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Optimized radial basis function neural network for improving approximate dynamic programming in pricing high dimensional options

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NEURAL COMPUTING & APPLICATIONS 2018年第6期30卷 1783-1794页

作者： Hajizadeh, Ehsan Mahootchi, Masoud Amirkabir Univ Technol Tehran Polytech Dept Ind Engn & Management Syst 424 Hafez Ave Tehran *** Iran

Pricing American basket option is one of the essential problems in quantitative finance. The complexity of this type of option has motivated many practitioners and researchers to develop simulation-based methods. In this paper, we develop an optimized radial basis function neural network (RBFNN), which is optimally tuned by the particle swarm optimization algorithm to enhance the efficiency and accuracy of approximate dynamic programming (ADP) for pricing the American basket option. Additionally, for the scenario generation, a simulation-based technique using a copula-GARCH method and Extreme Value Theory is performed to tackle the nonlinearity of dependencies between variables. The prices obtained through the proposed approach compared with those ones achieved from pure RBFNN and ADP in different situations. This is also illustrated that the obtained prices of American basket option can outperform the results obtained through the RBFNN and ADP approaches in terms of the predefined fitness measures.

关键词： Radial basis function neural network approximate dynamic programming Particle swarm optimization algorithm American basket options

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Real-time schedule of integrated heat and power system: A multi-dimensional stochastic approximate dynamic programming approach

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2022年 134卷 107427-107427页

作者： Xue, Xizhen Ai, Xiaomeng Fang, Jiakun Yao, Wei Wen, Jinyu Huazhong Univ Sci & Technol Sch Elect & Elect Engn State Key Lab Adv Electromagnet Engn & Technol Wuhan 430074 Peoples R China

This paper proposes a multi-dimensional approximate dynamic programming (ADP) algorithm for the real-time schedule of integrated heat and power system (IHPS) with battery and heat storage tank (HST). The multi-time period optimization problem is reformulated under the Markov Decision Process. The high dimensional state variables are aggregated into the state of charge (SOC) of battery and overall available heat (OAH) of HST to reduce the computation of value function approximation (VFA) while ensuring approximate accuracy. Under sufficient training by uncertainty scenarios of wind power, electricity price, electrical and heat load, the approximate value function (AVF) can derive empirical knowledge and help IHPS make decisions to cope with uncertainties. The proposed ADP algorithm can efficiently take advantage of multi-energy integration and provide a near-optimal operation strategy to ensure the economy of IHPS by recursively solving the Bellman's equation. Simulation results compared with existing methods validate the superiority of the proposed algorithm.

关键词： approximate dynamic programming Real-time schedule Integrated heat and power system Battery Heat storage tank

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An approximate dynamic programming approach for sequential pig marketing decisions at herd level

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期276卷 1056-1070页

作者： Pourmoayed, Reza Nielsen, Lars Relund Aarhus Univ Dept Econ & Business Econ Fuglesangs Alle 4 DK-8210 Aarhus V Denmark

One of the most important operations in the production of growing/finishing pigs is the marketing of pigs for slaughter. While pork production can be managed at different levels (animal, pen, section, or herd), it is beneficial to consider the herd level when determining the optimal marketing policy due to inter-dependencies, such as those created by fixed transportation costs and cross-level constraints. In this paper, we consider sequential marketing decisions at herd level. A high-dimensional infinite horizon Markov decision process (MDP) is formulated which, due to the curse of dimensionality, cannot be solved using standard MDP optimization techniques. Instead, approximate dynamic programming (ADP) is applied to solve the model and find the best marketing policy at herd level. Under the total expected discounted reward criterion, the proposed ADP approach is first compared with a standard solution algorithm for solving an MDP at pen level to show the accuracy of the solution procedure. Next, numerical experiments at herd level are given to confirm how the marketing policy adapts itself to varying costs (e.g., transportation cost) and cross-level constraints. Finally, a sensitivity analysis for some parameters in the model is conducted and the marketing policy found by ADP is compared with other well-known marketing polices, often applied at herd level. (C) 2019 Elsevier B.V. All rights reserved.

