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作者： Astaraky, Davood Uottawa

学位级别：master

The thesis focuses on a model that seeks to address patient scheduling step of the surgical scheduling process to determine the number of surgeries to perform in a given day. Specifically, provided a master schedule that provides a cyclic breakdown of total OR availability into specific daily allocations to each surgical specialty, we look to provide a scheduling policy for all surgeries that minimizes a combination of the lead time between patient request and surgery date, overtime in the ORs and congestion in the wards. We cast the problem of generating optimal control strategies into the framework of Markov Decision Process (MDP). The approximate dynamic programming (ADP) approach has been employed to solving the model which would otherwise be intractable due to the size of the state space. We assess performance of resulting policy and quality of the driven policy through simulation and we provide our policy insights and conclusions

关键词： approximate dynamic programming Surgical Scheduling Markov Decision Process

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Optimal decision-making of mutual fund temporary borrowing problem via approximate dynamic programming

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COMPUTERS & OPERATIONS RESEARCH 2023年第1期153卷

作者： Luo, Xuyang Song, Chunyue Zhejiang Univ Inst Ind Intelligence & Syst Engn State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China

Temporary borrowing is a liquidity risk management tool for mutual fund managers to meet investor redemption demands. We develop a new Markov decision process model to describe the temporary borrowing process, considering the multiple lending channels, the validity period of loans, and the uncertainties of cost, demand, and maximum loan amount simultaneously. An approximate dynamic programming (ADP) algorithm is initiated to solve the cost-minimizing temporary borrowing problem. We construct the value function as a separable approximation and prove the convexity of its components with respect to the available funds in different channels. Moreover, a new value function updating formula, DMAX, is designed to overcome value function overestimation. The proved convexity and the proposed formula contribute to fast and reliable value function estimation. Numerical experiments based on actual business data show that the proposed algorithm can obtain near-optimal decisions in deterministic cases and maintain high robustness in stochastic cases.

关键词： Finance Temporary borrowing Mutual fund redemption risk management approximate dynamic programming Uncertainty

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Flexible expansion planning of distribution system integrating multiple renewable energy sources: An approximate dynamic programming approach

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ENERGY 2021年 226卷 120367-120367页

作者： Sun, Qirun Wu, Zhi Gu, Wei Zhu, Tao Zhong, Lei Gao, Ting Southeast Univ Sch Elect Engn Nanjing Peoples R China Taizhou Elect Power Supply Co State Grid Zhejiang Elect Power Co Co Ltd Taizhou Peoples R China

Distribution system expansion planning is a long-term process with sequential multistage uncertain factors, so flexible planning methods are required to deal with the various potential investment risks. This paper presents an approximate dynamic programming based flexible distribution system expansion planning model, in which the long-term system load growth uncertainty and short-term power fluctuation are both considered. A flexible investment strategy based on Markov decision process is developed, in which the planning decisions are made sequentially with consideration of both the current costs and future variable costs under long-term load growth uncertainty. This problem is formulated as a large-scale multistage stochastic programming model, which is intractable due to the "curse of dimensionality". Thus, an approximate dynamic programming approach is used to decompose the original multistage optimization problem into sequential subproblems that can be easily solved. Case studies are carried out on a 24-node distribution system with three planning stages and a 54-node distribution system with five planning stages. Numerical results validate the feasibility and benefits of the proposed planning approach in obtaining a flexible expansion scheme, which can significantly reduce the investment risk and configure renewable energy equipment more reasonably. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Distribution system expansion planning Renewable energy approximate dynamic programming Markov decision process Flexible investment

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A LINEAR programming METHODOLOGY FOR approximate dynamic programming

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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE 2020年第2期30卷 363-375页

作者： Diaz, Henry Sala, Antonio Armesto, Leopoldo Univ Politecn Valencia Univ Inst Ind Control Syst & Comp Camino Vera S-N Valencia 46022 Spain Univ Politecn Valencia Design & Mfg Inst Camino Vera S-N Valencia 46022 Spain

The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for finite state and input spaces to obtain an exact solution. However, with function approximation or continuous state spaces, refinements are necessary. This paper presents a methodology to make approximate dynamic programming via LP work in practical control applications with continuous state and input spaces. There are some guidelines on data and regressor choices needed to obtain meaningful and well-conditioned value function estimates. The work discusses the introduction of terminal ingredients and computation of lower and upper bounds of the value function. An experimental inverted-pendulum application will be used to illustrate the proposal and carry out a suitable comparative analysis with alternative options in the literature.

