Advances and applications of chance-constrained approaches to systems optimisation under uncertainty

Abstract

A chance-constrained optimisation (CCOPT) model has a dual goal: guaranteeing performance as well as system reliability under uncertainty. The beginning of CCOPT methods dates back in the 1950s. Recently, CCOPT approaches are gaining momentum as modern engineering and finance applications are forced to consider reliability and risk metrics at the design and planning stages. Although theoretical development and practical applications have been made, many open problems remain to be addressed in this area. This article attempts to provide a brief survey of major application areas, structure properties, challenges and solution approaches to CCOPT. In particular, we present our research results achieved in the past few years.

Keywords:

• chance constraints
• nonlinear optimisation
• dynamic optimisation
• back-projection
• analytic approximation
• sparse-grid integration
• quasi-Monte Carlo method

Acknowledgements

This work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the grant No. LI 806/13-1. M. Klöppel is supported by the Carl-Zeiss-Stiftung.

Notes

1. When precisely written the function should be . The integrals in Equations (23) and (24) should be understood in this context.