A WAY TO REDUCE THE PROBLEM OF OPTIMAL FLEXIBLE CHEMICAL PROCESS DESIGN TO A SEQUENCE OF NONLINEAR PROGRAMMING PROBLEMS
When designing optimal chemical engineering processes under conditions of uncertainty in the initial physical, chemical and economic information, it is necessary to observe the condition of flexibility of the created system. To ensure the flexibility or working capacity of the designed CTS, it is necessary to determine such values of the design and control parameters at which CTS will fulfill the design requirements for it, regardless of changes in the external and internal operating conditions. In this case, the form of the problem may provide for the fulfillment of design requirements both for any changes in the conditions of the functioning of the HTS, and with a given level of probability. In the latter case, the solution of the problem involves the use of individual or joint probabilistic constraints. This paper is devoted to the consideration of design problems for flexible operational CTS, taking into account the initial information uncertainty in the formulation of one-stage optimization problems with individual probabilistic constraints. The problem’s optimality criterion has the form of the mathematical expectation of the function for evaluating the performance of the CTS. The direct solution of such problems requires the calculation of multidimensional integrals at each iteration of the optimization procedure. This requires large computational effort, the volume of which increases with an increase in the number of uncertain parameters. The paper proposes a method for reducing individual probabilistic constraints to the form of deterministic ones. The method is based on the approximation of the functions of design constraints by linear functions in the space of uncertain parameters and the approximation of the regions of the constraints by multidimensional rectangles. To exclude the operation of integration in the criteria of the problem, a piecewise-linear approximation of the function of estimating the performance of the CTS is used. As a result, an estimate of the criterion of the problem being solved in the form of a problem of deterministic nonlinear programming is obtained. To clarify the proposed approximations, the region of uncertainty is divided into subregions. In addition, the improvement of the quality of the obtained solution is carried out by clarifying the form of the areas of constraint satisfaction and finding their location in the original area of uncertainty. The efficiency of the method proposed is illustrated by solving a model example to be compared to the findings previously obtained.