关键词： linear programming approximate dynamic programming control applications neural networks

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A kernel-based approximate dynamic programming approach: Theory and application

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AUTOMATICA 2024年 162卷

作者： Forootani, Ali Iervolino, Raffaele Tipaldi, Massimo Baccari, Silvio Maynooth Univ Hamilton Inst Maynooth W23F2K8 Kildare Ireland Univ Naples Federico II Dept Elect Engn & Informat Technol I-80125 Naples Italy Polytech Univ Bari Dept Elect & Informat Engn I-70126 Bari Italy Univ Campania Luigi Vanvitelli Dept Math & Phys I-81100 Caserta Italy

This article proposes a novel kernel -based dynamic programming (DP) approximation method to tackle the typical curse of dimensionality of stochastic DP problems over the finite time horizon. Such a method utilizes kernel functions in combination with Support Vector Machine (SVM) regression to determine an approximate cost function for the entire state space of the underlying Markov Decision Process (MDP), by leveraging cost function computed for selected representative states. Kernel functions are used to define the so-called kernel matrix, while the parameter vector of the given kernel -based cost function approximation is computed by moving backwards in time from the terminal condition and by applying SVM regression. This way, the difficulty of selecting a proper set of features is also tackled. The proposed method is then extended to the infinite time horizon case. To show the effectiveness of the proposed approach, the resulting Recursive Residual approximate dynamic programming (RR -ADP) algorithm is applied to the sensor scheduling design in multi -process remote state estimation problems. (c) 2024 Elsevier Ltd. All rights reserved.

关键词： dynamic programming Markov Decision Process approximate dynamic programming Kernel function Support Vector Machine Sensor scheduling

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Multiple stage stochastic planning of integrated electricity and gas system based on distributed approximate dynamic programming

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ENERGY 2023年第1期270卷

作者： Zhang, Houwang Wu, Qiuwei Chen, Jian Lu, Lina Zhang, Jiangfeng Zhang, Shuyi Shandong Univ Sch Elect Engn Jinan 250002 Shandong Peoples R China Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China Hangzhou Dianzi Univ Informat Engn Coll Hangzhou 311305 Zhejiang Peoples R China State Grid Zhejiang Elect Power Res Inst Hangzhou 310014 Peoples R China State Grid Tianjin Chengnan Elect Power Supply Bra Tianjin 300201 Peoples R China

With the increasing coupling of integrated electricity and gas systems, it's essential to implement a proper planning scheme. The planning of the integrated electricity and gas systems usually consists of multiple planning stages and various uncertainties, making the problem difficult to solve. In this paper, combining the approximate dynamic programming method and the alternating direction multiplier method, a distributed approximate dynamic programming based multiple stage stochastic planning scheme is proposed for the integrated electricity and gas systems. The multiple stage stochastic planning scheme realizes the coordination of new installation and expansion of power grid lines, natural gas pipelines, substations, city gates, photovoltaics, wind turbines, gas turbines and energy storage devices, while considering both the long-term and the short-term uncertainties. The multiple stage stochastic planning model is reformulated as a Markov decision process with a sequential decision strategy, in which the investment variables are decided stage by stage with long-term uncertainties gradually revealed in the planning period. The distributed approximate dynamic programming algorithm is used to solve the multiple stage stochastic planning model, which is in the form of the Markov decision process, by decoupling in both temporal and spatial dimensions. Numerical tests on the test system with a 24-node power grid and a 30node natural gas network verify the effectiveness of the multiple stage stochastic planning model.

关键词： Integrated electricity and gas systems Multiple stage stochastic planning Markov decision process approximate dynamic programming Alternating direction multiplier method

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An approximate dynamic programming approach for solving an air combat maneuvering problem

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EXPERT SYSTEMS WITH APPLICATIONS 2022年 203卷

作者： Crumpacker, James B. Robbins, Matthew J. Jenkins, Phillip R. AF Inst Technol Dept Operat Sci 2950 Hobson Way Wright Patterson AFB Dayton OH 45433 USA

Within visual range air combat involves execution of highly complex and dynamic activities, requiring rapid, sequential decision-making to achieve success. Fighter pilots spend years perfecting tactics and maneuvers for these types of combat engagements, yet the ongoing emergence of unmanned, autonomous vehicle technologies elicits a natural question - can an autonomous unmanned combat aerial vehicle (AUCAV) be imbued with the necessary artificial intelligence to perform challenging air combat maneuvering tasks independently? We formulate and solve the air combat maneuvering problem (ACMP) to examine this important question, developing a Markov decision process (MDP) model to control a defending AUCAV seeking to destroy an attacking adversarial vehicle. The MDP model includes a 5-degree-of-freedom, point-mass aircraft state transition model to accurately represent both kinematics and energy while maneuvering. An approximate dynamic programming (ADP) approach is proposed wherein we develop and test an approximate policy iteration algorithm that implements value function approximation via neural network regression to attain high-quality maneuver policies for the AUCAV. A representative intercept scenario is specified for testing purposes wherein the AUCAV must engage and destroy an adversary aircraft attempting to penetrate the defended airspace. Several designed experiments are conducted to determine how aircraft velocity and adversary maneuvering tactics impact the efficacy of the proposed ADP solution approach and to enable efficient algorithm parameter tuning. ADP-generated policies are compared to two benchmark maneuver policies constructed from two reward shaping functions found in the ACMP literature, attaining improved mean probabilities of kill for 24 of 36 air combat situations considered

