Robust fixed-time consensus protocols for multi-agent systems with nonlinear state measurements

This paper solves the robust fixed-time consensus problem for multi-agent systems with nonlinear state measurements. Sufficient conditions are established for the proposed protocol to reach fixed-time consensus under time-varying undirected and fixed directed topology with the aid of Lyapunov functions. It is proved that the finite settling time of the presented protocol for robust consensus is uniformly bounded for any initial condition, which makes it possible for people to design and estimate the convergence time off-line. Numerical simulations are preformed to show the effectiveness of our proposed protocol.     

Distributed multi-agent optimization with state-dependent communication

We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents over a randomly varying network topology to update his information state. We assume a state-dependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents. We study a projected multi-agent subgradient algorithm under state-dependent communication. The state-dependence of the communication introduces significant challenges and couples the study of information exchange with the analysis of subgradient steps and projection errors. We first show that the multi-agent subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one. Under some assumptions on the stepsize sequence, we provide convergence rate bounds on a “disagreement metric” between the agent estimates. Our bounds are time-nonhomogeneous in the sense that they depend on the initial starting time. Despite this, we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization problem with probability one under different assumptions on the local constraint sets and the stepsize sequence.     

Bandwidth packing with priority classes

The bandwidth packing problem is defined as the selection and routing of messages from a given list of messages with prespecified requirements on demand for bandwidth. The messages have to be routed over a network with given topology so that the generated revenue is maximized. Messages to be routed are classified into two priority classes. An integer programming based formulation of this problem is proposed and a Lagrangean relaxation based methodology is described for solving this problem. A general purpose heuristic is then developed for generating feasible solutions of good quality. Several numerical experiments are conducted using a number of problem parameters such as number of messages, ratio of messages for lower and higher priority classes, capacity of links, and demand distribution of messages belonging to different classes and high quality solutions to the priority bandwidth packing problem are generated under the different situations.     

Impulsive control for one-side Lipschitz nonlinear MASs under semi-Markovian switching topologies with partially unknown transition probabilities

This article addresses the consensus problem of impulsive control for the multi-agent systems under uncertain semi-Markovian switching topologies. Considering the control and information exchanging cost in the implementation of multi-agent systems, an impulsive control protocol is developed not only to relieve the network burden but address the consensus problem. In addition, globally Lipschitz condition, as required in many existing literatures, is not needed in this article, so we introduce one-side Lipschitz condition to loosen the constraint of Lipschitz constant and widen the range of nonlinear application. According to cumulative distribution functions and Lyapunov functional, sufficient criteria are derived for the mean square consensus of multi-agent systems. It is shown that the impulsive sequence is not only inconsistent with switching sequence but also mode-dependent. Finally, simulation results are given to validate the superiority of the theoretical results.     

Multistate components assignment problem with optimal network reliability subject to assignment budget

The typical assignment problem for finding the optimal assignment of a set of components to a set of locations in a system has been widely studied in practical applications. However, this problem mainly focuses on maximizing the total profit or minimizing the total cost without considering component’s failure. In practice, each component should be multistate due to failure, partially failure, or maintenance. That is, each component has several capacities with a probability distribution and may fail. When a set of multistate components is assigned to a system, the system can be treated as a stochastic-flow network. The network reliability is the probability that d units of homogenous commodity can be transmitted through the network successfully. The multistate components assignment problem to maximize the network reliability is never discussed. Therefore, this paper focuses on solving this problem under an assignment budget constraint, in which each component has an assignment cost. The network reliability under a components assignment can be evaluated in terms of minimal paths and state-space decomposition. Subsequently an optimization method based on genetic algorithm is proposed. The experimental results show that the proposed algorithm can be executed in a reasonable time.     

A self-tuning heuristic for the design of communication networks

This paper addresses the design of communication networks that has a large application area. The problem is to design a minimum cost network subject to a given reliability level. Complexity of the problem is twofold: (1) finding a minimum-cost network topology that every pair of nodes can communicate with each other and (2) computing overall reliability to provide the reliability constraint. Over the last two decades, metaheuristic algorithms have been widely applied to solve this problem due to its NP-hardness. In this study, a self-tuning heuristic (STH), which is a new approach free from parameter tuning, is applied to the design of communication networks. Extensive computational results confirm that STH generates superior solutions to the problem in comparison to some well-known local search metaheuristics, and also more sophisticated metaheuristics proposed in the literature. The practical advantage of STH lies in both its effectiveness and simplicity in application to the design problem.     

