An Efficient Bi-Objective Optimization Workflow Using the Distributed Quasi-Newton Method and Its Application to Well-Location Optimization

SPE Journal ◽  
2021 ◽  
pp. 1-17
Author(s):  
Yixuan Wang ◽  
Faruk Alpak ◽  
Guohua Gao ◽  
Chaohui Chen ◽  
Jeroen Vink ◽  
...  
Keyword(s):  
Optimization Problems ◽  
Weighted Average ◽  
Optimization Method ◽  
Objective Functions ◽  
Location Optimization ◽  
Weighting Factors ◽  
Well Location ◽  
Derivative Free ◽  
Nondominated Points ◽  
Quasi Newton

Summary Although it is possible to apply traditional optimization algorithms to determine the Pareto front of a multiobjective optimization problem, the computational cost is extremely high when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly. The efficiency of the DQN optimizer stems from a distributed computing mechanism that effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel, and a set of nondominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The nondominated points found in the last iteration form a set of Pareto-optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance, which means even if some simulations fail at a given iteration, the DQN method’s distributed-parallelinformation-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration. The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well-location optimization (WLO) problems by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the mesh adaptive direct search (MADS) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems. To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization problems by taking advantage of model-based search algorithms with an effective information-sharing mechanism. NOTE: This paper is published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

An Efficient Bi-Objective Optimization Workflow Using the Distributed Quasi-Newton Method and Its Application to Field Development Optimization

2021 ◽  
Author(s):  
Yixuan Wang ◽  
Faruk Alpak ◽  
Guohua Gao ◽  
Chaohui Chen ◽  
Jeroen Vink ◽  
...  
Keyword(s):  
Objective Function ◽  
Information Sharing ◽  
Optimization Problems ◽  
Weighted Average ◽  
Optimization Method ◽  
Objective Functions ◽  
Weighting Factors ◽  
Derivative Free ◽  
Simulation Results ◽  
Quasi Newton

Abstract Although it is possible to apply traditional optimization algorithms to determine the Pareto front of a multi-objective optimization problem, the computational cost is extremely high, when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly. The efficiency of the DQN optimizer stems from a distributed computing mechanism which effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel and a set of non-dominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The non-dominated points found in the last iteration form a set of Pareto optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance. Even if some simulations fail at a given iteration, DQN’s distributed-parallel information-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration. The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well location optimization problems, by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the MADS (Mesh Adaptive Direct Search) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems. To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization problems by taking advantage of model-based search optimization algorithms with an effective information-sharing mechanism.

Benchmarking and Field-Testing of the Distributed Quasi-Newton Derivative-Free Optimization Method for Field Development Optimization

2021 ◽  
Author(s):  
Faruk Alpak ◽  
Yixuan Wang ◽  
Guohua Gao ◽  
Vivek Jain
Keyword(s):  
Optimization Problems ◽  
Field Testing ◽  
Optimization Method ◽  
Training Data ◽  
Local Optima ◽  
Field Development ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Data Points ◽  
Quasi Newton

