Article
Computer Science, Software Engineering
S. Bastrakov, A. Churkin, N. Yu Zolotykh
Summary: The paper introduces a new method using bit pattern trees to accelerate the elimination of variables from a system of linear inequalities, avoiding extensive enumeration. By utilizing Chernikov rules and bit pattern trees, the proposed algorithm demonstrates competitiveness in computational evaluation.
OPTIMIZATION METHODS & SOFTWARE
(2021)
Article
Computer Science, Software Engineering
Dimitris Bertsimas, Stefan C. M. ten Eikelder, Dick den Hertog, Nikolaos Trichakis
Summary: In this paper, we formalize the concept of Pareto Adaptive Robust Optimality (PARO) for linear two-stage Adaptive Robust Optimization (ARO) problems. We prove the existence of PARO solutions and present approaches for finding and approximating such solutions. We also demonstrate the value of using the Fourier-Motzkin Elimination technique in the analysis of ARO problems.
MATHEMATICAL PROGRAMMING
(2023)
Article
Biochemical Research Methods
Jia-Bao Liu, Muhammad Faisal Nadeem, Mohammad Azeem
Summary: This article discusses the importance of the concepts of partition and resolving sets in various fields of engineering, chemistry, and computer science. It explores the problem of partition dimension in graphs and provides bounds for convex polytopes. The contribution of the article lies in providing bounds for the complexity of computing the exact partition dimension.
COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING
(2022)
Article
Mathematics, Applied
Denghui Wu, Zhen-Hui Bu
Summary: This paper introduces a new concept of (p, q)-projection body, discusses a variant of the L-p Shephard problem, and answers two parts of the question by connecting with L-p projection body and Levy's embedding L-p.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Konrad Engel, Bastian Laasch
Summary: This paper investigates the modulus of Fourier transform of a convex polytope P on a hypersurface S in R^n with wavelength lambda, aiming to reconstruct P or compute its properties. The main analysis tool is an asymptotic formula for the Fourier transform of P as lambda approaches 0. The study is motivated by X-ray scattering of nanoparticles, where the Fourier transform of reflected beam wave vectors is measurable on a half sphere in experiments.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
(2022)
Article
Mathematics, Applied
Feiyu Zhang, Wendi Bao, Weiguo Li, Qin Wang
Summary: In this paper, a nonlinear sampling Kaczmarz-Motzkin (NSKM) method is proposed for solving large-scale nonlinear equations. Convergence of the method is proved under two different assumptions based on the local tangential cone condition and the Jensen's inequality. Two variants of the NSKM method, the projected sampling Kaczmarz-Motzkin (PSKM) method and the accelerated projected sampling Kaczmarz-Motzkin (APSKM) method, are presented for solving nonlinear equations with convex constraints. The convergence analysis is obtained by utilizing the nonexpansive property of the projection and the convergence of the NSKM method. Numerical results demonstrate that the NSKM method outperforms the nonlinear randomized Kaczmarz method in terms of calculation times with a suitable sample size. The APSKM and PSKM methods are practical and promising for constrained nonlinear problems.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Kazuo Murota, Akihisa Tamura
Summary: This paper discusses the important issue of discrete Fenchel duality in discrete convex analysis. It establishes a Fenchel-type min-max formula for a pair of integer-valued integrally convex and separable convex functions, with the proof based on Fourier-Motzkin elimination.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Ravi Kumar Gupta, Vishnu Mohan Mishra, N. K. Singh
Summary: This paper presents a control strategy for parallel operation of inverters to eliminate both DC and AC circulating current. It analyzes the cross-current between parallel connected inverters and proposes control methods to address the issues causing the cross-current. The effectiveness of the proposed control strategy is verified through MATLAB simulation.
ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH
(2022)
Article
Mathematics, Applied
Satoko Moriguchi, Kazuo Murota
Summary: This paper investigates the properties of L-convex sets and L-2-convex sets, as well as their connection to polymatroid intersection. It provides a polyhedral description of L-2-convex sets and reveals that the convex hull of an L-2-convex set is a box-TDI polyhedron. Two different proofs are presented, one relying on the conjugacy theorem in discrete convex analysis and the other based on Fourier-Motzkin elimination. The obtained results can be represented using graphs and have implications in discrete convex analysis.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Software Engineering
Laurence A. Wolsey, Hande Yaman
Summary: In this study, the researchers explore the use of single node flow cover inequalities to give the convex hull for more general mixed integer sets. They specifically focus on the case of a path with fixed capacities and costs for incoming and outgoing arcs at each node. The approach involves characterizing extreme points, deriving tight formulations, and using Fourier-Motzkin elimination for non-trivial projections. The validity of the conjecture for the single node flow set is supported by the results.