关键词： Air combat strategy approximate dynamic programming Artificial intelligence Defense Reinforcement learning

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A unified framework for efficient, effective, and fair resource allocation by food banks using an approximate dynamic programming approach

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2021年 100卷 102300-102300页

作者： Alkaabneh, Faisal Diabat, Ali Gao, Huaizhu Oliver Cornell Univ Syst Engn Ithaca NY 14853 USA New York Univ Abu Dhabi Div Engn Abu Dhabi 129188 U Arab Emirates NYU Tandon Sch Engn Dept Civil & Urban Engn Brooklyn NY 11201 USA Cornell Univ Sch Civil & Environm Engn Ithaca NY 14853 USA

In response to growing evidence linking food insecurity and poor nutrition to an increased risk of chronic health problems, such as diabetes and malnutrition, food bank personnel and policy makers must proactively seek new policies and practices that combat food insecurity and ensure that food bank systems function equitably and efficiently. We develop a framework for optimizing resource allocation by food banks among the agencies they serve. Our framework explicitly considers measures of the effectiveness and efficiency of the resource allocation problem faced by food banks, and it implicitly considers an equity performance measure. We measure effectiveness based on the nutritional value of the allocation decisions, efficiency as the utility of the agencies served, and equity as fairness in the allocation of food among those agencies. Specifically, we develop a dynamic programming model in which the primary decision is how much of each product to allocate/distribute to each agency. To deal with the highdimensional state space in the dynamic program, we construct approximations to the value function that are parameterized by a small number of parameters. Computational experiments using real-world data obtained from a food bank in New York State, which serves about 19,0 0 0 individuals per week, are used to evaluate the performance of our approach. When compared against the policy currently in use, our algorithm demonstrated a 7.73% improvement in total utility. Furthermore, when compared against the offline model, where randomness is revealed upfront, the gap between our algorithm and the offline model was less than 9.50%. On the effectiveness side, our framework demonstrated a 3.0% improvement in the nutrition of the served population. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： approximate dynamic programming food insecurity Markov decision processes resource allocation

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dynamic Intra-Cell Repositioning in Free-Floating Bike-Sharing Systems Using approximate dynamic programming

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TRANSPORTATION SCIENCE 2022年第4期56卷 799-826页

作者： Luo, Xue Li, Li Zhao, Lei Linc, Jianfeng Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Riding Artificial Intelligence Team Beijing 100102 Peoples R China

In bike-sharing systems, the spatiotemporal imbalance of bike flows leads to shortages of bikes at some locations and overages at some others, depending on the time of the day, resulting in user dissatisfaction. Repositioning needs to be performed timely to deal with the spatiotemporal imbalance and to meet user demand in time. In this paper, we study the dynamic intra-cell repositioning of bikes by a single mover in free-floating bike-sharing systems. Considering that users can drop off bikes almost anywhere in free-floating systems, we study the simultaneous reposition of bikes among gathering points and collection of bikes scattered along the paths between gathering points under stochastic demands at both the gathering points and along the paths. We formulate the problem as a Markov decision process (MDP), design a policy function approximation (PFA) algorithm, and apply the optimal computing budget allocation method (OCBA) to search for the optimal policy parameters. We perform a comprehensive numerical study using test instances constructed based on the real data set of a major free-floating bike-sharing company in China, which demonstrates the outperformance of the proposed PFA policy against the benchmark policies and the practical implications on the value of repositioning and the impact of bike scatteredness.

关键词： free-floating bike-sharing systems spatiotemporal imbalance dynamic repositioning bike scatteredness approximate dynamic programming

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Revisiting approximate dynamic programming and its Convergence

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IEEE TRANSACTIONS ON CYBERNETICS 2014年第12期44卷 2733-2743页

作者： Heydari, Ali South Dakota Sch Mines & Technol Dept Mech Engn Rapid City SD 57701 USA

Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed.

关键词： approximate dynamic programming nonlinear control systems optimal control

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