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1.
《Journal of The Franklin Institute》2022,359(2):1483-1502
In this paper, the distributed optimization problem is investigated by employing a continuous-time multi-agent system. The objective of agents is to cooperatively minimize the sum of local objective functions subject to a convex set. Unlike most of the existing works on distributed convex optimization, here we consider the case where the objective function is pseudoconvex. In order to solve this problem, we propose a continuous-time distributed project gradient algorithm. When running the presented algorithm, each agent uses only its own objective function and its own state information and the relative state information between itself and its adjacent agents to update its state value. The communication topology is represented by a time-varying digraph. Under mild assumptions on the graph and the objective function, it shows that the multi-agent system asymptotically reaches consensus and the consensus state is the solution to the optimization problem. Finally, several simulations are carried out to verify the correctness of our theoretical achievements. 相似文献
2.
《Journal of The Franklin Institute》2022,359(8):3692-3716
This paper considers a nonsmooth constrained distributed convex optimization over multi-agent systems. Each agent in the multi-agent system only has access to the information of its objective function and constraint, and cooperatively minimizes the global objective function, which is composed of the sum of local objective functions. A novel continuous-time algorithm is proposed to solve the distributed optimization problem and effectively characterize the appropriate gain of the penalty function. It should be noted that the proposed algorithm is based on an adaptive strategy to avoid introducing the primal-dual variables and estimating the related exact penalty parameters. Additional, it is demonstrated that the state solution of the proposed algorithm achieves consensus and converges to an optimal solution of the optimization problem. Finally, numerical simulations are given and the proposed algorithm is applied to solve the optimal placement problem and energy consumption problem. 相似文献
3.
《Journal of The Franklin Institute》2019,356(17):10196-10215
This paper deals with the large category of convex optimization problems on the framework of second-order multi-agent systems, where each distinct agent is assigned with a local objective function, and the overall optimization problem is defined as minimizing the sum of all the local objective functions. To solve this problem, two distributed optimization algorithms are proposed, namely, a time-triggered algorithm and an event-triggered algorithm, to make all agents converge to the optimal solution of the optimization problem cooperatively. The main advantage of our algorithms is to remove unnecessary communications, and hence reduce communication costs and energy consumptions in real-time applications. Moreover, in the proposed algorithms, each agent uses only the position information from its neighbors. With the design of the Lyapunov function, the criteria about the controller parameters are derived to ensure the algorithms converge to the optimal solution. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithms. 相似文献
4.
《Journal of The Franklin Institute》2022,359(16):9401-9421
This paper develops a distributed reconstruction algorithm, that can be implemented efficiently, for time-varying graph signals. The reconstruction problem is formulated as an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and the regularization term. The regularizer used is the nonsmoothness measure of the temporal difference signal. The classical Newton’s method can be used to solve the optimization problem. However, computation of the Hessian matrix inverse is required, and this does not scale well with the graph size. Furthermore, a distributed implementation is not possible. An approximation to the inverse Hessian, that exploits the graph topology, is developed here. The resulting iterative algorithm can be implemented in a distributed manner, and scales well with the graph size. Convergence analysis of the algorithm is presented, which shows convergence to the global optimum. Numerical results, using both synthetic and real world datasets, will demonstrate the superiority of the proposed reconstruction algorithm over existing methods. 相似文献
5.
Target localization is an important problem in distributed multiple-input multiple-output (MIMO) radar systems. In this paper, a new algorithm using bistatic range measurements is developed for target localization in distributed MIMO radars. Unlike most existing schemes, the proposed algorithm firstly applies semidefinite relaxation to convert the maximum likelihood localization problem into a convex optimization problem. Subsequently, a novel procedure is devised to improve the solution accuracy of the convex optimization problem. Our scheme exhibits evidently better threshold behavior than the state-of-the-art approaches. Moreover, it does not require any initial estimate of the target position. Simulation results verify the superiority of the proposed algorithm over various existing methods. 相似文献
6.
