Retrospective Optimization Research Articles

Multi-objective retrospective optimization using stochastic zigzag search

We propose a new retrospective optimization (RO) method for multi-objective simulation optimization (MOSO) problems. RO algorithms generate a sequence of sample-path (SP) problems and solve these SP problems iteratively using a nonlinear optimizer. In this study, a stochastic zigzag search algorithm is chosen in the RO framework to solve SP problems. The key idea of zigzag search is searching around the Pareto front by applying an efficient local-search procedure using the gradients of the objective functions. Many continuous MOSO problems have smooth objective functions and their non-dominated objective function values form a smooth surface in the image space. This fact motivates developing the zigzag search method embedded in RO for such relatively well-posed MOSO problems. A numerical implementation of this method—multi-objective retrospective optimization using zigzag search (MOROZS)—is presented particularly for continuous bi-objective simulation optimization (BOSO) problems with well-connected Pareto optimal solutions. MOROZS is designed for BOSO problems in which a simulation oracle returns both objective function values and gradients. Due to the local nature of zigzag search, MOROZS can only guarantee the asymptotic convergence to local Pareto optimality. The efficiency of MOROZS is studied using three BOSO problems with noisy objective functions and is compared to that of Genetic Algorithms based NSGA-II and a recently developed method MO-COMPASS.

Optimal Well Placement Under Uncertainty Using a Retrospective Optimization Framework

Summary Subsurface geology is highly uncertain, and it is necessary to account for this uncertainty when optimizing the location of new wells. This can be accomplished by evaluating reservoir performance for a particular well configuration over multiple realizations of the reservoir and then optimizing based, for example, on expected net present value (NPV) or expected cumulative oil production. A direct procedure for such an optimization would entail the simulation of all realizations at each iteration of the optimization algorithm. This could be prohibitively expensive when it is necessary to use a large number of realizations to capture geological uncertainty. In this work, we apply a procedure that is new within the context of reservoir management—retrospective optimization (RO)—to address this problem. RO solves a sequence of optimization subproblems that contain increasing numbers of realizations. We introduce the use of k -means clustering for selecting these realizations. Three example cases are presented that demonstrate the performance of the RO procedure. These examples use particle swarm optimization (PSO) and simplex linear interpolation (SLI)-based line search as the core optimizers (the RO framework can be used with any underlying optimization algorithm, either stochastic or deterministic). In the first example, we achieve essentially the same optimum using RO as we do using a direct optimization approach, but RO requires an order of magnitude fewer simulations. The results demonstrate the advantages of cluster-based sampling over random sampling for the examples considered. Taken in total, our findings indicate that RO using cluster sampling represents a promising approach for optimizing well locations under geological uncertainty.

Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation

We propose a family of retrospective optimization (RO) algorithms for optimizing stochastic systems with both integer and continuous decision variables. The algorithms are continuous search procedures embedded in a RO framework using dynamic simplex interpolation (RODSI). By decreasing dimensions (corresponding to the continuous variables) of simplex, the retrospective solutions become closer to an optimizer of the objective function. We present convergence results of RODSI algorithms for stochastic “convex” systems. Numerical results show that a simple implementation of RODSI algorithms significantly outperforms some random search algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).