Well placement optimization for carbon dioxide capture and storage via CMA-ES with mixed integer support

Carbon dioxide Capture and Storage (CCS) is a viable technique for reducing CO₂ emitted to the atmosphere. A simulation based optimization of well placement is a promising solution to geologic CO₂ storage (GCS), which is a part of CCS. Covariance matrix adaptation evolution strategy (CMA-ES) is considered to apply for well placement problem because it is a state-of-the-art black-box continuous optimization algorithm. However, insufficient search by the algorithm is anticipated since well placement problem often forms a mixed integer programming problem. In this paper, we investigate the use of variants of CMA-ES to the optimization of well placement and injection schedule as a mixed integer programming problem. First we investigate the effect of each algorithmic component to treat integer variables on mixed integer programming test functions. Then, some promising variants are applied to the well placement and injection scheduling problem for a CCS project. We observed that the CMA-ES with step-size lower bound behaved robust and found better solutions than the variants without the bound, independently of initial search points. We bring up some issues of current optimization framework including the mixed integer support in the CMA-ES and the formulation of the GCS optimization problem.