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Hierarchical Functionality Prioritization in Multicast ISAC: Optimal Admission Control and Discrete-Phase Beamforming

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arXiv 2024年

作者： Abanto-Leon, Luis F. Maghsudi, Setareh

We investigate the joint admission control and discrete-phase multicast beamforming design for integrated sensing and commmunications (ISAC) systems, where sensing and communications functionalities have different hierarchies. Specifically, the ISAC system first allocates resources to the higher-hierarchy functionality and opportunistically uses the remaining resources to support the lower-hierarchy one. This resource allocation problem is a nonconvex mixed-integer nonlinear program (MINLP). We propose an exact mixed-integer linear program (MILP) reformulation, leading to a globally optimal solution. In addition, we implemented three baselines for comparison, which our proposed method outperforms by more than 39%. © 2024, CC BY.

关键词： mixed-integer linear programming

Generating Likely Counterfactuals Using Sum-Product Networks

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arXiv 2024年

作者： Němeček, Jiří Pevný, Tomáš Mareček, Jakub

Explainability of decisions made by AI systems is driven by both recent regulation and user demand. These decisions are often explainable only post hoc, after the fact. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although "distance from the sample" is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using mixed-integer optimization (MIO). In the process, we propose an MIO formulation of a Sum-Product Network (SPN) and use the SPN to estimate the likelihood of a counterfactual, which can be of independent interest. © 2024, CC BY.

关键词： mixed-integer linear programming

Fixed Topology Minimum-Length Trees with Neighborhoods

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arXiv 2024年

作者： Blanco, Víctor González, Gabriel Puerto, Justo Universidad de Granada Spain Universidad de Sevilla Spain

In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a d-dimensional metric space while minimizing its total length provided that the nodes must be embedded to some restricted areas. This problem has significant applications in efficiently routing cables or pipelines in engineering designs. We propose novel mathematical optimization-based approaches to solve different versions of the problem based on the domain for the embedding. In cases where the embedding maps to a continuous space, we provide several mixed integer Nonlinear Optimization formulations. If the embedding is to a network, we derive a mixed integer linear programming formulation as well as a dimensionality reduction methodology that allows for solving larger problems in less CPU time. A data-driven methodology is also proposed to construct a proper network based on the instance of the problem. We report the results of a battery of computational experiments that validate our *** Codes 90C27, 05C05, 90C11, 90C30 © 2024, CC BY.

关键词： mixed-integer linear programming

Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems

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arXiv 2024年

作者： Omidi, Arash Mishra, Tanmay Almassalkhi, Mads R. The Department of Electrical and Biomedical Engineering University of Vermont BurlingtonVT United States

Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to two battery optimization use-cases: PV smoothing and revenue maximization, and it is compared with three other ERM formulations (nonlinear, linear, and mixed-integer). Specifically, ICNN-based methods appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across both use-cases. © 2024, CC BY.

关键词： mixed-integer linear programming

SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branch

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arXiv 2024年

作者： Feng, Shengyu Yang, Yiming Carnegie Mellon University United States

mixed integer linear Program (MILP) solvers are mostly built upon a Branch-and-Bound (B&B) algorithm, where the efficiency of traditional solvers heavily depends on hand-crafted heuristics for branching. The past few years have witnessed the increasing popularity of data-driven approaches to automatically learn these heuristics. However, the success of these methods is highly dependent on the availability of high-quality demonstrations, which requires either the development of near-optimal heuristics or a time-consuming sampling process. This paper averts this challenge by proposing Suboptimal-Demonstration-Guided Reinforcement Learning (SORREL) for learning to branch. SORREL selectively learns from suboptimal demonstrations based on value estimation. It utilizes suboptimal demonstrations through both offline reinforcement learning on the demonstrations generated by suboptimal heuristics and self-imitation learning on past good experiences sampled by itself. Our experiments demonstrate its advanced performance in both branching quality and training efficiency over previous methods for various MILPs. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Smart Ev Charging in Pv-Powered Workplace Parking Lots: A Case Study from Denmark

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SSRN

SSRN 2024年

作者： Secchi, Mattia Rivera, Carlos Hermana Zepter, Jan Martin Marinelli, Mattia Technical University of Denmark Department of Wind and Energy Systems Kgs. Lyngby2800 Denmark

The increased uptake of electric vehicles (EVs) requires public charging for EV owners without access to home chargers. We propose an easy-to-implement centralised unidirectional (V1G) smart charging algorithm for parking lots and compare it firstly against uncoordinated charging, then against decentralised SC approaches. Six scenarios are described, either minimising the CO2 emissions or the EV charging costs, eventually including a PV system. For an exemplary workplace parking lot in Denmark, the cost reduction is limited to 3\% by the pricing scheme, while emissions-based smart charging achieves 10\% CO2 emissions and a 2.9% charging costs reductions. The peak demand is also shaved without affecting the SC efficiency, while making optimal use of an existing rooftop PV system, with 13% costs and 11% emissions reductions respectively. Additionally, an algorithm is proposed to distribute the SC benefits between the EV owners based on the experienced delay, ensuring none incur a loss. © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Scenario-Based Robust Optimization of Tree Structures

