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arXiv 2023年

作者： Fallah, Samira Ralphs, Ted K. Boland, Natashia L. Department of Industrial and Systems Engineering Lehigh University United States School of Electrical Engineering Computing and Mathematical Sciences Curtin University PerthWA Australia

In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. In the first part of the paper, we detail the mathematical structure of the RVF, including characterizing the set of points at which it is differentiable, the gradients at such points, and the subdifferential at all nondifferentiable points. We then show that the EF of the multiobjective MILP is comprised of points on the boundary of the epigraph of the RVF and that any description of the EF suffices to describe the RVF and vice versa. Because of the close relationship of the RVF to the EF, we observe that methods for constructing the so-called value function (VF) of an MILP and methods for constructing the EF of a multiobjective optimization problem are effectively interchangeable. Exploiting this observation, we propose a generalized cutting-plane algorithm for constructing the EF of a multiobjective MILP that arises from an existing algorithm for constructing the classical MILP VF. The algorithm identifies the set of all integer parts of solutions on the EF. We prove that the algorithm converges finitely under a standard boundedness assumption and comes with a performance guarantee if terminated *** Codes 90C29, 90C46 Copyright © 2023, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Learning-based Two-tiered Online Optimization of Region-wide Datacenter Resource Allocation

arXiv

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arXiv 2023年

作者： Chen, Chang-Lin Zhou, Hanhan Chen, Jiayu Pedramfar, Mohammad Lan, Tian Zhu, Zheqing Zhou, Chi Ruiz, Pol Mauri Kumar, Neeraj Dong, Hongbo Aggarwal, Vaneet Elmore Family School of Electrical and Computer Engineering Purdue University West LafayetteIN47907 United States Department of Electrical and Computer Engineering The George Washington University WashingtonDC20052 United States Edwardson School of Industrial Engineering Purdue University West LafayetteIN47907 United States Meta Platforms Inc. Menlo ParkCA94025 United States

Online optimization of resource management for large-scale data centers and infrastructures to meet dynamic capacity reservation demands and various practical constraints (e.g., feasibility and robustness) is a very challenging problem. mixed integer programming (MIP) approaches suffer from recognized limitations in such a dynamic environment, while learning-based approaches may face with prohibitively large state/action spaces. To this end, this paper presents a novel two-tiered online optimization to enable a learning-based Resource Allowance System (RAS). To solve optimal server-to-reservation assignment in RAS in an online fashion, the proposed solution leverages a reinforcement learning (RL) agent to make high-level decisions, e.g., how much resource to select from the Main Switch Boards (MSBs), and then a low-level mixed integer linear programming (MILP) solver to generate the local server-to-reservation mapping, conditioned on the RL decisions. We take into account fault tolerance, server movement minimization, and network affinity requirements and apply the proposed solution to large-scale RAS problems. To provide interpretability, we further train a decision tree model to explain the learned policies and to prune unreasonable corner cases at the low-level MILP solver, resulting in further performance improvement. Extensive evaluations show that our two-tiered solution outperforms baselines such as pure MIP solver by over 15% while delivering 100× speedup in computation. Copyright © 2023, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Stability-Adjusted Cross-Validation for Sparse linear Regression

arXiv

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arXiv 2023年

作者： Cory-Wright, Ryan Gómez, Andrés Department of Analytics Marketing and Operations Imperial College Business School London United Kingdom Department of Industrial and Systems Engineering Viterbi School of Engineering University of Southern California CA United States

