An approach to solving the optimization problem under uncertainty

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Abstract
Two problems—calculation of the feasibility test and the two-stage optimization problem (TSOP) —arise in the design of engineering systems (chemical processes, electrical circuits) under conditions of uncertainty of original information, and are considered here. The solution of the first problem allows an estimate of the ability of an engineering system to preserve its capacity for work under changing external and internal factors during operations. Solving the TSOP permits an engineering system to preserve its capacity for work under inexact knowledge of model coefficients. Directly solving both problems requires the use of multiextremal non-differentiable optimization methods. In this paper, methods of solving both problems are suggested, which use only chemical methods of nonlinear programming For calculation of the feasibility test we propose an algorithm based on a spatial branch-and-bound method. Also, an efficient procedure for calculation of an upper estimation of feasibility test is developed. Two algorithms for solving TSOP are given. A distinctive feature of the algorithms is that during execution the upper and the lower estimates of the optimal value of an objective function of TSOP are calculated. The approach is based on the concept of a ‘branch-and-bound’ method.