In this paper, a quadratic Taylor expansion-based approximate dynamic programming (QTE-ADP) algorithm is proposed for the decentralized solution of multi-area AC-optimal power flow (MA-ACOPF). Different from tradition...
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In this paper, a quadratic Taylor expansion-based approximate dynamic programming (QTE-ADP) algorithm is proposed for the decentralized solution of multi-area AC-optimal power flow (MA-ACOPF). Different from traditional ADP algorithms, the proposed algorithm does not need to approximate the value function via a given function structure, but directly obtains the quadratic Taylor expansion (QTE) of value function based on KKT conditions. Moreover, compared with the commonly used linearized value function approximation techniques, the information used to approximate the value function is also extended from first order to second order in the proposed algorithm, which helps to improve the accuracy and efficiency of ADP. When using QTE-ADP to solve the MA-ACOPF problem, only the boundary voltage information needs to be interchanged between adjacent areas, which facilitates preserving the information privacy and decision independence of each area. Numerical simulations on several test systems demonstrate that the proposed algorithm has good performance in terms of accuracy, efficiency, and adaptability.
This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs h...
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This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.
Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP)...
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Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic programming relaxation (CQPR), and (b) the integral parts of the solutions to CQPR. We propose a new heuristic which adaptively fixes the variables according to the solution of CQPR. We report computational results for QKPs with up to 200 integer variables. Our numerical results illustrate that the new heuristic produces high-quality solutions to large-scale QKPs fast and robustly. (c) 2004 Elsevier Ltd. All rights reserved.
We consider an integrated production and delivery scheduling problem with non-stationary demand in a two-stage supply chain, where orders arrive dynamically and the demand is time-varying. Orders should be first proce...
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We consider an integrated production and delivery scheduling problem with non-stationary demand in a two-stage supply chain, where orders arrive dynamically and the demand is time-varying. Orders should be first processed on identical machines and then delivered to a single next-stage destination by the transporters with fixed departure times. The objective is to minimize the order waiting time via production-delivery scheduling. We formulate the problem into a Markov decision process model and develop an approximate dynamic programming (ADP) method. To shrink action (decision) space, we propose the shorter processing time first and first completion first delivery (SPTm/FCFD) principle to determine order processing sequences and order delivery, and then we establish two constraints to eliminate a fraction of inferior actions. Based on the SPTm/FCFD principle, we propose the SPT/FCFD rule, and show its optimality for two scenarios. In addition, we deploy five basis functions to approximate the value function. The superior performance of ADP policy is validated via numerical experiments, compared with four benchmark policies. We also empirically study the impact of demand features on the waiting time, and results show that these features significantly affect the performances of all polices. In practice, it is suggested to postpone the peak demand, when total demand exceeds the available production capacity.
Control system theory has been based oil certain well understood and accepted techniques, such as transfer function-based methods, adaptive control, robust control, non-linear systems theory, state-space methods, etc....
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Control system theory has been based oil certain well understood and accepted techniques, such as transfer function-based methods, adaptive control, robust control, non-linear systems theory, state-space methods, etc. However, recently, the hypothesis that methods of modelling and analysis of life science systems hold out the power of significantly improving the performance of man-made control systems has gained increased interest, while becoming more and more a fact. For instance, in the last few decades many successful results were obtained by combining the potential of artificial neural networks (ANNs) with classical control structures. It has been shown that certain types of ANN can extend the capabilities of adaptive controllers by making them applicable for more complex non-linear systems, and at the same time greatly improving the system performance. In this paper, we will present a biologically inspired structure that will learn the optimal state feedback controller for a linear system, while at the same time performing continuous-time online control for the system at hand. Being based on a reinforcement learning technique, the optimal controller will be obtained while only making use of the input-to-state system dynamics. Mathematically speaking, the solution of the algebraic Riccati equation underlying the control problem will be obtained without making use of any knowledge of the system internal dynamics.
We formulate the well-known economic lot scheduling problem (ELSP) with sequence-dependent setup times and costs as a semi-Markov decision process. Using an affine approximation of the bias function, we obtain a semi-...
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We formulate the well-known economic lot scheduling problem (ELSP) with sequence-dependent setup times and costs as a semi-Markov decision process. Using an affine approximation of the bias function, we obtain a semi-infinite linear program determining a lower bound for the minimum average cost rate. Under a very mild condition, we can reduce this problem to a relatively small convex quadratically constrained linear problem by exploiting the structure of the objective function and the state space. This problem is equivalent to the lower bound problem derived by Dobson [Dobson G (1992) The cyclic lot scheduling problem with sequence-dependent setups. Oper. Res. 40:736-749] and reduces to the well-known lower bound problem introduced in Bomberger [Bomberger EE (1966) A dynamicprogramming approach to a lot size scheduling problem. Management Sci. 12: 778-784] for sequence-dependent setups. We thus provide a framework that unifies previous work, and opens new paths for future research on tighter lower bounds and dynamic heuristics.
