Optimization under worst case constraints--a new global multimodel search procedure

A new method is presented that combines heuristic global optimization and multi-model simulation for reliability based risk averse design. The so-called new stack ordering method is motivated from hydrogeology, where high-reliable groundwater management solutions are sought for with a demanding set of equally probable model alternatives. The idea is to only exploit a small subset of these model alternatives or realizations to approximate the objective function to reduce computational costs. The presented automatic procedure dynamically adjusts the subset online during the course of iterative optimization. The test with theoretical reliability based benchmark problems shows that the new method is efficient in regard to optimality and reliability of found solutions already with small subsets of all models. Compared with a previously presented first version of stack ordering, the presented generalized approach proves to be more robust, computationally efficient and of great potential for related problems in reliability based optimization and design. This conclusion is supported by the fact that the new variant requires about one fifth of the objective function evaluations of the older version in order to achieve the same level of reliability. We also show that these findings can be translated to real world problems by bench marking the performance on a well capture problem.