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To select the sparsity and robustness of linear regressors, techniques like k-fold cross-validation are commonly used for hyperparameter tuning. However, cross-validation substantially increases the computational cost of sparse regression as it requires solving many mixed-integer optimization problems (MIOs) for each hyperparameter combination. Additionally, validation metrics often serve as noisy estimators of test set errors, with different hyperparameter combinations leading to models with different noise levels. Therefore, optimizing over these metrics is vulnerable to out-of-sample disappointment, especially in underdetermined settings. To improve upon this state of affairs, we make two key contributions. First, motivated by the generalization theory literature, we propose selecting hyperparameters that minimize a weighted sum of a cross-validation metric and a model’s output stability, thus reducing the risk of poor out-of-sample performance. Second, we leverage ideas from the mixed-integer optimization literature to obtain computationally tractable relaxations of k-fold cross-validation metrics and the output stability of regressors, facilitating hyperparameter selection after solving fewer MIOs. These relaxations result in an efficient cyclic coordinate descent scheme, achieving lower validation errors than via traditional methods such as grid search. On synthetic datasets, our confidence adjustment procedure improves out-of-sample performance by 2%–5% compared to minimizing the k-fold error alone. On 13 real-world datasets, our confidence adjustment procedure reduces test set error by 2%, on average. Copyright © 2023, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Optimal energy management and sizing of renewable energy and battery systems in residential sectors via a stochastic MILP model

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ELECTRIC POWER SYSTEMS RESEARCH 2020年 187卷 106483-106483页

作者： Farrokhifar, Meisam Aghdam, Farid Hamzeh Alahyari, Arman Monavari, Ali Safari, Amin Skolkovo Inst Sci & Technol Ctr Energy Sci & Technol Moscow Russia Univ Groningen Fac Sci & Engn Groningen Netherlands Azarbaijan Shahid Madani Univ Dept Elect Engn Tabriz Iran Roshdiyeh Higher Educ Inst Dept Elect Engn Tabriz Iran

Energy supply through integrated renewable energy sources (RESs) and battery systems will be of higher importance for future residential sectors. Optimal energy management and sizing for the components of residential systems can enhance efficiency, self-suffiency, and meanwhile can be cost-effective by reducing investment as well as operating costs. Accordingly, this paper proposes an exhaustive optimization model for determining the capacity of RESs, namely: wind turbines and photovoltaic (PV) systems. In this study, batteries and electric vehicles (EVs) are utilized in line with other sources to capture fluctuations of RESs. To model the uncertainties of RESs, energy prices, and load demands a linearized stochastic programming framework is applied. The proposed framework involves long-term and efficient resource development alongside with short-term management and utilization of these resources for supplying the demand load. In our study, we utilize the roulette wheel mechanism (RWM) method as well as proper probability distribution functions (PDFs) to generate scenarios for all sources of uncertainties, including wind turbines, PV systems, demand, and electricity market price. The approach is verified in two different cases, including an individual home and a larger micro-grid (MG). The results of multiple numerical simulations demonstrate the effectiveness of the proposed stochastic model.

关键词： Residential micro-grid Demand response programs Electric vehicles Uncertainty mixed-integer linear programming

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On a Wireless Sensor Network Problem with Spanning Tree Backbone 18

On a Wireless Sensor Network Problem with Spanning Tree Back...

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18th International Conference on Wireless Networks and Mobile Systems (WINSYS)

作者： Adasme, Pablo Firoozabadi, Ali Dehghan Univ Santiago Chile Dept Elect Engn Ave Ecuador 3519 Santiago Chile Univ Tecnol Metropolitana Dept Elect Av Jose Pedro Alessandri 1242 Santiago 7800002 Chile

ISBN: (纸本)9789897585296

Let G = (V, E) be a complete graph with set of nodes V = {1, . . .,} g and edge set E = {1, . . ., m} representing a wireless sensor network. In this paper, we consider the problem of finding a minimum cost spanning tree backbone formed with p is an element of Z(+) out of n nodes where p < n in such a way that the n - p remaining nodes of G are connected to the leaf nodes of the backbone structure at minimum connectivity cost. Notice that this problem arises as a combination of two classical combinatorial optimization problems, namely the p-Median and spanning tree problems. We propose two mixed-integer linear programming (MIP) formulations for this problem as well as a local search heuristic. The proposed models and algorithm can be used as a reference source for comparison purposes when designing future network protocols. We consider complete graph instances with Euclidean and random uniform costs. Our preliminary numerical results indicate that one of the proposed models performs slightly better than the other one in terms of solution quality and CPU times obtained with the Gurobi solver. Finally, the proposed heuristic allows one to obtain near-optimal solutions in remarkably less CPU time compared to the MIP models.

