T. M. Zubkova, E. N. Ishakova, M. A. Tokareva

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A method for multi-criteria optimization of the design parameters for technological object is described. The existing optimization methods are overviewed, and works in the field of basic research and applied problems are analyzed. The problem is formulated, based on the process requirements, making it possible to choose the geometrical dimensions of machine tips and the flow rate of the process, so that the resulting technical and economical parameters were optimal. In the problem formulation application of the performance method adapted to a particular domain is described. Task implementation is shown; the method of characteristics creation for the studied object in view of some restrictions for parameters in both analytical and graphical representation. On the basis of theoretical research the software system is developed that gives the possibility to automate the discovery of optimal solutions for specific problems. Using available information sources, that characterize the object of study, it is possible to establish identifiers, add restrictions from the one side, and in the interval as well. Obtained result is a visual depiction of dependence of the main study parameters on the others, which may have an impact on both the flow of the process, and the quality of products. The resulting optimal area shows the use of different design options for technological object in an acceptable kinematic range that makes it possible for the researcher to choose the best design solution.

Keywords: vector optimization, parametric synthesis, cubic spline, multi-criteria optimization, program system, optimum area, technological process, technological object

1.     Zubkova T.M. Parametricheskii sintez tekhnologicheskikh ob"ektov s ispol'zovaniem programmnykh sredstv [Parametritic synthesis of technological objects with using of software tools]. Vestnik Orenburgskogo gosudarstvennogo universiteta, 2006, no. 5, pp. 150–157.
2.     Nikonov O.I., Medvedev M.A. Metody vektornoi optimizatsii v rabote s kontragentami predpriyatii[Vector optimization technique in the problems of interaction between an enterprise and its counteragents]. Ekonomika Regiona, 2011, no. 3, pp. 217–224.
3.     Okhrushchak D.V., Skoblilova N.M., Stasyuk V.N., Mukhin A.M. Vektornaya optimizatsiya kombinirovannykh system fazovoi avtopodstroiki [Vector optimization of combined systems of automatic phase control]. Radioelectronics and Communications Systems, 2003, vol. 46, no. 8, pp. 30–34.
4.     Severin V.P. Vector optimization of integral quadratic estimates for automated control systems. Journal of Computer and Systems Sciences International, 2005, vol. 44, no. 2, pp. 207–216.
5.     SizikovA.P. Razrabotka predmetno-orientirovannykh system optimizatsii (na primere neftepererabatyvayushchego proizvodstva) [Disigning of object-oriented systems optimization (on the example of refinery)]. Upravlenie bolsimi sistemami, 2012, vol. 40, pp. 291–310.
6.     Bakhtin V.I., Gorokhovik V.V. Usloviya optimal'nosti pervogo i vtorogo poryadka v zadachakh vektornoi optimizatsii na metricheskikh prostranstvakh [Optimality conditions of the first and second order in vector optimization problems on metric spaces]. Proceedings of the Institute of Mathematics and Mechanics Ural Branch of RAS, 2009, vol. 15, no. 4, pp. 32–43.
7.     Brusov V.S., Suzdal'tsev A.L. Application of the set-theoretic approach to accounting of uncertainties in the solution of vector optimization problems. Automation and Remote Control, 2008, vol. 69, no. 4, pp. 630–636. doi: 10.1134/S0005117908040097
8.     Gavalec M., Gad M., Zimmermann K. Optimization problems under (max,min)-linear equation and/or inequality constraints. Fundamental’naya i Prikladnaya Matematika, 2012, vol. 17, no. 6, pp. 3–21.
9.     Kutateladze S.S. Multiobjective problems of convex geometry. Siberian Mathematical Journal, 2009, vol. 50, no. 5, pp. 887–897. doi: 10.1007/s11202-009-0099-z
10.  Titarenko V.N., Yagola A.G. Metod otsecheniya vypuklykh mnogogrannikov i ego primenenie k nekorrektnym zadacham [Method to cut convex polyhedrons and its application to ill-posed problems]. Vychislitel'nye metody i programmirovanie, 2000, vol. 1, no. 1, pp. 8–13.
11.  PiunovskiiA.B. Controlled random sequence: Methods of convex analysis and problems with functional constraints. Russian Mathematical Surveys, 1998, vol. 53, no. 6, pp. 1233–1293. doi: 10.1070/RM1998v053n06ABEH000090
12.  Emelichev V.A., Kuz'min K.G., Leonovich A.M. Stability in the combinatorial vector optimization problems. Automation and Remote Control, 2004, vol. 65, no. 2, pp. 227–240. doi: 10.1023/B:AURC.0000014719.45368.36
13.  Lebedeva T.T., Semenova N.V., Sergienko T.I. Stability of vector problems of integer optimization: Relationship with thestability of sets of optimal and nonoptimal solutions. Cybernetics and Systems Analysis, 2005, vol. 41, no. 4, pp. 551–558. doi: 10.1007/s10559-005-0090-z
14.  Rabinovich Ya.I. On comparison of approximate solutions in vector optimization problems.Computational Mathematics and Mathematical Physics, 2006, vol. 46, no. 10, pp. 1705–1716. doi: 10.1134/S0965542506100083
15.  Mikhailov G.A., Medvedev I.N. Vector estimators of the Monte Carlo method: Dual representation and optimization. Numerical Analysis and Applications, 2010, vol. 3, no. 4, pp. 344–356. doi: 10.1134/S1995423910040063
16.  Rudnev V.E., Volodin K.M., Luchanskii V.B., Petrov V.B. Formirovanie tekhnicheskikh ob"ektov na osnove sistemnogo analiza [Formation of technical objects on the basis of systematic analysis]. Moscow, Mashinostroenie Publ., 1991, 318 p.
17.  Kartashov L.P., Zubkova T.M. Parametricheskii i strukturnyi sintez tekhnologicheskikh ob"ektov na osnove sistemnogo podkhoda i matematicheskogo modelirovaniya [Parametric and structural synthesis of technological objects on the basis of a systematic approach and mathematical modeling]. Ekaterinburg, Ural Branch of Russian Academy of Sciences Publ., 2009, 225 p.
18.  Zubkova T.M., Ishakova E.N., Kuz'min M.I. Programmnaya sistema provedeniya parametricheskoi vektornoi optimizatsii [Software system of parametric vector optimization]. Certificate of state registration of the computer program, no. 2013660216, filing 02.09.2013.
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