We discuss an online decentralized decision making problem where the agents are coupled with affine inequality constraints. Alternating Direction Method of Multipliers (ADMM) is used as the computation engine and we d...
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We discuss an online decentralized decision making problem where the agents are coupled with affine inequality constraints. Alternating Direction Method of Multipliers (ADMM) is used as the computation engine and we discuss the convergence of the algorithm in an online setting. To be specific, when decisions have to be made sequentially with a fixed time step, there might not be enough time for the ADMM to converge before the scenario changes and the decision needs to be updated. In this case, a suboptimal solution is employed and we analyze the optimality gap given the convergence condition. Moreover, in many cases, the decision making problem changes gradually over time. We propose a warm-start scheme to accelerate the convergence of ADMM and analyze the benefit of the warm-start. The proposed method is demonstrated in a decentralized multiagent control barrier function problem with simulation.
Wastewater treatment plants (WWTPs) are energy intensive facilities. Controlling energy use in WWTPs could bring substantial benefits to people and environment. Understanding how energy efficient the wastewater treatm...
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Wastewater treatment plants (WWTPs) are energy intensive facilities. Controlling energy use in WWTPs could bring substantial benefits to people and environment. Understanding how energy efficient the wastewater treatment process is and what drives efficiency would allow treating wastewater in a more sustainable way. In this study, we employed the efficiency analysis trees approach, that combines machine learning and linear programming techniques, to estimate energy efficiency of wastewater treatment process. The findings indicated that considerable energy inefficiency among WWTPs in Chile existed. The mean energy efficiency was 0.287 suggesting that energy use should cut reduce by 71.3 % to treat the same volume of wastewater. This was equivalent to a reduction in energy use by 0.40 kWh/m3 on average. Moreover, only 4 out of 203 assessed WWTPs (1.97 %) were identified as energy efficient. It was also found that the age of treatment plant and type of secondary technology played an important role in explaining energy efficiency variations among WWTPs.
linear programming (LP) has been well studied in the scientific community for various engineering applications such as network flow problems, packet routing, portfolio optimization, and financial data management, etc....
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ISBN:
(纸本)9781479936311
linear programming (LP) has been well studied in the scientific community for various engineering applications such as network flow problems, packet routing, portfolio optimization, and financial data management, etc. In this paper, we first utilize the sparse matrix to investigate secure outsourcing for large-scale LP systems, which is considered as a prohibitively expensive computation for the clients with resource-constraint devices. Besides, we propose a secure and practical scheme which is suitable for any LP problem (feasible, infeasible or unbounded) even in the fully malicious model. Compared with the state-of-the-art algorithm [30], our proposed algorithm only requires O(n~2) computational overhead instead of O(n~ρ) for 2 < ρ ≤ 3. Furthermore, the client C can detect the misbehavior of cloud server S with the (optimal) probability 1 under the computational complexity of O(n).
Industrial electricity consumers with flexible demand can profit from adjusting their load to short-term prices or by providing balancing services to the grid. Markets which support this kind of short-term position ad...
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Industrial electricity consumers with flexible demand can profit from adjusting their load to short-term prices or by providing balancing services to the grid. Markets which support this kind of short-term position adjustment are the day-ahead market and balancing markets. We propose a formulation for a combined optimization model that computes an optimal distribution of flexibility between the balancing and day-ahead markets. The optimal solution also includes the specific bids for the day-ahead and balancing markets. Besides the expected profits of each market and their different rules for bidding, our model also takes their different roles in a continuous marketing of flexibility into account. To prevent overrating short-term profits we introduce a variable penalty term that adds a cost to unfavorable load schedules. We evaluate the optimization model in a rolling horizon case study based on the setting of a virtual battery at TRIMET Aluminum SE, which is derived from a flexible aluminum electrolysis process. For such a battery we compute a daily optimal split of flexibility and trading decisions based on data in the period 04/2021-03/2022. We show that the optimal split is more profitable than using only one market or a fixed split between the markets.
We provide novel dissipativity conditions for bounding the incremental L1 gain of systems. Moreover, we adapt existing results on the Lgain to the incremental setting and relate the incremental L1 and Lgain bounds thr...
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We provide novel dissipativity conditions for bounding the incremental L1 gain of systems. Moreover, we adapt existing results on the Lgain to the incremental setting and relate the incremental L1 and Lgain bounds through transposed systems. Building on work on optimization based approaches to constructing polyhedral Lyapunov functions, we make use of these conditions to obtain a linear programming based algorithm that can provide increasingly sharp bounds on the gains as a function of a given candidate polyhedral storage function or polyhedral set. The algorithm is also extended to allow for the design of constrained linear feedback controllers for performance, as measured by the bounds on the incremental gains. We apply the algorithm to a couple of numerical examples to illustrate the power, as well as some limitations, of this approach. & COPY;2023 Elsevier B.V. All rights reserved.
