Monotony Analysis and Sparse-Grid Integration for nonlinear Chance Constrained Process Optimization

Abebe Geletu (1) , Armin Hoffmann (2) , Klöppel Michael (1) , Pu Li (1)

1 Simulation and Optimal Processes
2 Dept. of Operations Research and Stochastics

The numerical solution of a nonlinear chance constrained optimization problem poses a major challenge. The idea of back-mapping (Wendt et al. 2002) is a viable approach for transforming chance constraints on output variables (with unknown distribution) into chance constraints on uncertain input variables (with known distribution) based on a monotony relation. Once transformation of chance constraints has been accomplished, the resulting optimization problem can be solved by using a gradient based algorithm. However, the computation of values and gradients of chance constraints and the objective function involves the evaluation of multidimensional integrals which is computationally very expensive. This study proposes an easy-to-use method to analyze monotonic relations between constrained outputs and uncertain inputs. In addition, sparse-grid integration techniques are used to reduce the computational time decisively. Two examples from process optimization under uncertainty demonstrate the performance of the proposed approach.

Mots clés: Physical Sciences

Domaines: Sciences de l'ingénieur [physics]

Abebe Geletu, Armin Hoffmann, Klöppel Michael, Pu Li. Monotony Analysis and Sparse-Grid Integration for nonlinear Chance Constrained Process Optimization. Engineering Optimization, 2011, ⟨10.1080/0305215X.2010.532552⟩. ⟨hal-00683839⟩