Distributed impulsive control consensus for a class of unknown nonlinear multi-agent systems based on event-triggered scheme

In this study, we are concerned with the impulsive consensus control problem for a class of nonlinear multi-agent systems (MASs) which have unknown dynamics and directed communication topology. The neural networks (NNs) method is the first utilized to construct distributed event-triggered impulsive consensus protocol. In contrast to the existing impulsive consensus protocol, the consensus protocol proposed in this paper does not need the dynamics of agents, which enhances the system robustness, and realizes distributed event-triggered communication between agents, which can reduce unnecessary consumption of communication resources. Sufficient conditions are derived to ensure the consensus of the controlled MASs and the exclusion of Zeno-behavior. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control protocol.     

Homological and topological properties of locally indicable groups

The classes of locally indicable groups, conservative groups andD-groups have each been defined in a different context, and have been studied for various reasons. These three classes are shown to coincide. The corresponding mod p versions of the classes are also shown to coincide, for any prime p. Applications to topology are given. In particular, new light is shed on work of Adams on a problem of Whitehead concerning asphericity in 2-complexes.     

Naming Game with Multiple Hearers

A new model called Naming Game with Multiple Hearers (NGMH) is proposed in this paper. A naming game over a population of individuals aims to reach consensus on the name of an object through pair-wise local interactions among all the individuals. The proposed NGMH model describes the learning process of a new word, in a population with one speaker and multiple hearers, at each interaction towards convergence. The characteristics of NGMH are examined on three types of network topologies, namely ER random-graph network, WS small-world network, and BA scale-free network. Comparative analysis on the convergence time is performed, revealing that the topology with a larger average (node) degree can reach consensus faster than the others over the same population. It is found that, for a homogeneous network, the average degree is the limiting value of the number of hearers, which reduces the individual ability of learning new words, consequently decreasing the convergence time; for a scale-free network, this limiting value is the deviation of the average degree. It is also found that a network with a larger clustering coefficient takes longer time to converge; especially a small-word network with smallest rewiring possibility takes longest time to reach convergence. As more new nodes are being added to scale-free networks with different degree distributions, their convergence time appears to be robust against the network-size variation. Most new findings reported in this paper are different from that of the single-speaker/single-hearer naming games documented in the literature.     

Software rejuvenation and resource reservation policies for optimizing server resource availability using cyclic nonhomogeneous Markov chains

Software rejuvenation is modeled in a client–server system, which provides resources to priority classes of users. To assure availability, resource reservation policies are adopted for the higher priority classes. In addition software rejuvenation is proposed to optimize resource availability. The system is modeled by a cyclic nonhomogeneous Markov chain to capture the variation of the arrival and service rates during a day period. An optimization problem is solved based on a similar previous work and given the optimal resource reservation policy obtained by its solution, rejuvenation is performed and the optimal rejuvenation policy is determined. As a measure of resource availability the blocking probability of each priority class is used. Performability indicators expressing the total cost are also derived, with respect to the optimal resource reservation and optimal rejuvenation policies, to examine whether rejuvenation benefits the system in terms of cost. To derive the blocking probabilities, the limiting probability distribution is computed using explicit generalized approximate inverse preconditioning for solving efficiently sparse linear systems of algebraic equations. Copyright © 2012 John Wiley & Sons, Ltd.     

A ring-mesh topology design problem for optical transport networks

This paper deals with a ring-mesh network design problem arising from the deployment of an optical transport network. The problem seeks to find an optimal clustering of traffic demands in the network such that the total cost of optical add-drop multiplexer (OADM) and optical cross-connect (OXC) is minimized, while satisfying the OADM ring capacity constraint, the node cardinality constraint, and the OXC capacity constraint. We formulate the problem as an integer programming model and propose several alternative modeling techniques designed to improve the mathematical representation of the problem. We then develop various classes of valid inequalities to tighten the mathematical formulation of the problem and describe an algorithmic approach that coordinates tailored routines with a commercial solver CPLEX. We also propose an effective tabu search procedure for finding a good feasible solution as well as for providing a good incumbent solution for the column generation based heuristic procedure that enhances the solvability of the problem. Computational results exhibit the viability of the proposed method.     

