All-Moscow seminar "Mathematical methods of decision analysis in economics, finance and politics"

On Wednesday, February 17, the National Research University Higher School of Economics hosted a regular meeting of the All-Moscow seminar "Mathematical methods for analyzing optimal solutions in economics, business and politics".

Topic: "Approximation and visualization of the Pareto frontier with the support of decision-making about the rules for managing the level of Lake Baikal and the cascade of Angara reservoirs"
Speakers: Ryabikov A.I. (Computing Center named after A.A. Dorodnitsyn, Federal Research Center "Informatics and Control" RAS)

Seminar leaders:
Doctor of Technical Sciences, prof. Aleskerov Fuad Tagievich
Doctor of Technical Sciences, prof. Podinovsky Vladislav Vladimirovich
Doctor of Technical Sciences, prof. Mirkin Boris Grigorievich

Annotation:
The problem of multicriteria optimization of control rules for the cascade of reservoirs of the Angara River, which includes Lake Baikal, is considered. The multicriteria of the problem is a consequence of the conflicting requirements for the control rules. These requirements include environmental, sanitary and safety requirements, as well as the requirements for various water users, including the energy and timber industry, utilities, transport (including transport along the Yenisei River “Severniy Zavoz”, etc. Within the framework of the problem of optimization of control rules, also called the problem of control with feedback, the optimal dependence of control on the current state (feedback) is constructed. As usual in control theory, it is assumed that the feedback structure is given and it is required to choose a vector of its parameters. The main difficulty of the problem under consideration is that the quality of control rules is described by criteria such as the level of security, which have the meaning of the proportion of steps at which the requirements for the system are met (or not met). These criteria are characterized by piecewise constant dependence on the parameters of the rules and, most importantly, by multi-extremity. The presence of such criteria leads to the fact that the global optimization of criteria convolutions, which is usually used in multicriteria problems, turns out to be impossible. The task is complicated due to the fact that decision-making involves different groups of influence with mismatched goals. The study uses two multicriteria approaches. First, a new interactive iterative procedure is used to find the only solution preferred by the expert ("Inherited solution method"). The procedure is suitable when the global optimization of the criteria convolution is impossible. The effective solution was found that reflects the preferences of the expert, but does not take into account the opinion of other influence groups. Next, the Dialogue Decision Maps approach is used, based on the approximation of the Edgeworth-Pareto hull of the set of attainable criterion vectors and further dialogue visualization of the Pareto frontier, which can be used by various groups influence. For the approximation of the Edgeworth-Pareto shell in the case of criteria such as the level of security, a group of methods is proposed ("Launch pad method"). There is also the description of the experience of analyzing the Pareto frontier and the choice of effective rules for managing the water resources of Lake Baikal and the cascade of reservoirs of the Angara River.