Analytical approximations for the solution of chance constrained optimization problems

Abstract

AbstractUncertain influences are inherent in many practical processes, stemming for instance from measurement errors in process optimization or missing knowledge about the future behavior of a given system, e.g., the financial markets. Therefore, it is desirable to explicitly consider uncertainties when optimizing such processes. One possible approach for this task is the usage of chance constrained optimization (CCOPT), which allows that the constraints are only held with a certain probability level. This enables the user to make a compromised decision between reliability and profitability. Solving CCOPT problems usually consists of two steps. First, transforming the chance constraints into deterministic ones and then solving the transformed problem with a standard NLP solver. Depending on the underlying process, several approaches exist for the transformation. Here, we investigate the usage of so called analytical approximations (AAs). In general, AA approaches do not lead to an exact deterministic representation of CCOPT problems. Nonetheless, it can be shown that a solution obtained by AA is always feasible for the original problem. Furthermore, the corresponding optimization problem generated by AA is computationally more tractable than the original formulation, making these approaches interesting for larger scale processes. We propose a new AA method and present a comparison with existing AA approaches, considering efficiency and suitability. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)