Development of normalized entropy based convergence standards in iterative Latin hypercube sampling applied for CO2 geological storage

Abstract

A criterion using the average amount of information, entropy of primary variables is developed in order to determine convergence of optimization calculations by the iterative Latin hypercube sampling (ILHS) as the multipoint search. In the ILHS, lengths of sample spaces are decreased as the process of optimal solution search advances. In this research, convergence of the optimization process is evaluated by calculating entropy of sample space length. Specifically the difference between normalized entropy and binary entropy function (BEF), "dη" is calculated and evaluated. The criterion is validated by well placement optimization problems about CO2 geological storage. The number of function evaluations is decreased by 70 to 80 %, keeping optimal solutions after the criterion is applied. Additionally, the criterion is available for problems including both continuous and dummy variables, which have a different convergence behavior.