TITLE:
Mathematical Apparatus for Selection of Optimal Parameters of Technical, Technological Systems and Materials Based on Vector Optimization
AUTHORS:
Yu Mashunin
KEYWORDS:
Vector Optimization, Methods of Solution of Vector Problems, Modeling of a Technical System, Modeling Operation of Technological Processes, Modeling of Structure of Material
JOURNAL NAME:
American Journal of Operations Research,
Vol.10 No.5,
September
27,
2020
ABSTRACT: We presented Mathematical apparatus of the choice of optimum parameters of technical, technological systems and materials on the basis of vector optimization. We have considered the formulation and solution of three types of tasks presented below. First, the problem of selecting the optimal parameters of technical systems depending on the functional characteristics of the system. Secondly, the problem of selecting the optimal parameters of the process depending on the technological characteristics of the process. Third, the problem of choosing the optimal structure of the material depending on the functional characteristics of this material. The statement of all problems is made in the form of vector problems of mathematical (nonlinear) programming. The theory and the principle of optimality of the solution of vector tasks it is explained in work of https://rdcu.be/bhZ8i. The implementation of the methodology is shown on a numerical example of the choice of optimum parameters of the technical, technological systems and materials. On the basis of mathematical methods of solution of vector problems we developed the software in the MATLAB system. The numerical example includes: input data (requirement specification) for modeling; transformation of mathematical models with uncertainty to the model under certainty; acceptance of an optimal solution with equivalent criteria (the solution of numerical model); acceptance of an optimal solution with the given priority of criterion.