MATHEMATICAL PROGRAMMING
(2021)
Article
Mathematics, Applied
Konrad Engel, Bastian Laasch
Summary: The article demonstrates that if two three-dimensional convex polytopes have the same integral values, they can coincide up to translation and/or reflection in a point. This conclusion has practical implications in crystallography for determining the uniqueness of nanoparticles based on their X-ray diffraction patterns.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
(2022)
Article
Mathematics
Albert Chau, Ben Weinkove
Summary: This article focuses on the Dirichlet problem for a class of semilinear equations on two-dimensional convex domains. A sufficient condition for the solution to be concave is provided, which is motivated by an idea of Kosmodem'yanskii and involves comparison with ellipses. Additionally, a result on the propagation of concavity of solutions from the boundary is proven, which holds true in all dimensions.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Stefan Steinerberger
Summary: This article investigates the properties of solutions to the nonlinear Poisson equation under given boundary conditions. The theorem proves that for monotonically increasing concave functions f with small Lipschitz constant, if the second derivative of the solution on the boundary is negative semi-definite, then the solution is concave. Furthermore, the article extends the conjecture of Saint Venant and proves that when the function f is monotonically increasing with a small Lipschitz constant, the solution of the equation achieves its maximum when the domain has a fixed measure.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2022)
Article
Engineering, Electrical & Electronic
Mohammed Ali Khan, Ahteshamul Haque, V. S. Bharath Kurukuru, Huai Wang, Frede Blaabjerg
Summary: This study proposes a control technique to improve the efficiency of distributed generation inverters, which can operate in both grid-connected and stand-alone mode. By using a harmonic elimination pulsewidth modulation scheme, harmonics are eliminated and total harmonic distortions are reduced to enhance performance. The results show that the output voltage is regulated for varying load conditions, with a THD of 2.4% observed under different load conditions.
IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS
(2021)
Article
Green & Sustainable Science & Technology
Haifeng Qiu, Wei Gu, Chao Ning, Xi Lu, Pengxiang Liu, Zhi Wu
Summary: This paper offers a reformulated multistage mixed-integer robust optimization method for regional power grid scheduling. A scheduling model is established considering real-world projects, and a dedicated reformulation algorithm is proposed to solve the intractable multistage mixed-integer robust optimization model. Numerical tests verify the superiority and applicability of the proposed method.
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY
(2023)
Article
Engineering, Multidisciplinary
Chu Sun, Geza Joos, Syed Qaseem Ali, Jean Nicolas Paquin, Carlos Mauricio Rangel, Fares Al Jajeh, Ilja Novickij, Francois Bouffard
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS
(2020)
Article
Engineering, Electrical & Electronic
Chu Sun, Geza Joos, Francois Bouffard
IEEE TRANSACTIONS ON POWER DELIVERY
(2020)
Article
Green & Sustainable Science & Technology
Yuchong Huo, Francois Bouffard, Geza Joos
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY
(2020)
Article
Green & Sustainable Science & Technology
Navdeep Kaur Dhaliwal, Francois Bouffard, Mark J. O'Malley
Summary: The rapid increase of renewable energy adoption in power systems requires flexibility to manage variability and uncertainty. This paper proposes a new approach to plan the dispatchable generation mix of a power system using historical data, bridging the gap between long-term capacity planning and short-term operational needs.
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY
(2021)
Article
Energy & Fuels
Yuchong Huo, Francois Bouffard, Geza Joos
Summary: In this paper, a new method for generating microgrid energy dispatch rule base using decision trees is proposed to match the control performance of full mixed-integer optimization while achieving effectiveness and computational efficiency.
Article
Energy & Fuels
Yuchong Huo, Francois Bouffard, Geza Joos
Summary: This paper applies a flexibility-based operational planning method to microgrid unit commitment, combining learning and explicit model predictive control to address challenges in low-power computing controllers. The proposed approach adjusts computational complexity to meet hardware limitations while maintaining optimality, overcoming drawbacks of traditional methods. Through case studies, the effectiveness of the approach is demonstrated in solving microgrid unit commitment problems.
