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Solving the dynamic Vehicle Routing Problem Under Traffic Congestion

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2016年第8期17卷 2367-2380页

作者： Kim, Gitae Ong, Yew Soon Cheong, Taesu Tan, Puay Siew Hanbat Natl Univ Dept Ind Management Engn Daejeon 305719 South Korea Nanyang Technol Univ Sch Comp Engn Singapore 639798 Singapore Nanyang Technol Univ Sch Comp Engn Computat Intelligence Res Lab Singapore 639798 Singapore Nanyang Technol Univ Joint Lab Collaborat Res Programme Complex Syst SIMTech Singapore 639798 Singapore Korea Univ Sch Ind Management Engn Seoul 136713 South Korea ASTAR Singapore Inst Mfg Technol Singapore 138632 Singapore

This paper proposes a dynamic vehicle routing problem (DVRP) model with nonstationary stochastic travel times under traffic congestion. Depending on the traffic conditions, the travel time between two nodes, particularly in a city, may not be proportional to distance and changes both dynamically and stochastically over time. Considering this environment, we propose a Markov decision process model to solve this problem and adopt a rollout-based approach to the solution, using approximate dynamic programming to avoid the curse of dimensionality. We also investigate how to estimate the probability distribution of travel times of arcs which, reflecting reality, are considered to consist of multiple road segments. Experiments are conducted using a real-world problem faced by Singapore logistics/delivery company and authentic road traffic information.

关键词： dynamic vehicle routing problem approximate dynamic programming uncertain travel times rollout algorithm

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Load Scheduling and Power Trading in Systems With High Penetration of Renewable Energy Resources

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IEEE TRANSACTIONS ON SMART GRID 2016年第4期7卷 1802-1812页

作者： Samadi, Pedram Wong, Vincent W. S. Schober, Robert Univ British Columbia Dept Elect & Comp Engn Vancouver BC V6T 2G9 Canada

In this paper, we focus on the problems of load scheduling and power trading in systems with high penetration of renewable energy resources (RERs). We adopt approximate dynamic programming to schedule the operation of different types of appliances including must-run and controllable appliances. We assume that users can sell their excess power generation to other users or to the utility company. Since it is more profitable for users to trade energy with other users locally, users with excess generation compete with each other to sell their respective extra power to their neighbors. A game theoretic approach is adopted to model the interaction between users with excess generation. In our system model, each user aims to obtain a larger share of the market and to maximize its revenue by appropriately selecting its offered price and generation. In addition to yielding a higher revenue, consuming the excess generation locally reduces the reverse power flow, which impacts the stability of the system. Simulation results show that our proposed algorithm reduces the energy expenses of the users. The proposed algorithm also facilitates the utilization of RERs by encouraging users to consume excess generation locally rather than injecting it back into the power grid.

关键词： approximate dynamic programming demand side management (DSM) load scheduling power trading

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Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

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INTERNATIONAL JOURNAL OF CONTROL 2016年第1期89卷 99-112页

作者： Lv, Yongfeng Na, Jing Yang, Qinmin Wu, Xing Guo, Yu Kunming Univ Sci & Technol Fac Mech & Elect Engn Kunming 650500 Peoples R China Zhejiang Univ Dept Control Sci & Engn Hangzhou 310027 Zhejiang Peoples R China

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

关键词： adaptive control optimal control approximate dynamic programming system identification nonlinear systems

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Reference Policies for Non-myopic Sequential Network Design and Timing Problems

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NETWORKS & SPATIAL ECONOMICS 2016年第4期16卷 1183-1209页

作者： Chow, Joseph Y. J. Sayarshad, Hamid R. NYU Dept Civil & Urban Engn New York NY 10003 USA Ryerson Univ Dept Civil Engn Toronto ON Canada