Abstract—In this paper the Adjustable Robust Maximum Flow Problem (ARMFP) is discussed. The problem is considered as a two-stage optimization problem with two kinds of variables, i.e., adjustable and non-adjustable v...
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Currently, unsupervised hyperspectral image (HSI) segmentation methods are mainly implemented by clustering. Nevertheless, hyperspectral data contain a large amount of noise during the acquisition process, resulting i...
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Currently, unsupervised hyperspectral image (HSI) segmentation methods are mainly implemented by clustering. Nevertheless, hyperspectral data contain a large amount of noise during the acquisition process, resulting in an abnormal distribution of many pixel points. Traditional clustering algorithms suffer from inaccurate segmentation when dealing with these data. For example, FCM is sensitive to anomalies in the clustering problem of HSI, which makes the clustering accuracy degraded. To address these problems, this letter proposes a method called fuzzy C-multiple-means (FCMM). The method divides data points with multiple subclusters into defined c clusters. Different from the bottom-up coalescent strategy, the proposed FCMM transforms the problem of merging multiple subclusters into an optimization problem for the fuzzy affiliation matrix and updates the partitioning of the q subclusters and c classes by an alternating iterative update method. This enhances the robustness of the algorithm and reduces the effect of outliers in the HSI datasets on the FCMM, which provides superior clustering results. Experiments on several HSI datasets validate the effectiveness of FCMM.
This paper considers a network of agents whose objective is for the aggregate of their states to converge to a solution of a linear program. We assume that each agent has limited information about the problem data and...
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ISBN:
(纸本)9781467360890
This paper considers a network of agents whose objective is for the aggregate of their states to converge to a solution of a linear program. We assume that each agent has limited information about the problem data and communicates with other agents at discrete times of its choice. Our main contribution is the development of a distributed continuous-time dynamics and a set of state-based rules, termed triggers, that an individual agent can use to determine when to broadcast its state to neighboring agents to ensure convergence. Our technical approach to the algorithm design and analysis overcomes a number of challenges, including establishing convergence in the absence of a common smooth Lyapunov function, ensuring that the triggers are detectable by agents using only local information, and accounting for the asynchronism in the state broadcasts of the agents. Simulations illustrate our results.
In this paper, we present a new algorithm for '/ solving linear programs that requires only Õ(√rank(A)L) iterations where A is the constraint matrix of a linear program with m constraints, n variables, and b...
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In this paper, we present a new algorithm for '/ solving linear programs that requires only Õ(√rank(A)L) iterations where A is the constraint matrix of a linear program with m constraints, n variables, and bit complexity L. Each iteration of our method consists of solving Õ(1) linear systems and additional nearly linear time computation. Our method improves upon the previous best iteration bounds by factor Ω̃((m/rank (A))) 1/4 ) of for methods with polynomial time computable iterations and by Ω̃((m/rank (A)) 1/2 ) for methods which solve at most Õ(1) linear systems in each iteration each achieved over 20 years ago. Applying our techniques to the linear program formulation of maximum flow yields an Õ(|E| √|V| log 2 U) time algorithm for solving the maximum flow problem on directed graphs with |E| edges, |V| vertices, and capacity ratio U. This improves upon the previous fastest running time of O(|E| min{|E| 1/2 , |V| 2/3 } log (|V| 2 /|E|) log(U)) achieved over 15 years ago by Goldberg and Rao and improves upon the previous best running times for solving dense directed unit capacity graphs of Õ(|E| min{|E| 1/2 , |V| 2/3 }) achieved by Even and Tarjan over 35 years ago and a running time of Õ(|E| 10/7 ) achieved recently by Madry.
Feature selection represents a major challenge in the biomedical data mining problem, and numerous algorithms have been proposed to select an optimal subset of features with the best classification performance. Howeve...
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ISBN:
(纸本)9781479972951
Feature selection represents a major challenge in the biomedical data mining problem, and numerous algorithms have been proposed to select an optimal subset of features with the best classification performance. However, the existing algorithms do not take into account the vast amount of biomedical knowledge from the literature and experienced researchers. This work proposes a novel feature selection algorithm, cLP, with the optimized binary classification accuracy. The proposed algorithm incorporates the biomedical knowledge as constraints in the linear programming based optimization model. The experimental data shows that cLP outperforms the other feature selection algorithms, and its constrained version performs similarly well with the unconstrained version. Although theoretically constraints will reduce the classification model performance, our data shows that the constrained cLP sometimes even outperforms the unconstrained version. This suggests that besides the benefit of including biomedical knowledge in the model, the constrained cLP may also achieve better classification performance.
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