out entirely on the basis of information contained in the corresponding input data, and to find how this decision set should change if more precise input data becomes available. The proposed work will also contribute to the methodologies of the general Information Theory.