Despite a growing number of studies in stochastic dynamic network optimization, the field remains less well defined and unified than other areas of network optimization. Due to the need for approximation methods like approximate dynamic programming, one of the most significant problems yet to be solved is the lack of adequate benchmarks. The values of the perfect information policy and static policy are not sensitive to information propagation while the myopic policy does not distinguish network effects in the value of flexibility. We propose a scalable reference policy value defined from theoretically consistent real option values based on sampled sequences, and estimate it using extreme value distributions. The reference policy is evaluated on an existing network instance with known sequences (Sioux Falls network from Chow and Regan 2011a): the Weibull distribution demonstrates good fit and sampling consistency with more than 200 samples. The reference policy is further applied in computational experiments with two other types of adaptive network design: a facility location and timing problem on the Simchi-Levi and Berman (1988) network, and Hyytia et al.'s (2012) dynamic dial-a-ride problem. The former experiment represents an application of a new problem class and use of the reference policy as an upper bound for evaluating sampled policies, which can reach 3 % gap with 350 samples. The latter experiment demonstrates that sensitivity to parameters may be greater than expected, particularly when benchmarked against the proposed reference policy.

关键词： approximate dynamic programming Sequential network design problems dynamic dial-a-ride problem Facility location problem Adapted stochastic process Markov decision process

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A neural-network-based online optimal control approach for nonlinear robust decentralized stabilization

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SOFT COMPUTING 2016年第2期20卷 707-716页

作者： Wang, Ding Liu, Derong Li, Hongliang Ma, Hongwen Li, Chao Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China

In this paper, the robust decentralized stabilization of continuous-time uncertain nonlinear systems with multi control stations is developed using a neural network based online optimal control approach. The novelty lies in that the well-known adaptive dynamic programming method is extended to deal with the nonlinear feedback control problem under uncertain and large-scale environment. Through introducing an appropriate bounded function and defining a modified cost function, it can be observed that the decentralized optimal controller of the nominal system can achieve robust decentralized stabilization of original uncertain system. Then, a critic neural network is constructed for solving the modified Hamilton-Jacobi-Bellman equation corresponding to the nominal system in an online fashion. The weights of the critic network are tuned based on the standard steepest descent algorithm with an additional term provided to guarantee the boundedness of system states. The stability analysis of the closed-loop system is carried out via the Lyapunov approach. At last, two simulation examples are given to verify the effectiveness of the present control approach.

关键词： Adaptive dynamic programming approximate dynamic programming Neural networks Online optimal control Robust decentralized stabilization Uncertain nonlinear systems

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SOLUTIONS AND DIAGNOSTICS OF SWITCHING PROBLEMS WITH LINEAR STATE dynamicS

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ANZIAM JOURNAL 2016年第3期57卷 339-351页

作者： Hinz, J. Yap, N. Univ Technol Sydney Sch Math & Phys Sci POB 123 Broadway NSW 2007 Australia Univ Technol Sydney UTS Business Sch Finance Discipline Grp POB 123 Broadway NSW 2007 Australia

Optimal control problems of stochastic switching type appear frequently when making decisions under uncertainty and are notoriously challenging from a computational viewpoint. Although numerous approaches have been suggested in the literature to tackle them, typical real-world applications are inherently high dimensional and usually drive common algorithms to their computational limits. Furthermore, even when numerical approximations of the optimal strategy are obtained, practitioners must apply time-consuming and unreliable Monte Carlo simulations to assess their quality. In this paper, we show how one can overcome both difficulties for a specific class of discrete-time stochastic control problems. A simple and efficient algorithm which yields approximate numerical solutions is presented and methods to perform diagnostics are provided.

关键词： Markov decisions approximate dynamic programming stochastic control duality

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Dual MPC with Reinforcement Learning

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IFAC-PapersOnLine 2016年第7期49卷 266-271页

作者： Morinelly, Juan E. Ydstie, B. Erik Chemical Engineering Department Carnegie Mellon University PittsburghPA15213 United States

An adaptive optimal control algorithm for systems with uncertain dynamics is formulated under a Reinforcement Learning framework. An embedded exploratory component is included explicitly in the objective function of an output feedback receding horizon Model Predictive Control problem. The optimization is formulated as a Quadratically Constrained Quadratic Program and it is solved to e-global optimality. The iterative interaction between the action specified by the optimal solution and the approximation of cost functions balances the exploitation of current knowledge and the need for exploration. The proposed method is shown to converge to the optimal policy for a controllable discrete time linear plant with unknown output parameters. © 2016

