This paper proposes a stochastic gradient based method for the solution of Risk Optimization (RO) problems. The proposed approach approximates the probability of failure evaluation by an expectation computation with the aid of the Chernoff bound. The resulting approximate problem is then solved using a Stochastic Gradient Descent (SGD) algorithm. Computational efficiency comes from the fact that the Chernoff bound avoids not only the direct computation of the failure probabilities during the optimization process, but also the computation of their gradients with respect to the design variables. Finally, to ensure the quality of the failure probability approximation, we propose a procedure to iteratively adjust the Chernoff bound parameters during the optimization procedure. Three numerical examples are presented to validate the methodology. The proposed approach succeeded in converging to the optimal solution in all cases.
Bibliographical noteKAUST Repository Item: Exported on 2022-05-17
Acknowledgements: Financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, and Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPQ - grant number 307133/2020-6.
ASJC Scopus subject areas
- Applied Mathematics
- Industrial and Manufacturing Engineering
- Safety, Risk, Reliability and Quality