Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets

Batyr Orazbayev, Kulman Orazbayeva, Yerbol Ospanov (), Salamat Suleimenova, Lyailya Kurmangaziyeva, Valentina Makhatova, Yerlan Izbassarov and Aigerim Otebaeva
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Batyr Orazbayev: Department of System Analysis and Control, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan
Kulman Orazbayeva: Department of Management, Esil University, Astana 010008, Kazakhstan
Yerbol Ospanov: Department of Automation and Information Technology, Shakarim University, Semey 070014, Kazakhstan
Salamat Suleimenova: Department of Computer Science, Korkyt Ata Kyzylorda University, Kyzylorda 120001, Kazakhstan
Lyailya Kurmangaziyeva: Department of Software Engineering, Dosmukhamedov Aytrau University, Atyrau 010008, Kazakhstan
Valentina Makhatova: Department of Software Engineering, Dosmukhamedov Aytrau University, Atyrau 010008, Kazakhstan
Yerlan Izbassarov: Department of Software Engineering, Dosmukhamedov Aytrau University, Atyrau 010008, Kazakhstan
Aigerim Otebaeva: Department of Software Engineering, Dosmukhamedov Aytrau University, Atyrau 010008, Kazakhstan

Mathematics, 2024, vol. 12, issue 18, 1-22

Abstract: Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.

Keywords: decision maker (DM); fuzzy constraints; heuristic method; multi-criteria optimization; simplex method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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