Large-scale dynamic system optimization using dual decomposition method with approximate dynamic programming

2021 ◽  
Vol 150 ◽  
pp. 104894
Author(s):  
Pegah Rokhforoz ◽  
Hamed Kebriaei ◽  
Majid Nili Ahmadabadi
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Decomposition Method ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
System Optimization ◽  
Dual Decomposition

scholarly journals Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 132 ◽  
Author(s):  
Harwinder Singh Sidhu ◽  
Prashanth Siddhamshetty ◽  
Joseph Kwon
Keyword(s):  
Mechanical Properties ◽  
Dynamic Programming ◽  
Hydraulic Fracturing ◽  
Young’S Modulus ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
Young's Modulus ◽  
Computational Cost ◽  
Control Technique ◽  
Rock Mechanical Properties

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation.

The Benders Dual Decomposition Method

2020 ◽  
Vol 68 (3) ◽  
pp. 878-895
Author(s):  
Ragheb Rahmaniani ◽  
Shabbir Ahmed ◽  
Teodor Gabriel Crainic ◽  
Michel Gendreau ◽  
Walter Rei
Keyword(s):  
Decomposition Method ◽  
High Performance ◽  
Large Scale ◽  
Benders Decomposition ◽  
Master Problem ◽  
Computational Results ◽  
Dual Decomposition ◽  
High Quality ◽  
Lagrangian Dual ◽  
Decomposition Strategies

Many methods that have been proposed to solve large-scale MILP problems rely on the use of decomposition strategies. These methods exploit either the primal or dual structures of the problems by applying the Benders decomposition or Lagrangian dual decomposition strategy, respectively. In “The Benders Dual Decomposition Method,” Rahmaniani, Ahmed, Crainic, Gendreau, and Rei propose a new and high-performance approach that combines the complementary advantages of both strategies. The authors show that this method (i) generates stronger feasibility and optimality cuts compared with the classical Benders method, (ii) can converge to the optimal integer solution at the root node of the Benders master problem, and (iii) is capable of generating high-quality incumbent solutions at the early iterations of the algorithm. The developed algorithm obtains encouraging computational results when used to solve various benchmark MILP problems.

scholarly journals Train Regulation Combined with Passenger Control Model Based on Approximate Dynamic Programming

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 303 ◽  
Author(s):  
Sijia Hao ◽  
Rui Song ◽  
Shiwei He ◽  
Zekang Lan
Keyword(s):  
Dynamic Programming ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
Control Model ◽  
High Dimensions ◽  
Proposed Model ◽  
Markov Decision ◽  
Train Operation ◽  
Interactive Relationship ◽  
Passenger Flows

Rescheduling is often needed when trains stay in segments or stations longer than specified in the timetable due to disturbances. Under crowded situations, it is more challenging to return to normal with heavy passenger flow. Considering making a trade-off between passenger loss and operating costs, we present a train regulation combined with a passenger control model by analyzing the interactive relationship between passenger behaviors and train operation. In this paper, we convert the problem into a Markov decision process and then propose the management strategy of regulating the running time and controlling the number of boarding passengers. Owing to the high dimensions of the large-scale problem, we applied the Approximate Dynamic Programming (ADP) approach, which approximates the value function with state features to improve computational efficiency. Finally, we designed three experimental scenarios to verify the effectiveness of our proposed model and approach. The results show that both the proposed model and the approach have a good performance in the cases with different passenger flows and different disturbances.

Large-scale hydropower system optimization using dynamic programming and object-oriented programming: the case of the Northeast China Power Grid

2013 ◽  
Vol 68 (11) ◽  
pp. 2458-2467 ◽  
Author(s):  
Ji-Qing Li ◽  
Yu-Shan Zhang ◽  
Chang-Ming Ji ◽  
Ai-Jing Wang ◽  
Jay R. Lund
Keyword(s):  
Dynamic Programming ◽  
Northeast China ◽  
Large Scale ◽  
Object Oriented ◽  
System Optimization ◽  
Curse Of Dimensionality ◽  
Optimal Operation ◽  
Object Oriented Programming ◽  
Computer Memory ◽  
Hydropower System

This paper examines long-term optimal operation using dynamic programming for a large hydropower system of 10 reservoirs in Northeast China. Besides considering flow and hydraulic head, the optimization explicitly includes time-varying electricity market prices to maximize benefit. Two techniques are used to reduce the ‘curse of dimensionality’ of dynamic programming with many reservoirs. Discrete differential dynamic programming (DDDP) reduces the search space and computer memory needed. Object-oriented programming (OOP) and the ability to dynamically allocate and release memory with the C++ language greatly reduces the cumulative effect of computer memory for solving multi-dimensional dynamic programming models. The case study shows that the model can reduce the ‘curse of dimensionality’ and achieve satisfactory results.

An Approximate Dynamic Programming Algorithm for Large-Scale Fleet Management: A Case Application

2009 ◽  
Vol 43 (2) ◽  
pp. 178-197 ◽  
Author(s):  
Hugo P. Simão ◽  
Jeff Day ◽  
Abraham P. George ◽  
Ted Gifford ◽  
John Nienow ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Fleet Management ◽  
Case Application
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