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arXiv 2024年

作者： Angelopoulos, Spyros Dürr, Christoph Elenter, Alex Melidi, Georgii Sorbonne Université CNRS LIP6 Paris France

We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based on a known set of frequencies of keys. Given k different scenarios, each defined by a distinct frequency distribution over the keys, our objective is to compute a single tree of best-possible performance, relative to any scenario. We consider, as performance metrics, the competitive ratio, which compares multiplicatively the cost of the solution to the tree of least cost among all scenarios, as well as the regret, which induces a similar, but additive comparison. For BSTs, we show that the problem is NP-hard across both metrics. We also show how to obtain a tree of competitive ratio ⌈log2(k + 1)⌉, and we prove that this ratio is optimal. For Huffman Trees, we show that the problem is, likewise, NP-hard across both metrics;we also give an algorithm of regret ⌈log2 k⌉, which we show is near-optimal, by proving a lower bound of ⌊log2 k⌋. Last, we give a polynomial-time algorithm for computing Pareto-optimal BSTs with respect to their regret, assuming scenarios defined by uniform distributions over the keys. This setting captures, in particular, the first study of fairness in the context of data structures. We provide an experimental evaluation of all algorithms. To this end, we also provide mixed integer linear program formulation for computing optimal trees. © 2024, CC BY.

关键词： mixed-integer linear programming

A Carryover Storage Valuation Framework for Medium-Term Cascaded Hydropower Planning: A Portland General Electric System Study

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arXiv 2024年

作者： Chen, Xianbang Liu, Yikui Zhong, Zhiming Fan, Neng Zhao, Zhechong Wu, Lei ECE Department Stevens Institute of Technology HobokenNJ07030 United States Electrical Engineering Department Sichuan University Chengdu610017 China Portland General Electric PortlandOR97204 United States Department of Systems and Industrial Engineering University of Arizona TucsonAZ85721 United States

Medium-term planning of cascaded hydropower (CHP) determines appropriate carryover storage levels in reservoirs to optimize the usage of available water resources. This optimization seeks to maximize the hydropower generated in the current period (i.e., immediate benefit) plus the potential hydropower generation in the future period (i.e., future value). Thus, in the medium-term CHP planning, properly quantifying the future value deposited in carryover storage is essential to achieve a balanced trade-off between immediate benefit and future value. To this end, this paper presents a framework to quantify the future value of carryover storage, which consists of three major steps: i) constructing a model to calculate the maximum possible hydropower generation that a given level of carryover storage can deliver in the future period;ii) extracting the implicit locational marginal water value (LMWV) of carryover storage for each reservoir by applying a partition-then-extract algorithm to the constructed model;and iii) developing a set of analytical rules based on the extracted LMWV to effectively calculate the future value. These rules can be seamlessly integrated into medium-term CHP planning models as tractable mixed-integer linear constraints to quantify the future value properly, and can be easily visualized to offer valuable insights for CHP operators. Finally, numerical results on a CHP system of Portland General Electric demonstrate the effectiveness of the presented framework in determining proper carryover storage values to facilitate medium-term CHP planning. © 2024, CC BY.

关键词： mixed-integer linear programming

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2023年 11卷

作者： Sanati, Hemen Moslehi, Ghasem Reisi-Nafchi, Mohammad Isfahan Univ Technol Dept Ind & Syst Engn Esfahan *** Iran

Given that about half of the produced energy in the world is consumed in industries, there has been an increasing con-cern about optimizing energy consumption in manufacturing sectors. As one of the most effective ways, proper produc-tion scheduling to reduce energy consumption is of crucial importance among researchers and manufacturers. This pa-per addresses an unrelated parallel machine energy-efficient scheduling problem with sequence-dependent setup times by considering different energy consumption tariffs. The setup times are studied in two modes: disjointed from/jointed to processing time. For each one of these problems, two mixed -integer linear programming models have been formulated. The presented models for the problem with setup time disjointed from processing time can solve up to 16 machines and 45 jobs. In contrast, this capability is changed to 20 machines and 40 jobs for processing time jointed to the setup time problem. Furthermore, a fix and relax heuristic algorithm is presented for large-size instances, which can solve instances of up to 20 machines and 100 jobs for each of the two considered prob-lems. (c) 2022 The Author(s). Published by Elsevier Ltd on behalf of Association of European Operational Research Societies (EURO). This is an open access article under the CC BY-NC-ND license

关键词： Energy-efficient scheduling mixed-integer linear programming Fix and relax Sequence-dependent setup time Tariffs