Abstract Recently, a novel distributed quasi-Newton (DQN) derivative-free optimization (DFO) method was developed for generic reservoir performance optimization problems including well-location optimization (WLO) and well-control optimization (WCO). DQN is designed to effectively locate multiple local optima of highly nonlinear optimization problems. However, its performance has neither been validated by realistic applications nor compared to other DFO methods. We have integrated DQN into a versatile field-development optimization platform designed specifically for iterative workflows enabled through distributed-parallel flow simulations. DQN is benchmarked against alternative DFO techniques, namely, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method hybridized with Direct Pattern Search (BFGS-DPS), Mesh Adaptive Direct Search (MADS), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). DQN is a multi-thread optimization method that distributes an ensemble of optimization tasks among multiple high-performance-computing nodes. Thus, it can locate multiple optima of the objective function in parallel within a single run. Simulation results computed from one DQN optimization thread are shared with others by updating a unified set of training data points composed of responses (implicit variables) of all successful simulation jobs. The sensitivity matrix at the current best solution of each optimization thread is approximated by a linear-interpolation technique using all or a subset of training-data points. The gradient of the objective function is analytically computed using the estimated sensitivities of implicit variables with respect to explicit variables. The Hessian matrix is then updated using the quasi-Newton method. A new search point for each thread is solved from a trust-region subproblem for the next iteration. In contrast, other DFO methods rely on a single-thread optimization paradigm that can only locate a single optimum. To locate multiple optima, one must repeat the same optimization process multiple times starting from different initial guesses for such methods. Moreover, simulation results generated from a single-thread optimization task cannot be shared with other tasks. Benchmarking results are presented for synthetic yet challenging WLO and WCO problems. Finally, DQN method is field-tested on two realistic applications. DQN identifies the global optimum with the least number of simulations and the shortest run time on a synthetic problem with known solution. On other benchmarking problems without a known solution, DQN identified compatible local optima with reasonably smaller numbers of simulations compared to alternative techniques. Field-testing results reinforce the auspicious computational attributes of DQN. Overall, the results indicate that DQN is a novel and effective parallel algorithm for field-scale development optimization problems.

scholarly journals A consensus-based global optimization method for high dimensional machine learning problems

2020 ◽  
Author(s):  
Jose Carrillo ◽  
Shi Jin ◽  
Lei Li ◽  
Yuhua Zhu
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Weighted Average ◽  
Planck Equation ◽  
Optimization Method ◽  
Learning Problems ◽  
High Dimensional ◽  
Nonconvex Functions ◽  
The Individual ◽  
Parameter Constraints

We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183{204, 2017], which is a gradient-free optimization method for general nonconvex functions. We rst replace the isotropic geometric Brownian motion by the component-wise one, thus removing the dimensionality dependence of the drift rate, making the method more competitive for high dimensional optimization problems. Secondly, we utilize the random mini-batch ideas to reduce the computational cost of calculating the weighted average which the individual particles tend to relax toward. For its mean- eld limit{a nonlinear Fokker-Planck equation{we prove, in both time continuous and semi-discrete settings, that the convergence of the method, which is exponential in time, is guaranteed with parameter constraints independent of the dimensionality. We also conduct numerical tests to high dimensional problems to check the success rate of the method.

scholarly journals Optimum design of 3R robot manipulador by using Improved Differential Evolution implemented in parallel computation

2020 ◽  
Vol 1 (2) ◽  
pp. 83-103
Author(s):  
Sezimária De Fátima Pereira Saramago ◽  
José Laércio Doricio ◽  
Milena Almeida Leite Brandão
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Robot Manipulator ◽  
Optimal Solution ◽  
Optimization Method ◽  
Objective Functions ◽  
Basic Algorithm ◽  
Promising Alternative ◽  
Multi Objective ◽  
De Algorithm

In recent decades the great interest in Evolutionary Algorithms (EAs) has boosted their development leading to a significant improvement in their efficiency and applicability. Thus, EAs have been applied to solve optimization problems in different areas of knowledge. A promising optimization method known as Differential Evolution (DE), which belongs to the class of AEs, has attracted the attention of researchers. The DE algorithm is simple, robust and efficient. However, by testing with classical optimization problems noticed that sometimes the results obtained with DE are not as satisfactory as expected or that in many cases the algorithm ends the search for the optimal solution prematurely. Recently, with the advancement and greater availability of computer technology, the scientific community has been thinking about the implementation of optimization algorithms in parallel in order to reduce the processing time. The main objective of this paper is to present an improvement of the Differential Evolution optimization method, proposing modifications to the basic algorithm by using shuffled complex and making it able to work with parallel computing. The proposed methodology is applied to the optimal design of an orthogonal 3R robot manipulator that takes into account the characteristics of its workspace. For this purpose, a multi-objective optimization problem is formulated to obtain the optimal geometric parameters for the robot. The maximum workspace volume, the maximum system stiffness and the optimum dexterity are considered as the multi-objective functions. The results show that the procedure represents a promising alternative for the type of problem presented above.