关键词： Combinatorial Optimization p-Median and Spanning Tree Problems mixed-integer linear programming Wireless Sensor Networks Local Search Algorithm

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Enhancing System Flexibility through Corrective Demand Response in Security-Constrained Unit Commitment 52

Enhancing System Flexibility through Corrective Demand Respo...

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52nd North American Power Symposium (NAPS)

作者： Ramesh, Arun Venkatesh Li, Xingpeng Univ Houston Dept Elect & Comp Engn Houston TX 77004 USA

ISBN: (纸本)9781728181929

Currently, system operators implement demand response by dispatching controllable loads for economic reasons in day-ahead scheduling. Particularly, demand shifting from peak hours when the cost of electricity is higher to non-peak hours to maintain system reliability by flattening the load profile. However, the system flexibility and economic benefits of such action in post-contingency scenarios are not explicitly considered in short-term operations. Hence, this paper highlights the benefits of demand response as a corrective action for potential post-contingency emergencies in day-ahead scheduling. A security-constrained unit commitment (SCUC) model which considers the flexibility offered through corrective demand response (CDR) to maintain system reliability when a line or generator outage occurs is proposed. The proposed model was tested on IEEE 24-bus system where simulation results point to significant total cost savings in daily operations. Moreover, the results point to better long-term reliability of generators along with the ability to use existing system flexibility and serve higher critical demands in base-case when CDR is implemented.

关键词： Corrective demand response Demand curtailment Power system flexibility mixed-integer linear programming Security-constrained unit commitment

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Exploiting Parallelism in Multi-Task Robot Allocation Problems

Exploiting Parallelism in Multi-Task Robot Allocation Proble...

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IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC)

作者： Miloradovic, Branko Curuklu, Baran Ekstrom, Mikael Papadopoulos, Alessandro, V Malardalen Univ Vasteras Sweden

ISBN: (纸本)9781665431989

Multi-Agent Systems (MASs) have been widely adopted in robotics, as a means to solve complex missions by subdividing them into smaller tasks. In such a context, Multi-Robot Task Allocation (MRTA) has been a relevant research area, with the main aim of providing formulations and solutions to different mission configurations, in order to optimize the planning and the execution of complex missions utilizing multiple robots. In recent years, robotic systems have become more powerful thanks to the adoption of novel computing platforms, enabling an increased level of parallelism, in terms of sensing, actuation, and computation. As a result, more complex missions can be achieved, at the cost of an increased complexity for the optimization of the mission planning. In this paper, we first introduce the distinction between physical and virtual tasks of the robots, and their relation in terms of parallel execution. Therefore, we propose a mathematical formalization of the mission planning problem for Multi-Task (MT) robots, in the presence of tasks that require only a Single-Robot (SR) to complete, and in the presence of Time-Extended Assignments (TAs). The problem is modeled with a mixed-integer linear programming (MILP) formulation, with the objective of minimizing the total makespan of the mission, exploiting the potential (physical and virtual) parallelism of the robots. The model is validated over some representative scenarios, and their respective solutions are obtained with the CPLEX optimization tool, showing the generality of the proposed formulation.

关键词： Multi-Robot Task Allocation Parallel Task Execution mixed-integer linear programming

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Increasing the PV Hosting Capacity in Unbalanced Three-Phase Distribution Networks Through Reconfiguration with Closed-Loop Operation 21

Increasing the PV Hosting Capacity in Unbalanced Three-Phase...

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21st IEEE International Conference on Environment and Electrical Engineering / 5th IEEE Industrial and Commercial Power Systems Europe (EEEIC/I and CPS Europe)

作者： Macedo, Leonardo H. Vargas, Renzo Home-Ortiz, Juan M. Mantovani, Jose R. S. Romero, Ruben Catalao, Joao P. S. UNESP Ilha Solteira Brazil Univ Fed Abc Santo Andre SP Brazil FEUP Porto Portugal INESC TEC Porto Portugal

