Statement and solution of optimization problems in metallurgy

The article discusses the problem of optimizing technological modes of metallurgical processes. The main stages of solving an optimization problem, justification and principles of selecting an optimization criterion, methods for solving multi-criteria vector optimization problems are considered. The authors developed a method for modeling and optimizing metallurgical processes. When implementing the method, two-loop optimization is performed by solving two types of multi-criteria optimization problems: finding the system parameters when determining the optimal conditions for the processes in the first loop, and determining the optimal modes of metallurgical technologies in the second loop. Calculation of optimal technological modes for metallurgical processes involves determining the control actions required to obtain a product of the specified composition and temperature while optimizing technical and economic indicators. To solve this problem, the authors used the mathe­matical models that relate the parameters of the flow and the process. The algorithm for calculating the optimal modes of metallurgical processes includes the following steps: generating initial data, calculating stages and sub-processes, calculating the relationship between the parameters of the flow and the process, determining the technical and economic indicators, and solving the optimization problem. The optimization problem is to determine the control actions for the process by finding the extremum of the required criterion, subject to constraints on the parameters of the final product and the conditions of material and heat balances. The problem is solved using nonlinear programming and the generalized reduced gradient method. Using this method, optimal modes of energy- and resource-saving technologies were developed for a new continuous metallurgical process: obtaining metal from pig iron and rolling scale, direct reduction of metal from dusty ores and iron-containing technogenic materials without agglomeration, obtaining manganese alloys from carbonate and oxide ores, processing titanium-magnetite concentrates, and determining the optimal parameters for the processes of nickel reduction from nickel concentrate and vanadium reduction from converter vanadium slag, which ensure maximum metal extraction.

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