Recent improvements in vehicle-to-everything (V2X) communication and onboard computing power have enabled the development of control algorithms that jointly optimize the vehicle velocity and powertrain control in Conn...
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Recent improvements in vehicle-to-everything (V2X) communication and onboard computing power have enabled the development of control algorithms that jointly optimize the vehicle velocity and powertrain control in Connected and Automated Vehicles (CAVs), commonly referred to as the Eco-Driving problem. This paper presents a novel and computationally efficient algorithm to optimize the velocity planning and energy management in a CAV with a hybrid electric powertrain. The Eco-Driving problem is formulated as a dynamic, constrained optimization problem in the spatial domain, where information about the upcoming speed limits and road topography is assumed known. This problem is solved by embedding an Equivalent Consumption Minimization Strategy (ECMS) into a dynamicprogramming (DP) optimization to obtain a sub-optimal solution that provides results close to the global optimum at a fraction of the computational cost. Further, a multi-layer hierarchical control architecture is proposed as a path to a causal, real-time implementation. The DP-ECMS algorithm is converted into a Model Predictive Control (MPC) framework by using principles of approximate dynamic programming (ADP). This causal implementation is finally benchmarked to a global optimal solution obtained with DP for different scenarios.
We address the problem of determining optimal stepsizes for estimating parameters in the context of approximate dynamic programming. The sufficient conditions for convergence of the stepsize rules have been known for ...
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We address the problem of determining optimal stepsizes for estimating parameters in the context of approximate dynamic programming. The sufficient conditions for convergence of the stepsize rules have been known for 50 years, but practical computational work tends to use formulas with parameters that have to be tuned for specific applications. The problem is that in most applications in dynamicprogramming, observations for estimating a value function typically come from a data series that can be initially highly transient. The degree of transience affects the choice of stepsize parameters that produce the fastest convergence. In addition, the degree of initial transience can vary widely among the value function parameters for the same dynamic program. This paper reviews the literature on deterministic and stochastic stepsize rules, and derives formulas for optimal stepsizes for minimizing estimation error. This formula assumes certain parameters are known, and an approximation is proposed for the case where the parameters are unknown. Experimental work shows that the approximation provides faster convergence than other popular formulas.
Recently, the optimization of power flows in portable hybrid power-supply systems (HPSSs) has become an important issue with the advent of a variety of mobile systems and hybrid energy technologies. In this paper, a c...
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Recently, the optimization of power flows in portable hybrid power-supply systems (HPSSs) has become an important issue with the advent of a variety of mobile systems and hybrid energy technologies. In this paper, a control strategy is considered for dynamically managing power flows in portable HPSSs employing batteries and supercapacitors. Our dynamic power management strategy utilizes the concept of approximate dynamic programming (ADP). ADP methods are important tools in the fields of stochastic control and machine learning, and the utilization of these tools for practical engineering problems is now an active and promising research field. We propose an ADP-based procedure based on optimization under constraints including the iterated Bellman inequalities, which can be solved by convex optimization carried out offline, to find the optimal power management rules for portable HPSSs. The effectiveness of the proposed procedure is tested through dynamic simulations for smartphone workload scenarios, and simulation results show that the proposed strategy can successfully cope with uncertain workload demands.
For Mobility-on-Demand systems, the imbalance between vehicle supply and demand is a longstanding challenge, leading to losses of orders and long waiting times. Relocating idle vehicles to high-demand regions can enha...
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For Mobility-on-Demand systems, the imbalance between vehicle supply and demand is a longstanding challenge, leading to losses of orders and long waiting times. Relocating idle vehicles to high-demand regions can enhance system efficiency, thus improving the quality of service. Enforcing vehicle relocation via either link-node or grid-based representation makes it hard to capture the interrelated dynamics with private vehicles while being computationally intensive. The macroscopic fundamental diagram (MFD) provides a powerful tool to model the interrelated dynamics while individual vehicle details may be absent in the regional-level representation. Therefore, we propose a bi-level rebalancing scheme to maximize the served orders in the system. The urban area is first partitioned into several subregions. For the upper level, the interrelated dynamics of private vehicles and on-demand vehicles are modeled based on the MFD. Then a stochastic programming problem is formulated and solved using approximate dynamic programming (ADP) to determine the number of desired vehicles in each subregion and cross-border. For the lower level, a Voronoi-based distributed coverage control algorithm is implemented by each vehicle to obtain position guidance efficiently. The bi-level framework is evaluated on a simulator of the real road network of Shenzhen, China. Simulation results demonstrate that, compared to other policies, the proposed approach can serve more requests with less waiting time.
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