Simultaneous and Sequential Estimation of Optimal Placement and Controls of Wells With a Covariance Matrix Adaptation Algorithm

SPE Journal ◽  
2016 ◽  
Vol 21 (02) ◽  
pp. 501-521 ◽  
Author(s):  
Fahim Forouzanfar ◽  
Walter E. Poquioma ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Temporal Correlation ◽  
Production Optimization ◽  
Sequential Optimization ◽  
Joint Optimization ◽  
Well Placement ◽  
Covariance Matrix Adaptation

Summary In this paper, we present both simultaneous and sequential algorithms for the joint optimization of well trajectories and their life-cycle controls. The trajectory of a well is parameterized in terms of six variables that define a straight line in three dimensions. In the simultaneous joint optimization algorithm, the set of controls of a well throughout the life cycle of the reservoir is constructed as a linear combination of the left singular vectors that correspond to the largest singular values of a specified temporal covariance matrix. This covariance matrix is used to impose a temporal correlation on the controls at each well. In this approach, well controls are parameterized in terms of a few optimization parameters to reduce the dimension of the joint optimization problem. Moreover, the imposed smoothness on the well controls will result in temporally smooth well controls. We use an implementation of the covariance matrix adaptation–evolution strategy (CMA-ES) optimization algorithm to solve the defined optimization problem. In the sequential optimization algorithm, first, the trajectories of the wells are optimized with the CMA-ES optimization algorithm whereas the controls of the wells are prespecified. After the optimum trajectories of the wells are obtained, the life-cycle production optimization step is performed to find the optimal well controls for the specified well trajectories. For the production optimization step, we compare the performance of three optimization algorithms that are the standard ensemble-based optimization algorithm (EnOpt), the standard CMA-ES algorithm, and a variant of the CMA-ES algorithm in which we set the initial covariance matrix equal to a prespecified covariance that imposes a temporal correlation on the controls of each well. The performance of the proposed algorithms is tested for the joint optimization of well trajectories and controls of injectors and producers for the PUNQ reservoir model. The proposed simultaneous well placement/well control optimization algorithm obtained better results than did the sequential optimization framework. The CMA-ES algorithm performed well for both well placement and production optimization purposes. Moreover, the CMA algorithm with a prespecified covariance that imposes a temporal correlation on the well controls obtained a higher net present value compared with EnOpt for the life-cycle production optimization step of the sequential framework.

A Sequential-Quadratic-Programming-Filter Algorithm with a Modified Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear State Constraints

SPE Journal ◽  
2020 ◽  
Vol 25 (04) ◽  
pp. 1938-1963 ◽  
Author(s):  
Zhe Liu ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Quadratic Programming ◽  
Optimization Algorithm ◽  
Sequential Quadratic Programming ◽  
Optimization Problem ◽  
State Constraints ◽  
Optimization Problems ◽  
Filter Method ◽  
Reservoir Model ◽  
Nonlinear State

Summary Solving a large-scale optimization problem with nonlinear state constraints is challenging when adjoint gradients are not available for computing the derivatives needed in the basic optimization algorithm used. Here, we present a methodology for the solution of an optimization problem with nonlinear and linear constraints, where the true gradients that cannot be computed analytically are approximated by ensemble-based stochastic gradients using an improved stochastic simplex approximate gradient (StoSAG). Our discussion is focused on the application of our procedure to waterflooding optimization where the optimization variables are the well controls and the cost function is the life-cycle net present value (NPV) of production. The optimization algorithm used for solving the constrained-optimization problem is sequential quadratic programming (SQP) with constraints enforced using the filter method. We introduce modifications to StoSAG that improve its fidelity [i.e., the improvements give a more accurate approximation to the true gradient (assumed here to equal the gradient computed with the adjoint method) than the approximation obtained using the original StoSAG algorithm]. The modifications to StoSAG vastly improve the performance of the optimization algorithm; in fact, we show that if the basic StoSAG is applied without the improvements, then the SQP might yield a highly suboptimal result for optimization problems with nonlinear state constraints. For robust optimization, each constraint should be satisfied for every reservoir model, which is highly computationally intensive. However, the computationally viable alternative of letting the reservoir simulation enforce the nonlinear state constraints using its internal heuristics yields significantly inferior results. Thus, we develop an alternative procedure for handling nonlinear state constraints, which avoids explicit enforcement of nonlinear constraints for each reservoir model yet yields results where any constraint violation for any model is extremely small.