《Journal of The Franklin Institute》2022,359(18):11135-11154
A class of resource allocation problems with equality constraint are considered in this paper, such as economic dispatch problem in smart grid systems, which is essentially an optimization problem. Inspired by the Lagrange multiplier method, the resource allocation problem is transformed into a multi-agent consensus problem for large-scale networked distributed nodes. A consensus-based distributed fixed-time optimization algorithm is presented, where the information exchange network is depicted by a strongly connected and weight-balanced digraph. This type of communication network can ensure that the equality constraint always holds. Moreover, a new globally fixed-time stability theorem for nonlinear systems is first given in this paper. Based on this theorem and consensus theory, the optimal resource allocation scheme can be given in a fixed time. Finally, the application and comparison of the designed algorithm show that the algorithm can effectively solve the allocation problem of power resources such as economic dispatch. 相似文献
7.
We consider the problem of placing copies of objects in a distributed web server system to minimize the cost of serving read and write requests when the web servers have limited storage capacities. We formulate the problem as a 0–1 optimization problem and present a hybrid particle swarm optimization algorithm to solve it. The proposed hybrid algorithm makes use of the strong global search ability of particle swarm optimization (PSO) and the strong local search ability of tabu search to obtain high quality solutions. The effectiveness of the proposed algorithm is demonstrated by comparing it with the genetic algorithm (GA), simple PSO, tabu search, and random placement algorithm on a variety of test cases. The simulation results indicate that the proposed hybrid approach outperforms the GA, simple PSO, and tabu search. 相似文献
8.
《Journal of The Franklin Institute》2021,358(13):6741-6758
In this paper, a distributed time-varying convex optimization problem with inequality constraints is discussed based on neurodynamic system. The goal is to minimize the sum of agents’ local time-varying objective functions subject to some time-varying inequality constraints, each of which is known only to an individual agent. Here, the optimal solution is time-varying instead of constant. Under an undirected and connected graph, a distributed continuous-time consensus algorithm is designed by using neurodynamic system, signum functions and log-barrier penalty functions. The proposed algorithm can be understood through two parts: one part is used to reach consensus and the other is used to achieve gradient descent to track the optimal solution. Theoretical studies indicate that all agents will achieve consensus and the proposed algorithm can track the optimal solution of the time-varying convex problem. Two numerical examples are provided to validate the theoretical results. 相似文献
9.
10.
《Journal of The Franklin Institute》2022,359(17):10267-10280
This paper investigates the distributed prescribed- time optimization for time-varying objective functions. As opposed to the state-of-the-art in this field, our protocol is developed upon the methodology of time-domain transformation, based on which original prescribed-time problem is simplified as uniformly bounded counterpart in new spatiotemporal coordinate. Compared with the finite- and fixed-time works, the settling time of both consensus and optimization is independent of initial states as well as other parameters and therefore can be completely prespecified. Besides, the selection of parameters is free of any global information, which implies its feasibility in even fully distributed scenarios. Finally, a simulation is performed on cooperative hunting problem to validate the effectiveness of theoretical results. 相似文献
11.
Aijuan Wang Wanping Liu Tiehu Li Tingwen Huang 《Journal of The Franklin Institute》2021,358(6):3033-3050
This paper proposes a privacy-preserving consensus algorithm which enables all the agents in the directed network to eventually reach the weighted average of initial states, and while preserving the privacy of the initial state of each agent. A novel privacy-preserving scheme is proposed in our consensus algorithm where initial states are hidden in random values. We also develop detailed analysis based on our algorithm, including its convergence property and the topology condition of privacy leakages for each agent. It can be observed that final consensus point is independent of their initial values that can be arbitrary random values. Besides, when an eavesdropper exists and can intercept the data transmitted on the edges, we introduce an index to measure the privacy leakage degree of agents, and then analyze the degree of privacy leakage for each agent. Similarly, the degree for network privacy leakage is derived. Subsequently, we establish an optimization problem to find the optimal attacking strategy, and present a heuristic optimization algorithm based on the Sequential Least Squares Programming (SLSQP) to solve the proposed optimization problem. Finally, numerical experiments are designed to demonstrate the effectiveness of our algorithm. 相似文献
12.