A variable neighbourhood search algorithm for the constrained task allocation problem

A variable neighbourhood search algorithm that employs new neighbourhoods is proposed for solving a task allocation problem whose main characteristics are: (i) each task requires a certain amount of resources and each processor has a capacity constraint which limits the total resource of the tasks that are assigned to it; (ii) the cost of solution includes fixed costs when using processors, task assignment costs, and communication costs between tasks assigned to different processors. A computational study shows that the algorithm performs well in terms of time and solution quality relative to other local search procedures that have been proposed.     

Optimal server resource reservation policies for priority classes of users under cyclic non-homogeneous markov modeling

Resource availability optimization is studied on a server–client system where different users are partitioned into priority classes. The aim is to provide higher resource availability according to the priority of each class. For this purpose, resource reservation is modeled by a homogeneous continuous time Markov chain (CTMC), but also by a cyclic non-homogeneous Markov chain (CNHMC) as there is a cyclic behavior of the users’ requests for resources. The contribution of the work presented consists in the formulation of a multiobjective optimization problem for both the above cases that aims to determine the optimal resource reservation policy providing higher levels of resource availability for all classes. The optimization problem is solved either with known methods or with a proposed kind of heuristic algorithm. Finally, explicit generalized approximate inverse preconditioning methods are adopted for solving efficiently sparse linear systems that are derived, in order to compute resource availability.     

抢占型优先服务机制下多类排队网络的扩散逼近

证明一个满负荷交通极限定理以证实在抢占型优先服务机制下多类排队网络的扩散逼近,进而为该系统提供有效的随机动力学模型．所研究的排队网络典型地出现在现代通讯系统中高速集成服务分组数据网络,其中包含分组数据包的若干交通类型,每个类型涉及若干工作处理类（步骤）,并且属于同一交通类型的工作在可能接受服务的每一个网站被赋予相同的优先权等级,更进一步地,在整个网络中,属于不同交通类型的分组数据包之间无交互路由．     

Optimal allocation of stock levels and stochastic customer demands to a capacitated resource

This paper considers a new class of stochastic resource allocation problems that requires simultaneously determining the customers that a capacitated resource must serve and the stock levels of multiple items that may be used in meeting these customers’ demands. Our model considers a reward (revenue) for serving each assigned customer, a variable cost for allocating each item to the resource, and a shortage cost for each unit of unsatisfied customer demand in a single-period context. The model maximizes the expected profit resulting from the assignment of customers and items to the resource while obeying the resource capacity constraint. We provide an exact solution method for this mixed integer nonlinear optimization problem using a Generalized Benders Decomposition approach. This decomposition approach uses Lagrangian relaxation to solve a constrained multi-item newsvendor subproblem and uses CPLEX to solve a mixed-integer linear master problem. We generate Benders cuts for the master problem by obtaining a series of subgradients of the subproblem’s convex objective function. In addition, we present a family of heuristic solution approaches and compare our methods with several MINLP (Mixed-Integer Nonlinear Programming) commercial solvers in order to benchmark their efficiency and quality.     

Analysis and stability of consensus in networked control systems

In this paper, the consensus problem in networks of integrators is investigated. After recalling the classical diffusive protocol, we present in a unified framework some results on the rate of convergence previously presented in the literature. Then, we introduce two switching communication protocols, one based on a switching coupling law between neighboring nodes, the other on the conditional activation of links in the network. We show that the former protocol induces the monotonicity of each system in the network, enhancing the speed of convergence to consensus. Moreover, adopting this novel protocol, we are able to control the network, steering the nodes’ dynamics to a desired consensus value. The aim of the latter protocol is instead to select adaptively the activation of the edges of the network, in accordance with the dynamics of the network. After showing the effectiveness of both approaches through numerical simulations, the stability properties of these protocols are discussed.     