scholarly journals Modified Covariance Matrix Adaptation – Evolution Strategy algorithm for constrained optimization under uncertainty, application to rocket design

2015 ◽  
Vol 6 ◽  
pp. A1 ◽  
Author(s):  
Rudy Chocat ◽  
Loïc Brevault ◽  
Mathieu Balesdent ◽  
Sébastien Defoort
Keyword(s):  
Constrained Optimization ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Under Uncertainty ◽  
Constrained Optimization Problem ◽  
Covariance Matrix Adaptation ◽  
Principal Axes ◽  
Adaptation Evolution ◽  
Handling Method

The design of complex systems often induces a constrained optimization problem under uncertainty. An adaptation of CMA-ES(λ, μ) optimization algorithm is proposed in order to efficiently handle the constraints in the presence of noise. The update mechanisms of the parametrized distribution used to generate the candidate solutions are modified. The constraint handling method allows to reduce the semi-principal axes of the probable research ellipsoid in the directions violating the constraints. The proposed approach is compared to existing approaches on three analytic optimization problems to highlight the efficiency and the robustness of the algorithm. The proposed method is used to design a two stage solid propulsion launch vehicle.

Hierarchical Long-Term and Short-Term Production Optimization

SPE Journal ◽  
2010 ◽  
Vol 16 (01) ◽  
pp. 191-199 ◽  
Author(s):  
G.M.. M. van Essen ◽  
P.M.J.. M.J. Van den Hof ◽  
J.D.. D. Jansen
Keyword(s):  
Life Cycle ◽  
Optimization Problem ◽  
Primary Objective ◽  
Production Optimization ◽  
Cycle Performance ◽  
Short Term ◽  
Secondary Objective ◽  
Life Cycle Optimization ◽  
Term Performance

Summary Model-based dynamic optimization of oil production has a significant potential to improve economic life-cycle performance, as has been shown in various studies. However, within these studies, short-term operational objectives are generally neglected. As a result, the optimized injection and production rates often result in a considerable decrease in short-term production performance. In reality, however, it is often these short-term objectives that dictate the course of the operational strategy. Incorporating short-term goals into the life-cycle optimization problem, therefore, is an essential step in model-based life-cycle optimization. We propose a hierarchical optimization structure with multiple objectives. Within this framework, the life-cycle performance in terms of net present value (NPV) serves as the primary objective and shortterm operational performance is the secondary objective, such that optimality of the primary objective constrains the secondary optimization problem. This requires that optimality of the primary objective does not fix all degrees of freedom (DOF) of the decision variable space. Fortunately, the life-cycle optimization problem is generally ill-posed and contains many more decision variables than necessary. We present a method that identifies the redundant DOF in the life-cycle optimization problem, which can subsequently be used in the secondary optimization problem. In our study, we used a 3D reservoir in a fluvial depositional environment with a production life of 7 years. The primary objective is undiscounted NPV, while the secondary objective is aimed at maximizing shortterm production. The optimal life-cycle waterflooding strategy that includes short-term performance is compared to the optimal strategy that disregards short-term performance. The experiment shows a very large increase in short-term production, boosting first-year production by a factor of 2, without significantly compromising optimality of the primary objective, showing a slight drop in NPV of only -0.3%. Our method to determine the redundant DOF in the primary objective function relies on the computation of the Hessian matrix of the objective function with respect to the control variables. Although theoretically rigorous, this method is computationally infeasible for realistically sized problems. Therefore, we also developed a second, more pragmatic, method relying on an alternating sequence of optimizing the primary-and secondary-objective functions. Subsequently, we demonstrated that both methods lead to nearly identical results, which offers scope for application of hierarchical long-term and short-term production optimization to realistically sized flooding-optimization problems.

scholarly journals Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 56
Author(s):  
Wei Li
Keyword(s):  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Population Diversity ◽  
Evolution Strategy ◽  
Multimodal Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

