Adaptive Scenario Subset Selection for Worst-Case Optimization and its Application to Well Placement Optimization

TL;DR

This paper introduces AS3-CMA-ES, an adaptive scenario subset selection method combined with CMA-ES, to efficiently solve worst-case optimization problems with fewer simulations, demonstrated on well placement optimization for CCS.

Contribution

The paper proposes a novel adaptive scenario subset selection (AS3) method combined with CMA-ES, improving efficiency and solution quality in worst-case optimization problems.

Findings

AS3-CMA-ES reduces the number of simulations compared to brute-force and surrogate-assisted methods.

The approach finds better solutions due to more frequent restarts.

Effective in well placement optimization for CCS.

Abstract

In this study, we consider simulation-based worst-case optimization problems with continuous design variables and a finite scenario set. To reduce the number of simulations required and increase the number of restarts for better local optimum solutions, we propose a new approach referred to as adaptive scenario subset selection (AS3). The proposed approach subsamples a scenario subset as a support to construct the worst-case function in a given neighborhood, and we introduce such a scenario subset. Moreover, we develop a new optimization algorithm by combining AS3 and the covariance matrix adaptation evolution strategy (CMA-ES), denoted AS3-CMA-ES. At each algorithmic iteration, a subset of support scenarios is selected, and CMA-ES attempts to optimize the worst-case objective computed only through a subset of the scenarios. The proposed algorithm reduces the number of simulations required by executing simulations on only a scenario subset, rather than on all scenarios. In numerical experiments, we verified that AS3-CMA-ES is more efficient in terms of the number of simulations than the brute-force approach and a surrogate-assisted approach lq-CMA-ES when the ratio of the number of support scenarios to the total number of scenarios is relatively small. In addition, the usefulness of AS3-CMA-ES was evaluated for well placement optimization for carbon dioxide capture and storage (CCS). In comparison with the brute-force approach and lq-CMA-ES, AS3-CMA-ES was able to find better solutions because of more frequent restarts.