关键词： Reinforcement learning Adaptive control systems Constrained optimization Cost functions dynamic programming Iterative methods Model predictive control Predictive control systems Quadratic programming Adaptive Control Adaptive optimal control approximate dynamic programming Dual control Iterative interaction Optimal controls Quadratically constrained quadratic programs Receding horizon model

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Air Cargo Network Revenue Management

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TRANSPORTATION SCIENCE 2016年第4期50卷 1206-1222页

作者： Barz, Christiane Gartner, Daniel Univ Zurich Dept Business Adm CH-8044 Zurich Switzerland Cardiff Univ Sch Math Cardiff CF10 3XQ S Glam Wales

In this paper we discuss heuristics for network air cargo revenue management. We start from a dynamic programming formulation of air cargo network revenue management. Since the curse of dimensionality makes this problem intractable, we suggest several methods, based on linear programming, approximate dynamic programming, and decomposition to obtain both upper bounds and heuristics. We prove relationships between the upper bounds. Furthermore, we analyze the performance of both the bounds as well as the heuristics in a numerical study. In this numerical study, we find that a dynamic programming decomposition yields the tightest bounds. The heuristic based on the decomposition dominates other approaches by giving higher expected net revenues both when applied on the single-leg and on the network cargo problem.

关键词： cargo revenue management network revenue management approximate dynamic programming air cargo

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Communication-Motion Planning for Wireless Relay-Assisted Multi-Robot System

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IEEE WIRELESS COMMUNICATIONS LETTERS 2016年第6期5卷 568-571页

作者： Wu, Yunlong Zhang, Bo Yi, Xiaodong Tang, Yuhua Natl Univ Def Technol Coll Comp State Key Lab High Performance Comp Changsha 410073 Hunan Peoples R China

This letter focuses on a scenario in which a team of sensing robots survey an area with predefined routes, and transmit the monitored information to a remote base station through a mobile relay. In this scenario, automatically adjusting the position of the mobile relay for maintaining wireless link quality while the sensing robots are moving is a challenging problem. In this letter, we consider the problem of minimizing the total energy consumption. We propose using dynamic programming (DP) and single-step optimization. By comparing the pros and cons of both methods, we propose a novel approximate optimal communication-motion planning (AOCMP) method based on approximate dynamic programming (ADP). Simulation results demonstrate that AOCMP may sharply decrease the computation time compared with DP, while performs better than single-step optimization which proves that AOCMP achieves a beneficial energy-complexity tradeoff for solving high-dimension problems.

关键词： Optimal communication-motion planning relays robots approximate dynamic programming

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Optimal day-ahead trading and storage of renewable energies-an approximate dynamic programming approach

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2010年第1期1卷 61-77页

作者： Loehndorf, Nils Minner, Stefan Univ Vienna Dept Business Adm Brunner Str 72 A-1210 Vienna Austria

A renewable power producer who trades on a day-ahead market sells electricity under supply and price uncertainty. Investments in energy storage mitigate the associated financial risks and allow for decoupling the timing of supply and delivery. This paper introduces a model of the optimal bidding strategy for a hybrid system of renewable power generation and energy storage. We formulate the problem as a continuous-state Markov decision process and present a solution based on approximate dynamic programming. We propose an algorithm that combines approximate policy iteration with Least Squares Policy Evaluation (LSPE) which is used to estimate the weights of a polynomial value function approximation. We find that the approximate policies produce significantly better results for the continuous state space than an optimal discrete policy obtained by linear programming. A numerical analysis of the response surface of rewards on model parameters reveals that supply uncertainty, imbalance costs and a negative correlation of market price and supplies are the main drivers for investments in energy storage. Supply and price autocorrelation, on the other hand, have a negative effect on the value of storage.

关键词： Renewable energies Energy storage Day-ahead market Optimal bidding strategy approximate dynamic programming

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