Ensemble-based Constrained Optimization Using an Exterior Penalty Method

In science and engineering, non-linear constrained optimization has been a useful mathematical technique for many practical applications. Of interest to us is its applicability in the modeling and prediction of hydrocarbon reservoir production. In this paper, a new efficient, robust, and accurate optimal solution strategy based on the exterior penalty function (EPF) method and the adaptive ensemble-based optimization (EnOpt) approach (with backtracking line-search technique) for non-linear constrained optimization problems is presented. The purpose of this work is to provide a better user-friendly strategy which mitigates the problem often faced with the current constraints handling technique utilized when using the EnOpt method to solve constrained problems of water or EOR flooding. This study notes that the problem contributes to uncertainties in the gradient computation of the objective function and hence leads to the poor convergence rate of the standard EnOpt method. In this work, we used the EPF method to transform a given constrained optimization problem to a sequence of unconstrained subproblems and then sequentially solve the subproblems by unconstrained EnOpt procedure until convergence to the solution of the original problem. To demonstrate the advantage of the proposed methodology, we used it to solve analytical 2D bound constrained Rosenbrock's problem and a practical high dimensional bound constrained water flooding optimization problem associated with a 2D 5Spot field and a 3D Reek reservoir field. The numerical results are compared with EnOpt using classical Lagrangian approach, as well as the traditional EnOpt. Our findings showed that the proposed solution method has a fast convergence rate and is more accurate and robust.