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1.
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   

2.
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   

3.
This paper proposes two-stage continuous-time triggered algorithms for solving distributed optimization problems with inequality constraints over directed graphs. The inequality constraints are penalized by adopting log-barrier penalty method. The first stage of the proposed algorithms is capable of finding the optimal point of each local optimization problem in finite time. In the second stage of the proposed algorithms, zero-gradient-sum algorithms with time-triggered and event-triggered communication strategies are considered in order to reduce communication costs. Then, with the help of LaSalle’s invariance principle, it is proved that the state solution of each agent reaches consensus at the optimal point of the considered penalty distributed optimization problem, and Zeno behavior is also excluded. Finally, numerical examples are given to illustrate the effectiveness of the proposed algorithms.  相似文献   

4.
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   

5.
This paper concentrates on a class of decentralized convex optimization problems subject to local feasible sets, equality and inequality constraints, where the global objective function consists of a sum of locally smooth convex functions and non-smooth regularization terms. To address this problem, a synchronous full-decentralized primal-dual proximal splitting algorithm (Syn-FdPdPs) is presented, which avoids the unapproximable property of the proximal operator with respect to inequality constraints via logarithmic barrier functions. Following the proposed decentralized protocol, each agent carries out local information exchange without any global coordination and weight balancing strategies introduced in most consensus algorithms. In addition, a randomized version of the proposed algorithm (Rand-FdPdPs) is conducted through subsets of activated agents, which further removes the global clock coordinator. Theoretically, with the help of asymmetric forward-backward-adjoint (AFBA) splitting technique, the convergence results of the proposed algorithms are provided under the same local step-size conditions. Finally, the effectiveness and practicability of the proposed algorithms are demonstrated by numerical simulations on the least-square and least absolute deviation problems.  相似文献   

6.
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   

7.
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   

8.
Design of an optimal controller requires optimization of multiple performance measures that are often noncommensurable and competing with each other. Design of such a controller is indeed a multi-objective optimization problem. Non-dominated sorting in genetic algorithms-II (NSGA-II) is a popular non-domination based genetic algorithm for solving multi-objective optimization problems. This paper investigates the application of NSGA-II technique for the design of a flexible AC transmission system (FACTS)-based controller. The design objective is to improve the stability of the power system with minimum control effort. The proposed technique is applied to generate Pareto set of global optimal solutions to the given multi-objective optimization problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Further, a detailed analysis on the selection of control signals (both local and remote signals) on the effectiveness of the proposed controller is carried out and simulation results are presented under various loading conditions and disturbances to show the effectiveness and robustness of the proposed approach.  相似文献   

9.
In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms.  相似文献   

10.
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   

11.
In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.  相似文献   

12.
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   

13.
《Journal of The Franklin Institute》2023,360(13):10100-10126
This paper studies the distributed optimal coordinated control problem for Euler–Lagrange multi-agent systems with connectivity preservation. The aim is to force agents to achieve the optimal solution minimizing the sum of the local objective functions while guaranteeing the connectivity of the communication graph. For practical purposes, the gradient vector of the local objective function is allowed to use only at the real-time generalized position instead of at the auxiliary system state. To make the control parameters independent of the global information and guarantee the fully distributed manner of controller, the adaptive control is introduced to update the coupling weights of the relative states among neighbors. Moreover, to reduce the resource for control updates, the event-driven communication is employed for the updates of both the relative states and the gradient of the connectivity-preserving potential function. Based on the Lyapunov analysis framework, it is proved that agents can converge to the optimal solution with connectivity preservation and Zeno behavior is excluded for the two event-triggering conditions. Finally, the effectiveness of the proposed method is verified by a numerical simulation example.  相似文献   

14.
为了有效求解TSP问题,提出一种融合蚁群算法、遗传算法、粒子群优化算法思想的混合算法。该算法基于最大-最小蚁群系统框架,在选择下一个城市时采用局部搜索策略避免陷入局部最优,在每次循环结束时用演化交叉策略优化得到的全局最短路径,从而提高求解TSP问题的求解精度及收敛速度。TSPLIB中不同规模的TSP问题的仿真实验结果表明了该算法的有效性与可行性。  相似文献   

