Mathematical modeling and optimization of the "compozition-property" of multicomponent mixtures
The approach to the solution of a problem of selection of optimum structure of a multicomponent mixture is offered and the software package is developed for its realization. The essence of this approach consists in the following. If theoretical dependences of properties of a mixture and economic requirements on which are known the choice of optimum structure of a mixture is made, the problem of optimization is formulated. If theoretical dependences of properties of a mixture and economic criteria on componental structure aren't present. That on the basis of the analysis of aprioristic information on nature of these dependences gets out the most suitable plan of experiments. Experiments by the set plan are made. Results of experiments are processed by a method of the smallest squares and mathematical models are under construction. Then the constructed mathematical models are checked on adequacy. After creation of adequate mathematical models of properties of a mixture and economic criteria the problem of optimization of componental structure of a mixture is formulated. As a rule problems of optimization of componental structure of a mixture are problems of optimization with many criteria. For a choice of the most effective method of the decision the analysis of mathematical model of a task is carried out and on its basis the method gets out. In work it is given an example solutions of a problem of selection of componental structure of a rod mixture having the minimum cost and possessing the physical and chemical characteristics lying in set ranges. For the solution of this task the method «ψ-transformations» which allows to solve not convex nonlinear problems of optimization with multiextreme criterion functions is used.