On scheduling with the non-idling constraint

In this paper, we give an overview of the main results obtained on the complexity of scheduling under the non-idling constraint, i.e, when the jobs assigned to each machine must be processed with no intermediate delay. That constraint is met in practice when the cost of intermediate idle time is too high due to the idle time itself and/or the machine restarting. The non idling constraint is a strong constraint that often needs a new solving approach and most results about classical scheduling problems do not easily extend to the non-idling variant of the problem. In this survey, we mainly consider the non-idling variants of the basic scheduling problems. So, we first present basic properties, complexity results and some algorithms concerning the one-machine non-idling scheduling problem. Then we consider the $m$ -machine non idling scheduling problem. We show that a few basic problems may be solved by rather easy extensions of the algorithm solving their classical counterpart. However, the complexity status of the non idling version of quite easy polynomial basic problems remains an open question. We finally consider a more constrained version of non-idling, called the “homogeneously non idling” constraint, where for any subset of machines, the union of their busy intervals must make an interval and we present the structural property that leads to a polynomial algorithm for unit time jobs and a weak precedence. We conclude by giving some research directions that seem quite interesting to study both for theoretical and practical issues.     

Sampled-data distributed protocol for coordinated aggregation of multi-agent systems subject to communication delays

This paper studies the coordinated aggregation problem of a multi-agent system. Particularly, all the agents reach a consensus within a pre-specified target region. However, only a subset of agents have access to this target region, and each agent merely interacts with its neighbors by communication. Moreover, there exist unknown heterogeneous delays in communication channels. The underlying communication topology is characterized by a digraph. To accommodate the practical digital disposal, a sampled-data distributed protocol is proposed, where the sampling is asynchronous in the sense that the sampling periods of distinct agents are heterogeneous. The resulting closed-loop system from the proposed sampled-data distributed protocol is in a hybrid fashion that the continuous system is fed-back by using discrete states at sampling instants. The convergence performance of this hybrid closed-loop system is analyzed based on the contraction theory. More specifically, it is first shown that all the states are coordinated to aggregate within the target region, i.e., coordinated aggregation. With this result, it is next shown that all the states are coordinated towards a consensus, i.e., state agreement. These together guarantee the fulfillment of the concerned coordinated aggregation objective. Finally, a simulation example is given to validate the theoretical results.     

The single-server scheduling problem with convex costs

Being probably one of the oldest decision problems in queuing theory, the single-server scheduling problem continues to be a challenging one. The original formulations considered linear costs, and the resulting policy is puzzling in many ways. The main one is that, either for preemptive or nonpreemptive problems, it results in a priority ordering of the different classes of customers being served that is insensitive to the individual load each class imposes on the server and insensitive to the overall load the server experiences. This policy is known as the cμ-rule. We claim and show that for convex costs, the optimal policy depends on the individual loads. Therefore, there is a need for an alternative generalization of the cμ-rule. The main feature of our generalization consists on first-order differences of the single stage cost function, rather than on its derivatives. The resulting policy is able to reach near optimal performances and is a function of the individual loads.     

Models for a Steiner multi-ring network design problem with revenues

The Steiner multi-ring network design problem with revenues consists of designing node-disjoint multiple rings connected by a specific node (hub) and passing through all the nodes with high priority of service and some of the nodes with low priority of service. The number of nodes in each ring has an upper bound to assure a certain level of service. Besides the usual arc link costs, we also consider revenues between each pair of nodes in the same ring, even when they are not connected by a direct link. The objective is to minimize the difference between the total connection cost and total revenue. The problem is a generalization of the problem studied in Gouveia and Pires (Eur J Oper Res 133:21–31, 2001a) and it can also be seen as a combination of variants of two NP-Hard problems, the vehicle routing problem and the maximum edge-weighted clique problem. We introduce and discuss two types of integer linear programming formulations and propose some valid inequalities to strengthen the linear programming relaxation. Computational results are presented to evaluate the quality of the linear programming relaxation bounds associated with these formulations as well as efficiency of the models to obtain the optimal integer solutions.