This research introduces a blood distribution system under vendor-managed inventory that considers uncertain supply and demand. We present it as the Blood stochastic Inventory Routing Problem, formulating it as a two-...
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This research introduces a blood distribution system under vendor-managed inventory that considers uncertain supply and demand. We present it as the Blood stochastic Inventory Routing Problem, formulating it as a two-stage stochastic programming model. To solve this problem, this study proposes a three-stage matheuristic that combines a perturbation heuristic, Adaptive Large Neighborhood Search, and an exact approach. From historical data of Surabaya Blood Center in Indonesia, six sets of new instances are generated under different settings. Computational results show that our proposed three-stage matheuristic outperforms CPLEX and a two-stage matheuristic by gaining optimal or better solutions within a significantly shorter computational time. Moreover, it is robust for solving large problems, as evidenced by its ability to find high-quality solutions within a reasonable time. Finally, managerial insights are derived by evaluating performance matrices under different uncertainty levels and scenarios. According to these insights, some practical strategies are suggested with respect to the decision-maker's risk preferences and demand characteristics.
This paper addresses the problem of energy coordination among customers in a local energy market to meet heating needs. Accordingly, this paper proposes a demand response framework for the energy coordination of multi...
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This paper addresses the problem of energy coordination among customers in a local energy market to meet heating needs. Accordingly, this paper proposes a demand response framework for the energy coordination of multiple residential prosumers in a hierarchical coordination game -theoretic scenario. That consists of a benevolent coordinator and multiple residential prosumers integrated with solar PV under demand uncertainties as a consequence of forecasting errors in weather data and non-shiftable load. The coordinator and customers are considered to be a leader and various followers, respectively. The coordinator employs a cost -shared strategy to reduce peak demand. Customers maximize individual welfare by employing stochastic programming through demand flexibility realized via electric baseboard heaters and electric thermal storage. Subsequently, the proposed strategy is implemented through a cyber-physical infrastructure incorporating a distributed computing platform with embedded systems and extensive simulations using accurate weather and real -life energy consumption data. A comparative analysis is performed using a deterministic baseline with perfect information, i.e. no forecasting errors. In addition, the proposed mechanism is tested on an adapted CIGRE low -voltage benchmark system. Simulation results demonstrate the techno-economical feasibility of the proposed solution in uncertain environments. Furthermore, they recommend practical strategies for short-term planning of grids highly penetrated by renewables and intelligent devices by increasing their flexibility and leveraging salient features of cyber-physical systems.
Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochas...
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Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization problem with discrete scenario support. While much research effort has been devoted to tractable reformulations for DRO problems, especially those with continuous scenario support, few efficient numerical algorithms are developed, and most of them can neither handle the nonsmooth second-stage cost function nor the large number of scenarios K effectively. We fill the gap by reformulating the DRO problem as a trilinear min-max-max saddle point problem and developing novel algorithms that can achieve an O(1/E) iteration complexity which only mildly depends on K. The major computations involved in each iteration of these algorithms can be conducted in parallel if necessary. Besides, for solving an important class of DRO problems with the Kantorovich ball ambiguity set, we propose a slight modification of our algorithms to avoid the expensive computation of the probability vector projection at the price of an O( K) times more iterations. Finally, preliminary numerical experiments are conducted to demonstrate the empirical advantages of the proposed algorithms.
Mobile-edge computing (MEC) is considered as a promising technology to reduce the energy consumption (EC) and task accomplishment latency of smart mobile user equipments (UEs) by offloading computation-intensive tasks...
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Mobile-edge computing (MEC) is considered as a promising technology to reduce the energy consumption (EC) and task accomplishment latency of smart mobile user equipments (UEs) by offloading computation-intensive tasks to the nearby MEC servers. However, the Quality of Experience (QoE) for computation highly depends on the wireless channel conditions when computation tasks are offloaded to MEC servers. In this article, by considering the imperfect channel-state information (CSI), we study the joint offloading decision, transmit power, and computation resources to minimize the weighted sum of EC of all UEs while guaranteeing the probabilistic constraint in multiuser MEC-enabled Internet-of-Things (IoT) networks. This formulated optimization problem is a stochastic mixed-integer nonconvex problem and challenging to solve. To deal with it, we develop a low-complexity two-stage algorithm. In the first stage, we solve the relaxed version of the original problem to obtain offloading priorities of all UEs. In the second stage, we solve an iterative optimization problem to obtain a suboptimal offloading decision. As both stages include solving a series of nonconvex stochastic problems, we present a constrained stochastic successive convex approximation-based algorithm to obtain a near-optimal solution with low complexity. The numerical results demonstrate that the proposed algorithm provides comparable performance to existing approaches.