关键词： OR in agriculture approximate dynamic programming Markov decision process Herd management Stochastic dynamic programming

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approximate dynamic programming for the aeromedical evacuation dispatching problem: Value function approximation utilizing multiple level aggregation

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2020年 91卷 102020-000页

作者： Robbins, Matthew J. Jenkins, Phillip R. Bastian, Nathaniel D. Lunday, Brian J. Air Force Inst Technol 2950 Hobson Way Wright Patterson AFB OH 45433 USA US Mil Acad 2101 New South Post Rd West Point NY 10996 USA

Sequential resource allocation decision-making for the military medical evacuation of wartime casualties consists of identifying which available aeromedical evacuation (MEDEVAC) assets to dispatch in response to each casualty event. These sequential decisions are complicated due to uncertainty in casualty demand (i.e., severity, number, and location) and service times. In this research, we present a Markov decision process model solved using a hierarchical aggregation value function approximation scheme within an approximate policy iteration algorithmic framework. The model seeks to optimize this sequential resource allocation decision under uncertainty of how to best dispatch MEDEVAC assets to calls for service. The policies determined via our approximate dynamic programming (ADP) approach are compared to optimal military MEDEVAC dispatching policies for two small-scale problem instances and are compared to a closest-available MEDEVAC dispatching policy that is typically implemented in practice for a large-scale problem instance. Results indicate that our proposed approximation scheme provides high-quality, scalable dispatching policies that are more easily employed by military medical planners in the field. The identified ADP policies attain 99.8% and 99.5% optimal for the 6- and 12-zone problem instances investigated, as well as 9.6%, 9.2%, and 12.4% improvement over the closest-MEDEVAC policy for the 6-, 12-, and 34-zone problem instances investigated. Published by Elsevier Ltd.

关键词： Military aeromedical evacuation Emergency medical services system Markov decision process approximate dynamic programming

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approximate dynamic programming for constrained linear systems: A piecewise quadratic approximation approach☆

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AUTOMATICA 2024年 160卷

作者： He, Kanghui Shi, Shengling van den Boom, Ton De Schutter, Bart Delft Univ Technol Delft Ctr Syst & Control Delft Netherlands

approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its computation is sometimes prohibitive. This paper introduces an approach combining the two methodologies to overcome their individual limitations. The predictive control law for constrained linear quadratic regulation (CLQR) problems has been proven to be piecewise affine (PWA) while the value function is piecewise quadratic. We exploit these formal results from MPC to design an ADP method for CLQR problems with a known model. A novel convex and piecewise quadratic neural network with a local-global architecture is proposed to provide an accurate approximation of the value function, which is used as the cost-to-go function in the online dynamic programming problem. An efficient decomposition algorithm is developed to generate the control policy and speed up the online computation. Rigorous stability analysis of the closed-loop system is conducted for the proposed control scheme under the condition that a good approximation of the value function is achieved. Comparative simulations are carried out to demonstrate the potential of the proposed method in terms of online computation and optimality.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： approximate dynamic programming Reinforcement learning Model predictive control Value function approximation Neural networks Constrained linear quadratic regulation

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Scheduling elective surgeries with Markov decision process and approximate dynamic programming

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IFAC-PapersOnLine 2019年第13期52卷 1831-1836页

作者： Zhang, Jian Dridi, Mahjoub Moudni, Abdellah El Laboratoire de Nanomédecine Imagerie et Thérapeutique Université Bourgogne Franche-Comté UTBM rue Thierry Mieg Belfort cedex90010 France

This paper deals with the dynamic advance scheduling of elective surgeries with multiple sources of uncertainties taken into consideration. A waiting list is established to facilitate the management of elective patients from different specialties. Each patient in the waiting list is assigned a dynamic priority which is dependent on the relative importance of specialty, urgency level, and actual waiting time. At the end of each week, the number and type of elective surgeries to be performed in the following week should be properly determined to minimize an integrated cost function, including the costs incurred by performing and delaying surgeries as well as the penalties for overuse of operating rooms and shortage of recovery beds. The studied problem is formulated as an infinite-horizon Markov decision process (MDP) model. Considering that conventional dynamic programming algorithms cannot efficiently solve MDP models for real-sized problems, we develop an approximate dynamic programming (ADP) approach that combines recursive least-squares temporal difference learning and mixed integer programming. Results of numerical experiments validate the efficiency and accuracy of the proposed ADP approach and indicate that this approach can be employed by hospital managers in the future to efficiently solve real-sized surgery scheduling problems. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： dynamic programming Cost functions Integer programming Markov processes Scheduling Surgery approximate dynamic programming dynamic programming algorithm Elective surgeries Markov Decision Processes Mixed integer programming Numerical experiments Recursive least square (RLS) Scheduling problem

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Quadratic approximate dynamic programming for input-affine systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2014年第3期24卷 432-449页

作者： Keshavarz, Arezou Boyd, Stephen Stanford Univ Stanford CA 94305 USA

We consider the use of quadratic approximate value functions for stochastic control problems with input-affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic programming policy in such cases requires the solution of an explicit convex optimization problem, such as a quadratic program, which can be carried out efficiently. We describe a simple and general method for approximate value iteration that also relies on our ability to solve convex optimization problems, in this case, typically a semidefinite program. Although we have no theoretical guarantee on the performance attained using our method, we observe that very good performance can be obtained in *** (c) 2012 John Wiley & Sons, Ltd.