The standard covariance matrix adaptation evolution strategy (CMA-ES) is highly effective at locating a single global optimum. However, it shows unsatisfactory performance for solving multimodal optimization problems (MMOPs). In this paper, an improved algorithm based on the MA-ES, which is called the matrix adaptation evolution strategy with multi-objective optimization algorithm, is proposed to solve multimodal optimization problems (MA-ESN-MO). Taking advantage of the multi-objective optimization in maintaining population diversity, MA-ESN-MO transforms an MMOP into a bi-objective optimization problem. The archive is employed to save better solutions for improving the convergence of the algorithm. Moreover, the peaks found by the algorithm can be maintained until the end of the run. Multiple subpopulations are used to explore and exploit in parallel to find multiple optimal solutions for the given problem. Experimental results on CEC2013 test problems show that the covariance matrix adaptation with Niching and the multi-objective optimization algorithm (CMA-NMO), CMA Niching with the Mahalanobis Metric and the multi-objective optimization algorithm (CMA-NMM-MO), and matrix adaptation evolution strategy Niching with the multi-objective optimization algorithm (MA-ESN-MO) have overall better performance compared with the covariance matrix adaptation evolution strategy (CMA-ES), matrix adaptation evolution strategy (MA-ES), CMA Niching (CMA-N), CMA-ES Niching with Mahalanobis Metric (CMA-NMM), and MA-ES-Niching (MA-ESN).

Well Placement Optimization With Cat Swarm Optimization Algorithm Under Oilfield Development Constraints

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Chen Hongwei ◽  
Feng Qihong ◽  
Zhang Xianmin ◽  
Wang Sen ◽  
Zhou Wensheng ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Well Placement ◽  
Swarm Optimization ◽  
Penalization Method ◽  
De Algorithm ◽  
Placement Optimization ◽  
Well Placement Optimization ◽  
Oilfield Development ◽  
Handling Method

Proper well placement can improve the oil recovery and economic benefits during oilfield development. Due to the nonlinear and complex properties of well placement optimization, an effective optimization algorithm is required. In this paper, cat swarm optimization (CSO) algorithm is applied to optimize well placement for maximum net present value (NPV). CSO algorithm, a heuristic algorithm that mimics the behavior of a swarm of cats, has characteristics of flexibility, fast convergence, and high robustness. Oilfield development constraints are taken into account during well placement optimization process. Rejection method, repair method, static penalization method, dynamic penalization method and adapt penalization method are, respectively, applied to handle well placement constraints and then the optimal constraint handling method is obtained. Besides, we compare the CSO algorithm optimization performance with genetic algorithm (GA) and differential evolution (DE) algorithm. With the selected constraint handling method, CSO, GA, and DE algorithms are applied to solve well placement optimization problem for a two-dimensional (2D) conceptual model and a three-dimensional (3D) semisynthetic reservoir. Results demonstrate that CSO algorithm outperforms GA and DE algorithm. The proposed CSO algorithm can effectively solve the constrained well placement optimization problem with adapt penalization method.

scholarly journals Cross Entropy Covariance Matrix Adaptation Evolution Strategy Solving the Bi-Level Bidding Optimization Problem in Local Energy Markets with Renewables

2021 ◽  
Author(s):  
Dharmesh Dabhi ◽  
Kartik Pandya ◽  
Joao Soares ◽  
Fernando Lezama ◽  
Zita Vale
Keyword(s):  
Covariance Matrix ◽  
Distribution System ◽  
Optimization Problem ◽  
Energy Markets ◽  
Evolution Strategy ◽  
Cross Entropy ◽  
Local Energy ◽  
Covariance Matrix Adaptation ◽  
Level Problem ◽  
Adaptation Evolution

Abstract: The increased penetration of renewables in distribution power systems has motivated researchers to take significant interest in local energy transactions. The major goal of Local Energy Markets (LEM) is to promote the participation of small consumers in energy transactions and providing an opportunity for transactive energy systems. Such energy transactions in LEM are considered as a bi-level optimization problem in which all agents at upper and lower levels try to maximize their profits. But typical bi-level problem is very complex as it is inherently nonlinear, discontinued and strongly NP-hard. So, this article proposes the application of hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem of LEM. The proposed CE-CMAES secured the 1st rank in Testbed-2 entitled, “Bi-level optimization of end-users’ bidding strategies in local energy markets (LM)” at international competitions on Smart Grid Problems, held at GECCO 2020 and WCCI 2020. CE method is used for global exploration of search space and CMAES is used for local exploitation as its adaptive step-size mechanism prevents its premature convergence. A practical distribution system with renewable energy penetration is considered for simulation. The comparative analysis shows that the overall cost, mean fitness and Ranking Index (R.I) obtained from CE-CMAES are superior to those obtained from the state-of-the-art participated algorithms. Wilcoxon Signed Rank Statistical test also proves that CE-CMAES is statistically different from the tested algorithms.

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