Batyr Orazbayev
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.
- Rykov A.S. Poiskovaja optimizacija. Metody deformiruemyh konfi-guracij. -Nauka, Moscow, 1993.Google Scholar
- Volin Ju. M., Ostrovskij G. M. Mnogokriterial'naja optimizacija tehnologicheskih processov v uslovijah neopredelennosti. Avt. i telemeh., Vol.53, iss. 3, 2007, pp. 165--180.Google Scholar
- Bobkov V.I., Borisov V.V., Dli M.I., Meshalkin V.P. Mnogokriteri-al'naja optimizacija jenergojeffektivnosti tehnologicheskih processov ter-micheskoj podgotovki syr'ja. Teoret. osnovy him. Technologii, vol. 49, Iss. 6, 2015, pp.665--678. https://elibrary.ru/item.asp?id=24730551Google Scholar
- Biegler L.T., Lang Y.D, Lin W.J. Multi-scale Optimization for Process Systems Engineering. Comp. and Chem. Eng, vol.60, iss.10, 2014, pp.17--30.Google ScholarCross Ref
- Ostrovsky G.M., Ziyatdinov N.N., Lapteva T.V., Silvestrova A. Optimization of chemical process design with chance constraints by an iterative partitioning approach, Industrial and Eng. Chem. Research, vol.54, iss.13, 2015, pp. 3412--3429.Google ScholarCross Ref
- Kahraman C. Fuzzy Multi-Criteria Decision Making. Theories and Appli-cations with Recent Developments. -Springer, New York, 2008. Google ScholarDigital Library
- Fengqi You, I.E. Grossmann. Design of responsive supply chains under demand uncertainty. Comp. and Chem. Eng., Iss. 32, 2008, p. 3090.Google ScholarCross Ref
- Dubois D. The role of fuzzy sets indecision sciences: Old techniques and new directions, Fuzzy Sets and Systems, vol. 184, 2011, pp. 3--17. Google ScholarDigital Library
- Rykov A.S., Orazbaev B.B. Zadachi i metody prinjatija reshenij. Mnogokriterial'nyj nechetkij vybor. - MISIS, Moscow, 1995.Google Scholar
- Orazbayev B.B., Orazbayeva K.N., Kurmangaziyeva L.T., Makhatova V.E. Multicriteria op-timisation problems for chemical engineering systems and algo-rithms for their solution based on fuzzy mathematical methods. EXCLI Journal. Vol.14, 2015, pp. 984--998.Google Scholar
- Grossmann I.E. Challenges in the Application of Mathematical Programming in the Enter-prise-wide Optimization of Process Industries. Teoret. osnovy him. tehnologii. Vol. 48. Iss.5, 2014, pp. 500--518.Google Scholar
- Solov'ev N.A, Semenov A.M. Jekspertnye sistemy. - Orenburg, 2009, p.231.Google Scholar
- Sulejmenov B.A. Intellektual'nye i gibridnye sistemy upravlenija tehnologicheskimi processami. Pikula i K. Almaty, 2009, p. 304.Google Scholar
- Dzharratino D. Jekspertnye sistemy: principy razrabotki i pro-grammirovanie. Iss.4, I.D. Vil'jams, Moskow, 2007. P.1152.Google Scholar
- Orazbaev B.B. Teorija i praktika metodov nechetkih mnozhestv. Uchebnik dlja studentov VUZov. Bastau, Almaty, 2014. P.455.Google Scholar
- Orazbaev B.B. Metody modelirovanija i prinjatija reshenij dlja upravlenija proizvodstvom v nechetkoj srede. ENU im. L.N. Gumile-va, Astana, 2016. P. 398.Google Scholar
- Zajchenko Ju.P. Issledovanie operacij: nechetkaja optimizacija. Vyshha shkola, Kiev, 1991. P. 347.Google Scholar
- Lapteva T.V., Zijatdinov N.N., Ostrovskij G.M., Pervuhin D.D. Optimizacija himiko-tehnologicheskih processov s verojatnostnymi ogranichenijami. Teoret. osnovy him. tehnologii.vol.44, iss. 5, P.507.Google Scholar
- Ostrovskij G.M., Zijatdinov N.N., Lapteva T.V., Pervuhin D.D. Od-nojetapnaja zadacha optimizacii s mjagkimi ogranichenijami. Teoret. osnovy him. tehnologii. Vol. 43, iss. 4, 2009. P.441.Google Scholar
- Pershin O.Ju. Pareto-optimal'nye i leksikograficheskie reshenija chastichno-celochislennyh zadach, linejnyh po nepreryvnym peremennym. AiT, iss. 2, 1994, pp.139--148.Google Scholar
- Shumskij V.M., Zyrjanova L.A. Inzhenernye zadachi v neftepererabotke i neftehimii. Himija, Moskow, 1981.Google Scholar
Index Terms
- Problems of Multi-Criteria Optimization in the Fuzzy Environment and Heuristic Methods of Their Solution
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