This paper studies adaptive optimization problem of continuous-time multi-agent systems. Multi-agents with second-order dynamics are considered. Each agent is equipped with a time-varying cost function which is known only to an individual agent. The objective is to make multi-agents velocities minimize the sum of local functions by local interaction. First, a distributed adaptive algorithm is presented, in which each agent depends only on its own velocity and neighbors velocities. It is indicated that all agents can track the optimal velocity. Then we apply the distributed adaptive algorithm to flocking of multi-agents. It is proved that all agents can track the optimal trajectory. The agents will maintain connectivity and avoid the inter-agent collision. Finally, two simulations are included to illustrate the results. 相似文献
13.
《Journal of The Franklin Institute》2023,360(8):5333-5353
In recent years, distributed algorithms have been increasingly used to solve the economic dispatch (ED) problem of multi-energy systems (MES) due to the advantages of high flexibility, strong robustness, and privacy. However, the MES based on the distributed optimization architecture must bear higher cyber-attack risks, so as to maintain the safe and stable operation of MES. To address this issue, an event-triggered fully distributed algorithm is proposed to solve the ED problem, which can effectively mitigate the communication burden. On this basis, an attack resilient strategy against false data injection (FDI) attacks is implemented in the proposed fully distributed algorithm, which can eliminate incorrect measurement of incremental cost and power generation data caused by cyber-attacks. In addition, a reputation value protocol embedded in the proposed attack resilient strategy is designed to effectively reduce the potential of direct isolation of the node. Finally, case studies are given in this paper to validate the effectiveness of the proposed distributed control scheme on a 9-bus MES. 相似文献
14.
In this paper, the distributed optimization problem over multi-cluster networks is considered. Different from the existing works, this paper studies the optimization algorithm under uncoordinated step sizes. More specifically, by combining a random sleep strategy and the round-robin communication among clusters, a new hierarchical algorithm is developed to solve the considered problem. In the proposed algorithm, the random sleep strategy enables each agent to independently choose either performing the projected subgradient descent, or keeping the previous estimate by a Bernoulli decision, based on which the step size of each agent is selected as an uncoordinated form that only relates to the independent Bernoulli decision variable. Technically, by introducing a key definition on the algorithm history, it is proven that the estimates of the proposed algorithm can converge to the optimal solution even with the uncoordinated step sizes. In addition, we also study the convergence performance of the proposed algorithm with simpler constant step sizes. In this case, it is proven that the random sleep strategy can efficiently improve the convergence accuracy of the algorithm. Finally, the theoretical findings are verified via simulation examples. 相似文献
15.
F.F. Shoji 《Journal of The Franklin Institute》1982,313(5):267-271
This brief communication establishes a two-step iterative algorithm based on the orthogonal projection for reducing order of the high-order system transfer function or state variable equations. A two-step iterative algorithm which has been developed by the authors (1) consists of the residue and pole (or eigenvalue) optimization with respect to the objective function. Here, the optimum residues in the first step can be determined by using the reciprocal basis in the projection theorem. The reciprocal basis allows one to avoid performing the Grammian inversion. Selecting the new basis, the optimum poles in the second step can be also applied for the orthogonal projection. Although the resulting reduced-order models derived from this geometrical point of view are consistent with models of a two-step iterative algorithm, the algorithm is thus a computationally much simpler way to derive the formula. 相似文献
16.
Yibing Sun Minyue Fu Bingchang Wang Huanshui Zhang 《Journal of The Franklin Institute》2017,354(14):6200-6216
In this paper, we consider a distributed dynamic state estimation problem for time-varying systems. Based on the distributed maximum a posteriori (MAP) estimation algorithm proposed in our previous study, which studies the linear measurement models of each subsystem, and by weakening the constraint condition as that each time-varying subsystem is observable, this paper proves that the error covariances of state estimation and prediction obtained from the improved algorithm are respectively positive definite and have upper bounds, which verifies the feasibility of this algorithm. We also use new weighting functions and time-varying exponential smoothing method to ensure the robustness and improve the forecast accuracy of the distributed state estimation method. At last, an example is used to demonstrate the effectiveness of the proposed algorithm together with the parameter identification. 相似文献
17.