Aerodynamic Shape Optimization Using Improved Territorial Particle Swarm Algorithm

2012 ◽  
Author(s):  
Amir Nejat ◽  
Pooya Mirzabeygi ◽  
Masoud Shariat-Panahi
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Particle Swarm ◽  
Weighted Average ◽  
Particle Swarm Algorithm ◽  
Density Estimator ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Multi Objective

In this paper, a new robust optimization technique with the ability of solving single and multi-objective constrained design optimization problems in aerodynamics is presented. This new technique is an improved Territorial Particle Swarm Optimization (TPSO) algorithm in which diversity is actively preserved by avoiding overcrowded clusters of particles and encouraging broader exploration. Adaptively varying “territories” are formed around promising individuals to prevent many of the lesser individuals from premature clustering and encouraged them to explore new neighborhoods based on a hybrid self-social metric. Also, a new social interaction scheme is introduced which guided particles towards the weighted average of their “elite” neighbors’ best found positions instead of their own personal bests which in turn helps the particles to exploit the candidate local optima more effectively. The TPSO algorithm is developed to take into account multiple objective functions using a Pareto-Based approach. The non-dominated solutions found by swarm are stored in an external archive and nearest neighbor density estimator method is used to select a leader for the individual particles in the swarm. Efficiency and robustness of the proposed algorithm is demonstrated using multiple traditional and newly-composed optimization benchmark functions and aerodynamic design problems. In final airfoil design obtained from the Multi Objective Territorial Particle Swarm Optimization algorithm, separation point is delayed to make the airfoil less susceptible to stall in high angle of attack conditions. The optimized airfoil also reveals an evident improvement over the test case airfoil across all objective functions presented.

Optimization Method RasID-GA for Numerical Constrained Optimization Problems

2007 ◽  
Vol 11 (5) ◽  
pp. 469-477 ◽  
Author(s):  
Dongkyu Sohn ◽  
◽  
Shingo Mabu ◽  
Kotaro Hirasawa ◽  
Jinglu Hu
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Random Search ◽  
Optimal Solution ◽  
Solution Space ◽  
Optimization Method ◽  
Penalty Functions ◽  
Objective Functions ◽  
Constrained Optimization Problems

This paper proposes Adaptive Random search with Intensification and Diversification combined with Genetic Algorithm (RasID-GA) for constrained optimization. In the previous work, we proposed RasID-GA which combines the best properties of RasID and Genetic Algorithm for unconstrained optimization problems. In general, it is very difficult to find an optimal solution for constrained optimization problems because their feasible solution space is very limited and they should consider the objective functions and constraint conditions. The conventional constrained optimization methods usually use penalty functions to solve given problems. But, it is generally recognized that the penalty function is hard to handle in terms of the balance between penalty functions and objective functions. In this paper, we propose a constrained optimization method using RasID-GA, which solves given problems without using penalty functions. The proposed method is tested and compared with Evolution Strategy with Stochastic Ranking using well-known 11 benchmark problems with constraints. From the Simulation results, RasID-GA can find an optimal solution or approximate solutions without using penalty functions.

scholarly journals Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
F. Soleymani ◽  
S. Shateyi
Keyword(s):  
Optimization Problems ◽  
Efficiency Index ◽  
Fixed Number ◽  
Computational Science ◽  
Optimal Order ◽  
Objective Functions ◽  
Eighth Order ◽  
Numerical Tests ◽  
Derivative Free ◽  
Optimal Efficiency

Optimization problems defined by (objective) functions for which derivatives are unavailable or available at an expensive cost are emerging in computational science. Due to this, the main aim of this paper is to attain as high as possible of local convergence order by using fixed number of (functional) evaluations to find efficient solvers for one-variable nonlinear equations, while the procedure to achieve this goal is totally free from derivative. To this end, we consider the fourth-order uniparametric family of Kung and Traub to suggest and demonstrate two classes of three-step derivative-free methods using only four pieces of information per full iteration to reach the optimal order eight and the optimal efficiency index 1.682. Moreover, a large number of numerical tests are considered to confirm the applicability and efficiency of the produced methods from the new classes.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

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