A significant share of stochastic optimization problems in practice can be cast as two-stage stochastic programs. If uncertainty is available through a finite set of scenarios, which frequently occurs, and we are inte...
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A significant share of stochastic optimization problems in practice can be cast as two-stage stochastic programs. If uncertainty is available through a finite set of scenarios, which frequently occurs, and we are interested in accounting for risk aversion, the expectation in the recourse cost can be replaced with a worst-case function (i.e., robust optimization) or another risk-functional, such as conditional value-at-risk. In this paper we are interested in the latter situation especially when the number of scenarios is large. For computational efficiency we suggest a (clustering and) constraint generation algorithm. We establish convergence of these two algorithms and demonstrate their effectiveness through various numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.
We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second stage. It is known that the second-stage optima...
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We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second stage. It is known that the second-stage optimal value function is piecewise linear-quadratic with possible kinks and discontinuities at the boundaries of certain convex polyhedral sets. This structure is exploited to provide conditions implying that first and higher order terms of the integrand's ANOVA decomposition (Math. Comp. 79 (2010), 953-966) have mixed weak first order partial derivatives. This leads to a good smooth approximation of the integrand and, hence, to good convergence rates of randomized QMC methods if the effective (superposition) dimension is low.
This article deals with the stochastic scheduling of a microgrid (MG) to balance the economical and resilience metrics. In the proposed model, the MG resilience indices are integrated into the economic criteria to ens...
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This article deals with the stochastic scheduling of a microgrid (MG) to balance the economical and resilience metrics. In the proposed model, the MG resilience indices are integrated into the economic criteria to ensure the resilience of MG operation alongside the main MG actors' profit/loss. The MG fragility index, recovery efficiency index, MG voltage index, and lost load index are considered in the proposed planning model. Further, to make the results more realistic, the uncertainties associated with energy price and wind production, alongside with planning of energy storage systems and electric vehicles parking lots are considered. To achieve a better solution for the security-constraint operation of MG, AC network equations are included in the system modeling. Finally, a large-scale MG based on the IEEE-33 bus testbed is utilized to evaluate the effectiveness of the proposed stochastic scheduling program.
The vast majority of stochastic optimization problems require the approximation of the underlying probability measure, e.g., by sampling or using observations. It is therefore crucial to understand the dependence of t...
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The vast majority of stochastic optimization problems require the approximation of the underlying probability measure, e.g., by sampling or using observations. It is therefore crucial to understand the dependence of the optimal value and optimal solutions on these approximations as the sample size increases or more data becomes available. Due to the weak convergence properties of sequences of probability measures, there is no guarantee that these quantities will exhibit favorable asymptotic properties. We consider a class of infinite-dimensional stochastic optimization problems inspired by recent work on PDE-constrained optimization as well as functional data analysis. For this class of problems, we provide both qualitative and quantitative stability results on the optimal value and optimal solutions. In both cases, we make use of the method of probability metrics. The optimal values are shown to be Lipschitz continuous with respect to a minimal information metric and consequently, under further regularity assumptions, with respect to certain Fortet-Mourier and Wasserstein metrics. We prove that even in the most favorable setting, the solutions are at best Holder continuous with respect to changes in the underlying measure. The theoretical results are tested in the context of Monte Carlo approximation for a numerical example involving PDE-constrained optimization under uncertainty.
Lift-and-project (L &P) cuts are well-known general 0-1 programming cuts which are typically deployed in branch-and-cut methods to solve MILP problems. In this article, we discuss ways to use these cuts within the...
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Lift-and-project (L &P) cuts are well-known general 0-1 programming cuts which are typically deployed in branch-and-cut methods to solve MILP problems. In this article, we discuss ways to use these cuts within the framework of Benders' decomposition algorithms for solving two-stage mixed-binary stochastic problems with binary first-stage variables and continuous recourse. In particular, we show how L &P cuts derived for the master problem can be strengthened with the second-stage information. An adapted L-shaped algorithm and its computational efficiency analysis is presented. We show that the strengthened L &P cuts can significantly reduce the number of iterations and the solution time.
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization pr...
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ISBN:
(数字)9781665491136
ISBN:
(纸本)9781665491136
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and consider algorithmic tools to scale it to higher numbers of qubits. We investigate stochastic gradient descent and two sketch-and-solve algorithms. For all three algorithms, we compute the gradient efficiently using matrix-vector instead of matrix-matrix computations. Allowing for a runtime on the order of one hour, our implementation using either sketch-and-solve algorithm is able to compile 9 qubit, 27 CNOT circuits;12 qubit, 24 CNOT circuits;and 15 qubit, 15 CNOT circuits. Without our algorithmic tools, standard optimization does not scale beyond 9 qubit, 9 CNOT circuits, and, beyond that, is theoretically dominated by barren plateaus.
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