In a multi-agent framework, distributed optimization problems are generally described as the minimization of a global objective function, where each agent can get information only from a neighborhood defined by a network topology. To solve the problem, this work presents an information-constrained strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the so-called distributed replicator equation (DRE) converges to an optimal global outcome by means of the local-information exchange subject to the topological constraints of the graph. To show the application of the proposed strategy, we implement the DRE to solve an economic dispatch problem with distributed generation. We also present some simulation results to illustrate the theoretic optimality and stability of the equilibrium points and the effects of typical network topologies on the convergence rate of the algorithm. 相似文献
18.
TSP问题是一类典型的NP完全问题,禁忌搜索算法是解决此类问题的智能优化方法之一。文章在研究了禁忌搜索算法的基本原理和算法步骤的基础上,建立了求解TSP问题的数学模型,设计了一个求解TSP问题的禁忌搜索算法程序,并进行了实验测试,实验结果表明,禁忌搜索算法能够有效地解决TSP问题。 相似文献
19.
Youcheng Niu Haijing Wang Zheng Wang Dawen Xia Huaqing Li 《Journal of The Franklin Institute》2019,356(16):9763-9787
This paper investigates distributed convex optimization problems over an undirected and connected network, where each node’s variable lies in a private constrained convex set, and overall nodes aim at collectively minimizing the sum of all local objective functions. Motivated by a variety of applications in machine learning problems with large-scale training sets distributed to multiple autonomous nodes, each local objective function is further designed as the average of moderate number of local instantaneous functions. Each local objective function and constrained set cannot be shared with others. A primal-dual stochastic algorithm is presented to address the distributed convex optimization problems, where each node updates its state by resorting to unbiased stochastic averaging gradients and projects on its private constrained set. At each iteration, for each node the gradient of one local instantaneous function selected randomly is evaluated and the average of the most recent stochastic gradients is used to approximate the true local gradient. In the constrained case, we show that with strong-convexity of the local instantaneous function and Lipschitz continuity of its gradient, the algorithm converges to the global optimization solution almost surely. In the unconstrained case, an explicit linear convergence rate of the algorithm is provided. Numerical experiments are presented to demonstrate correctness of the theoretical results. 相似文献
20.
《Information processing & management》2023,60(2):103175
Task assignment, the core problem of Spatial Crowdsourcing (SC), is often modeled as an optimization problem with multiple constraints, and the quality and efficiency of its solution determines how well the SC system works. Fairness is a critical aspect of task assignment that affects worker participation and satisfaction. Although the existing studies on SC have noticed the fairness problem, they mainly focus on fairness at the individual level rather than at the group level. However, differences among groups in certain attributes (e.g. race, gender, age) can easily lead to discrimination in task assignment, which triggers ethical issues and even deteriorates the quality of the SC system. Therefore, we study the problem of task assignment with group fairness for SC. According to the principle of fair budget allocation, we define a well-designed constraint that can be considered in the task assignment problem of SC systems, resulting in assignment with group fairness. We mainly consider the task assignment problem in a common One-to-One SC system (O2-SC), and our goal is to maximize the quality of the task assignment while satisfying group fairness and other constraints such as budget and spatial constraints. Specifically, we first give the formal definition of task assignment with group fairness constraint for O2-SC. Then, we prove that it is essentially an NP-hard combinatorial optimization problem. Next, we provide a novel fast algorithm with theoretical guarantees to solve it. Finally, we conduct extensive experiments using both synthetic and real datasets. The experimental results show that the proposed constraint can significantly improve the group fairness level of algorithms, even for a completely random algorithm. The results also show that our algorithm can efficiently and effectively complete the task assignment of SC systems while ensuring group fairness. 相似文献