Problems of Multi-Criteria Optimization in the Fuzzy Environment and Heuristic Methods of Their Solution

Abstract

The actual problems of chemical-technological systems were studied, and multi-criteria optimization problems in a fuzzy environment were solved in this work. The methods of the fuzzy set theory and various compromise optimization schemes were used to formalize mathematical statements. By modifying and adapting the methods of the main criterion, maximin and Pareto set, the new statements of the solved problem are obtained in the form of fuzzy mathematical programming problems, and effective methods for their solution are developed. The proposed methods allow solving a fuzzy problem without its preliminary transformation into equivalent deterministic ones and allow making maximum use of the fuzzy initial information. Thus, the problem of optimization is stated and solved in the fuzzy environment preserving and using fuzzy information in the form of experience, knowledge, judgment of the person (experts, decision-makers). The work presents the results of the application of the proposed heuristic method for multi-criteria optimization of the delayed coking unit of the Atyrau oil refinery, which operates in the fuzzy environment. The obtained results show the effectiveness of the proposed method for solving a multi-criteria problem in the fuzzy environment, since, compared to the results of the known methods, it ensures the best results in terms of basic indices and calculates the fuzzy constraint membership functions, i.e. allows controlling the level of fuzzy constraints execution.