Article
Engineering, Electrical & Electronic
Xiaoting Wang, Rong-Peng Liu, Xiaozhe Wang, Yunhe Hou, Francois Bouffard
Summary: This letter proposes a data-driven sparse polynomial chaos expansion-based surrogate model for the stochastic economic dispatch problem considering uncertainty from wind power. Simulation studies on an integrated electricity and gas system demonstrate the efficiency and accuracy of the proposed method compared to Monte Carlo simulations.
IEEE TRANSACTIONS ON POWER SYSTEMS
(2022)
Article
Engineering, Electrical & Electronic
Chu Sun, Syed Qaseem Ali, Geza Joos, Francois Bouffard
Summary: A new virtual synchronous machine control approach is proposed in this article, which combines fast-acting and slow-acting energy storage systems to simulate inertia, provide damping, and long-term energy services. An energy recovery control is designed to maintain a constant energy reserve.
IEEE TRANSACTIONS ON POWER ELECTRONICS
(2022)
Article
Energy & Fuels
Imen Jendoubi, Francois Bouffard
Summary: This study proposes a novel RL-based energy management approach for scheduling controllable devices within an electric network. It efficiently solves multi-dimensional, multi-objective, and partially observable power system problems. The novelty lies in the implementation of a hierarchical RL-based control strategy, the introduction of multi-agent reinforcement learning (MARL) for efficient coordination, and the integration of hierarchical RL and MARL theory for a robust control framework. Comparative performance evaluation and experimental results validate the effectiveness of the proposed control framework.
Article
Green & Sustainable Science & Technology
Sayani Seal, Benoit Boulet, Vahid R. Dehkordi, Francois Bouffard, Geza Joos
Summary: This article presents a centralized MPC-based home energy management system (HEMS) that utilizes an electric vehicle (EV) as a mobile energy storage unit. The system controls the zone-based heating system and manages the energy flow among various components including home baseload, home-battery and EV battery charging and discharging, in-house solar energy generation, and storage. A Monte-Carlo based uncertainty analysis is used to evaluate the robustness of the MPC against the randomness in EV arrival and departure schedule. The responsiveness of the centralized MPC is demonstrated through a vehicle to home communication scenario.
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY
(2023)
Article
Energy & Fuels
Imen Jendoubi, Francois Bouffard
Summary: With the ongoing energy transition, electric power and energy systems are becoming increasingly multi-dimensional and complex with higher levels of uncertainty. Reinforcement learning provides a data-driven alternative to traditional model-based control methods, allowing efficient control of such systems without prior system dynamics modeling or predictions. This study proposes a multi-agent deep reinforcement learning-based control framework for solving multi-dimensional power dispatch problems in systems with multiple uncertainties.
SUSTAINABLE ENERGY GRIDS & NETWORKS
(2022)
Article
Computer Science, Information Systems
Huiliang Zhang, Sayani Seal, Di Wu, Francois Bouffard, Benoit Boulet
Summary: Building energy management is crucial for improving system efficiency and reducing greenhouse gas emissions. The challenges and uncertainties in the field have increased with the rise of renewable energy and diverse electrical appliances. While classical model predictive control has been effective, data-driven solutions like data-driven MPC and reinforcement learning-based methods have gained research interest. However, the integration of these methods and the selection of suitable control algorithms require further discussion.
Proceedings Paper
Energy & Fuels
Anindita Golder, Francois Bouffard
Summary: This paper proposes a three-step method for sizing and operating a microgrid, which includes generating typical days representing annual profiles, using a linear optimization problem to select and size microgrid assets, and developing a decision tree-based energy management system based on the design formulation results. These methods are then applied to a remote mine as a case study.
2021 IEEE ELECTRICAL POWER AND ENERGY CONFERENCE (EPEC)
(2021)
Proceedings Paper
Energy & Fuels
Sanja Dzeletovic, Francois Bouffard, Hannah Michalska, Geza Joos
2020 IEEE POWER & ENERGY SOCIETY GENERAL MEETING (PESGM)
(2020)
Proceedings Paper
Energy & Fuels
Chu Sun, Syed Qaseem Ali, Geza Joos, Francois Bouffard
2020 IEEE ENERGY CONVERSION CONGRESS AND EXPOSITION (ECCE)
(2020)