关键词： approximate dynamic programming stochastic control convex optimization

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Vehicle scheduling under stochastic trip times: An approximate dynamic programming approach

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2018年 96卷 144-159页

作者： He, Fang Yang, Jie Li, Meng Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China Tsinghua Univ Tsinghua Daimler Joint Res Ctr Sustainable Transp Beijing 100084 Peoples R China Tsinghua Univ Dept Civil Engn Beijing 100084 Peoples R China

Due to unexpected demand surge and supply disruptions, road traffic conditions could exhibit substantial uncertainty, which often makes bus travelers encounter start delays of service trips and substantially degrades the performance of an urban transit system. Meanwhile, rapid advances of information and communication technologies have presented tremendous opportunities for intelligently scheduling a bus fleet. With the full consideration of delay propagation effects, this paper is devoted to formulating the stochastic dynamic vehicle scheduling problem, which dynamically schedules an urban bus fleet to tackle the trip time stochasticity, reduce the delay and minimize the total costs of a transit system. To address the challenge of "curse of dimensionality", we adopt an approximate dynamic programming approach (ADP) where the value function is approximated through a three-layer feed-forward neural network so that we are capable of stepping forward to make decisions and solving the Bellman's equation through sequentially solving multiple mixed integer linear programs. Numerical examples based on the realistic operations dataset of bus lines in Beijing have demonstrated that the proposed neural network -based ADP approach not only exhibits a good learning behavior but also significantly outperforms both myopic and static polices, especially when trip time stochasticity is high.

关键词： Vehicle scheduling Stochastic trip times Delay propagation approximate dynamic programming

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Incorporating network considerations into pavement management systems: A case for approximate dynamic programming

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2013年 33卷 134-150页

作者： Medury, Aditya Madanat, Samer Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

The objective of infrastructure management is to provide optimal maintenance, rehabilitation and replacement (MR&R) policies for a system of facilities over a planning horizon. While most approaches in the literature have studied the decision-making process as a finite resource allocation problem, the impact of construction activities on the road network is often not accounted for. The state-of-the-art Markov decision process (MDP)-based optimization approaches in infrastructure management, while optimal for solving budget allocation problems, become internally inconsistent upon introducing network constraints. In comparison, approximate dynamic programming (ADP) enables solving complex problem formulations by using simulation techniques and lower dimension value function approximations. In this paper, an ADP framework is proposed, wherein capacity losses due to construction activities are subjected to an agency-defined network capacity threshold. A parametric study is conducted on a stylized network configuration to infer the impact of network-based constraints on the decision-making process. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Infrastructure management Markov decision process approximate dynamic programming

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Cooperative Ecological Adaptive Cruise Control for Plug-In Hybrid Electric Vehicle Based on approximate dynamic programming

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2023年第3期72卷 3132-3145页

作者： Li, Jie Liu, Yonggang Fotouhi, Abbas Wang, Xiangyu Chen, Zheng Zhang, Yuanjian Li, Liang Chongqing Univ State Key Lab Mech Transmiss Chongqing 400044 Peoples R China Chongqing Univ Coll Mech & Vehicle Engn Chongqing 400044 Peoples R China Cranfield Univ Adv Vehicle Engn Ctr Sch Aerosp Transport & Mfg Cranfield MK43 0AL England Tsinghua Univ State Key Lab Automot Safety & Energy Beijing 100084 Peoples R China Kunming Univ Sci & Technol Fac Transportat Engn Kunming 650500 Peoples R China Loughborough Univ Dept Aeronaut & Automot Engn Loughborough LE11 3TU Leics England

Eco-driving control generates significant energy-saving potential in car-following scenarios. However, the influence of preceding vehicle may impose unnecessary velocity waves and deteriorate fuel economy. In this research, a learning-based method is exploited to achieve satisfied fuel economy for connected plug-in hybrid electric vehicles (PHEVs) with the advantage of vehicle-to-vehicle communication system. A data-driven energy consumption model is leveraged to generate reinforcement signals for approximate dynamic programming (ADP) with the consideration of nonlinear efficiency characteristics of hybrid powertrain system. An advanced ADP scheme is designed for connected PHEVs driving in car-following scenarios. In addition, the cooperative information is incorporated to further improve the fuel economy of the vehicle under the premise of driving safety. The proposed method is mode-free and showcases acceptable computational efficiency as well as adaptability. The simulation results demonstrate that the fuel economy during car-following processes is remarkably improved through cooperative driving information, thereby partially paving the theoretical basis for energy-saving transportation.

关键词： approximate dynamic programming cooperative adaptive cruise control eco-driving plug-in hybrid electric vehicle velocity optimization

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