We focus on the optimal resource allocation problems with global equality constraints and convex function inequality constraints over heterogeneous linear multi-agent systems. The resource allocation problem aims to minimize the total objective function through neighboring information exchange. First, based on the state variable information, Karush-Kuhn-Tucker(KKT) conditions, and proportionalintegral control concept, we propose an initialization-free distributed optimization algorithm, where each agent is driven by the gradient(subgradient) of its local objective function and local constraint convex function. In addition, the penalty factor control parameter is changed adaptively. Next, we propose an output-based distributed optimization algorithm that uses a Luenberger observer when the state variable is not accessible. Based on Lyapunov stability, it is proved that the proposed algorithms converge to the optimal solution of the resource allocation problem. Finally, simulation examples are used to demonstrate the effectiveness of the proposed algorithms.
We study the distributed resource allocation problem for heterogeneous multiagent systems over an undirected graph, an essential issue in multiagent system coordinated control and complex network system control. The decision variable is subject to global equality and local convex set constraints, and the objective is smooth and convex. It aims to minimize the global objective function by exchanging neighboring information between agents. An adaptive distributed algorithm is designed using the distance function-based exact penalty function method. A state- and time-based triggering condition is designed to avoid continuous communication and reduce the communication burden. From a random initial state, the proposed algorithm asymptotically converges to the optimal value by means of LaSalle’s invariance principle. Finally, examples are provided to demonstrate the effectiveness of our algorithm.
Threshold Function (TF) is a subset of Boolean function that can be represented with a single linear threshold gate (LTG). In the research about threshold logic, the identification of TF is an important task that determines whether a given function is a TF or not. In this paper, we propose a sufficient and necessary condition for a function being a TF. With the proposed sufficient and necessary condition, we devise a TF identification algorithm. The experimental results show that the proposed approach saves 80% CPU time for identifying all the 8-input NP-class TFs as compared with the state-of-the-art. Furthermore, the LTGs corresponding to the identified TFs obtained by the proposed approach have smaller weights and threshold values than the state-of-the-art.
As an important indicator for measuring the development level of low-carbon tourism, reducing the carbon emissions of tourism transportation has become an essential strategic goal and task for the sustainable development of tourism. Among many tourism vehicles, high-speed rails have a significant role in reducing the carbon emissions of tourism transportation. To clarify the impact of high-speed rails on the development efficiency of low-carbon tourism, using the relevant data of Zhengzhou urban agglomeration from 2010 to 2020, the DEA-BCC model and the Malmquist index method were used to measure these data. The results show the following: (1) the average comprehensive development efficiency of the Zhengzhou metropolitan high-speed rail for low-carbon tourism is low, and the comprehensive development efficiency of each city varies greatly; (2) the impact of high-speed rails on the development efficiency of low-carbon tourism in some underdeveloped areas is increasing. The impact on the development efficiency of low-carbon tourism in more developed areas is declining; (3) affected by COVID-19, tourism carbon emissions have shown a downward trend, reflecting the importance of low-carbon travel to low-carbon tourism to a certain extent. The research results not only verify the existing research conclusions but also verify the role of high-speed rails in the development of low-carbon tourism, and have practical value with respect to targeted guidance for the development of low-carbon tourism.
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