ISBN: (数字)9781665436137

ISBN: (纸本)9781665436137

This article presents a novel mixed-integer nonlinear linear programming (MINLP) model to increase the photovoltaic (PV) hosting capacity in unbalanced three- phase electrical distribution systems. The problem considers the optimal operation of capacitor banks and network reconfiguration with radial and closed-loop operation. The objective function maximizes the PV hosting capacity of the system. A set of linearization strategies are employed to convert the presented MINLP model into a mixed-integer linear programming (MILP) problem. By considering the MILP formulation, optimality is guaranteed by using off-the-shelf optimization solvers. Several tests are carried out using a 25-node unbalanced three-phase distribution system. When examining network reconfiguration with radial and closed-loop operation, the results demonstrate that the proposed formulation is effective in increasing the penetration of PV sources.

关键词： Closed-loop operation hosting capacity mixed-integer linear programming network reconfiguration unbalanced three-phase electrical distribution networks

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Solving stochastic hydro unit commitment using benders decomposition and modified stochastic dual dynamic programming

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FRONTIERS IN ENERGY RESEARCH 2022年 10卷

作者： Li, Zhuangzhuang Yang, Ping Yang, Yi Lu, Guanpeng Tang, Yufeng South China Univ Technol Sch Elect Power Engn Guangzhou Peoples R China South China Univ Technol Guangdong Key Lab Clean Energy Technol Guangzhou Peoples R China

This paper proposes a stochastic hydro unit commitment (SHUC) model for a price-taker hydropower producer in a liberalized market. The objective is to maximize the total revenue of the hydropower producer, including the immediate revenue, future revenue (i.e., opportunity cost), and startup and shutdown cost. The market price uncertainty is taken into account through the scenario tree. The solution of the model is a challenging task due to its non-convex and high-dimensional characteristics. A solution method based on the Benders Decomposition (BD) and Modified Stochastic Dual Dynamic programming (MSDDP) is proposed to solve the problem efficiently. Firstly, the BD is applied to decompose the original problem into a Benders master problem representing the hydro unit commitment and a Benders subproblem representing the optimal operation of the hydropower plants. The Benders subproblem, which contains a large number of integer variables, is further decomposed by the period and solved by the MSDDP proposed in this paper. Finally, we verify the effectiveness of the SHUC model and the performance of the proposed solution method in case studies.

关键词： hydro unit commitment hydropower mixed-integer linear programming stochastic programming benders decomposition (BD) stochastic dual dynamic programming (SDDP)

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Using PV systems and parking lots to provide virtual inertia and frequency regulation provision in low inertia grids

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ELECTRIC POWER SYSTEMS RESEARCH 2022年第0期207卷 107859-107859页

作者： Khazali, Amirhossein Rezaei, Navid Saboori, Hedayat Guerrero, Josep M. Iran Univ Sci & Technol Elect Engn Dept Tehran Iran Univ Kurdistan Elect Engn Dept Sanandaj Iran Aalborg Univ Ctr Res Microgrids CROM Dept Energy Technol Aalborg Denmark Kermanshah Univ Technol Elect Engn Dept Kermanshah Iran

In this research, a novel formulation for smart frequency control and virtual inertia support in a low inertia grid is proposed. The approach takes advantage of EV parking lots and PV distributed resources abilities for this purpose directly or through aggregators. The model also considers governor control of the conventional plants in addition to the controllable loads, namely under-frequency load shedding devices. The model seeks to minimize the total amount of disconnected load in case of severe contingencies. Furthermore, the rate of change of frequency (ROCOF) is formulated and employed as another objective function. The control parameters are optimally tuned by mixed integer linear programming (MILP) model to minimize the amount of load shedding while satisfying the specified frequency constraints. linearity of the model assures achieving the global optima and is suitable for large-scale real-life systems without convergence concerns. The proposed smart control scheme is implemented on the IEEE 39-bus system, where the simulation results demonstrate a dramatic decrease of load shedding from 0.1676 p.u to 0.1235 p.u for one of the cases by the incorporation of converter based frequency providers. The system ROCOF, moreover, is reduced from-2.94 Hz/s to-1.93 Hz/s which indicates the efficiency of the methodology.

关键词： Frequency control Virtual inertia EV parking lot Photovoltaic resource mixed-integer linear programming

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