15.
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   

16.
In this paper, the distributed optimal consensus control of a group of Euler-Lagrange systems under input saturation is considered. The objective function is only known by each agent itself. Meanwhile it is assumed that the velocities of the systems are unknown. To solve this problem, the filters and observers are designed for each agent. The magnitudes of the control input could be guaranteed within the bounds which are given in advance. It is shown that global optimal consensus control could be achieved under the proposed bounded controllers. The states of all agents will reach a consensus which minimizes the sum of the objective functions of all agents. Simulation results illustrate the effectiveness of the control schemes.  相似文献   

17.
Collaborative frequent itemset mining involves analyzing the data shared from multiple business entities to find interesting patterns from it. However, this comes at the cost of high privacy risk. Because some of these patterns may contain business-sensitive information and hence are denoted as sensitive patterns. The revelation of such patterns can disclose confidential information. Privacy-preserving data mining (PPDM) includes various sensitive pattern hiding (SPH) techniques, which ensures that sensitive patterns do not get revealed when data mining models are applied on shared datasets. In the process of hiding sensitive patterns, some of the non-sensitive patterns also become infrequent. SPH techniques thus affect the results of data mining models. Maintaining a balance between data privacy and data utility is an NP-hard problem because it requires the selection of sensitive items for deletion and also the selection of transactions containing these items such that side effects of deletion are minimal. There are various algorithms proposed by researchers that use evolutionary approaches such as genetic algorithm(GA), particle swarm optimization (PSO) and ant colony optimization (ACO). These evolutionary SPH algorithms mask sensitive patterns through the deletion of sensitive transactions. Failure in the sensitive patterns masking and loss of data have been the biggest challenges for such algorithms. The performance of evolutionary algorithms further gets degraded when applied on dense datasets. In this research paper, victim item deletion based PSO inspired evolutionary algorithm named VIDPSO is proposed to sanitize the dense datasets. In the proposed algorithm, each particle of the population consists of n number of sub-particles derived from pre-calculated victim items. The proposed algorithm has a high exploration capability to search the solution space for selecting optimal transactions. Experiments conducted on real and synthetic dense datasets depict that VIDPSO algorithm performs better vis-a-vis GA, PSO and ACO based SPH algorithms in terms of hiding failure with minimal loss of data.  相似文献   

18.
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19.
In this paper, we study the problem of decentralized optimization to minimize a finite sum of local convex cost functions over an undirected network. Compared with the existing works, we focus on improving the communication efficiency of the stochastic gradient tracking method and propose an effective event-triggering decentralized stochastic gradient tracking algorithm, namely, ET-DSGT. ET-DSGT utilizes the event-triggering mechanism in which each agent only broadcasts its estimators at the event time to effectively avoid real-time communication, thus improving communication efficiency. In addition, we present a theoretical analysis to show that ET-DSGT with a decaying step-size can converge to the exact global minimum. Moreover, we show that for each agent, the time interval between two successive triggering times is greater than the iteration interval under certain conditions. Finally, we provide several simulations to demonstrate the effectiveness of ET-DSGT.  相似文献   

20.
This paper studies the charging/discharging scheduling problem of plug-in electric vehicles (PEVs) in smart grid, considering the users’ satisfaction with state of charge (SoC) and the degradation cost of batteries. The objective is to collectively determine the energy usage patterns of all participating PEVs so as to minimize the energy cost of all PEVs while ensuring the charging needs of PEV owners. The challenges herein are mainly in three folds: 1) the randomness of electricity price and PEVs’ commuting behavior; 2) the unknown dynamics model of SoC; and 3) a large solution space, which make it challenging to directly develop a model-based optimization algorithm. To this end, we first reformulate the above energy cost minimization problem as a Markov game with unknown transition probabilities. Then a multi-agent deep reinforcement learning (DRL)-based data-driven approach is developed to solve the Markov game. Specifically, the proposed approach consists of two networks: an extreme learning machine (ELM)-based feedforward neural network (NN) for uncertainty prediction of electricity price and PEVs’ commuting behavior and a Q network for optimal action-value function approximation. Finally, the comparison results with three benchmark solutions show that our proposed algorithm can not only adaptively decide the optimal charging/discharging policy by on-line learning process, but also yield a lower energy cost within an unknown market environment.  相似文献   

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