Distributed Resource Allocation Problem Research Articles

Adaptive Neurodynamic Approach to Multiple Constrained Distributed Resource Allocation.

In this article, an adaptive neurodynamic approach over multiagent systems is designed to solve nonsmooth distributed resource allocation problems (DRAPs) with affine-coupled equality constraints, coupled inequality constraints, and private set constraints. It is to say, agents focus on tracking the optimal allocation to minimize the team cost under more general constraints. Among the considered constraints, multiple coupled constraints are dealt with by introducing auxiliary variables to make Lagrange multipliers reach consensus. Furthermore, aiming to address private set constraints, an adaptive controller is proposed with the aid of the penalty method, thus avoiding the disclosure of global information. Through using the Lyapunov stability theory, the convergence of this neurodynamic approach is analyzed. In addition, to reduce the communication burden of systems, the proposed neurodynamic approach is improved by introducing an event-triggered mechanism. In this case, the convergence property is also explored, and the Zeno phenomenon is excluded. Finally, a numerical example and a simplified problem on a virtual 5G system are implemented to demonstrate the effectiveness of the proposed neurodynamic approaches.

Distributed continuous-time proximal algorithm for nonsmooth resource allocation problem with coupled constraints

This paper studies the distributed resource allocation problem with nonsmooth local cost functions subject to the coupled equality and inequality constraints. In particular, each local cost function is expressed as the sum of a differentiable function and two nonsmooth functions. By using the operator splitting and primal–dual method, a continuous-time distributed proximal algorithm is developed, which can be applied to more general local cost functions that are convex but not necessarily smooth. In addition, the proposed algorithm is fully distributed in the sense that the gain parameter can be determined locally and does not require any global information of the network. By applying Lyapunov stability analysis and convex optimization theory, it is shown that the decision variables of all the agents converge to an optimal solution. Finally, a simulation example is carried out to demonstrate the effectiveness of the proposed algorithm.

Multiagent System With Periodic and Event-Triggered Communications for Solving Distributed Resource Allocation Problem

This article mainly investigates how to reduce the communication cost in multiagent system (MAS) for distributed optimization. First, a continuous-time distributed optimization model based on MAS is proposed for resource allocation (RA) with periodic communication. All agents in the system do not need to be in constant contact with their neighbors, but contact at set intervals. This will greatly reduce the communication consumption of the system. Second, to further reduce the communication cost, MAS with event-triggered communication is proposed based on periodic communication. It is proved that the system is convergent to an optimal solution of the investigated problem subject to bound and equality constraints. Finally, two examples with simulations are given to verify the performance of the proposed system.

From drinking philosophers to asynchronous path-following robots

In this paper, we consider the multi-robot path execution problem where a group of robots move on predefined paths from their initial to target positions while avoiding collisions and deadlocks in the face of asynchrony. We first show that this problem can be reformulated as a distributed resource allocation problem and, in particular, as an instance of the well-known Drinking Philosophers Problem (DrPP). By careful construction of the drinking sessions capturing shared resources, we show that any existing solutions to DrPP can be used to design robot control policies that are collectively collision and deadlock-free. We then propose modifications to an existing DrPP algorithm to allow more concurrent behavior, and provide conditions under which our method is deadlock-free. Our method does not require robots to know or to estimate the speed profiles of other robots and results in distributed control policies. We demonstrate the efficacy of our method on simulation examples, which show competitive performance against the state-of-the-art.

A distributed extremum seeking based resource allocation algorithm over switching networks

AbstractIn this article, a distributed resource allocation problem for second‐order multi‐agent systems over undirected switching topologies is investigated. For the distributed resource allocation problem, most of the existing algorithms depend on the gradient of cost function with specific expression, which may be unknown to agents. To deal with unknown cost functions, the extremum seeking control is introduced in the designed distributed resource allocation algorithm to estimate the gradient of the cost function only by the value of the cost. Besides, an estimator is proposed to estimate the optimal Lagrange multiplier associated with the equality constraint. The communication graph is supposed to be switched among a set of undirected subgraphs, which may be connected or unconnected. For undirected and connected switching graphs, the average dwell‐time constraint is used to describe the switching frequency. For the undirected graphs, containing connected and unconnected ones, both the average dwell‐time and the time‐ratio constraints are used to model the switching signal. For the two cases, the semi‐globally practically asymptotical stability of the designed algorithm is established. The obtained results are verified by an example.

Distributed extremum‐seeking based resource allocation algorithm with input dead‐zone

SummaryThis paper studies distributed resource allocation problem for agents with input dead‐zone, which is not considered in the existing work. At first, the primal problem is transformed to an auxiliary problem by using the exact penalty method to deal with local inequality constraints. It is assumed that the explicit expressions of cost functions and local inequality constraints are unknown to agents but the values of the cost and constraint functions can be obtained. Under such a setup, the extremum seeking control is used to estimate the gradient information. Thus, to obtain the optimal allocation, a novel distributed algorithm is designed by the virtue of the extremum seeking control and a dynamic compensating mechanism which is used to handle the effects of the input dead‐zone. Due to a two time‐scale structure of the designed distributed algorithm, the semi‐globally practically asymptotical convergence of all agents' decisions to the optimal allocation is obtained by the singular perturbation technique. Finally, numerical examples of economic dispatch in smart grids are given to verify the effectiveness of our proposed method.

Dual-attention assisted deep reinforcement learning algorithm for energy-efficient resource allocation in Industrial Internet of Things

This paper investigates the distributed resource allocation problem for energy-efficient data forwarding in resource-constrained Industrial Internet of Things (IIoT). We formulate this problem as a decentralized partially observable Markov decision process (Dec-POMDP) and propose a novel energy-efficient resource allocation algorithm based on the dual-attention assisted deep reinforcement learning (DRL) model, namely DADR, which adopts the centralized training and distributed executed (CTDE) framework to provide the intelligent decision-making ability for resource-constrained nodes. In DADR, we design a multi-scale convolutional attention module (CAM) in actor network that can extract the local state’s feature information from different dimensions; meanwhile, we propose a novel critic network based on dual-attention module and experience reconstruction module which provides a more objective and correct state evaluation from a global perspective. Moreover, the proposed critic network can solve the partially observable and non-stationary problems in multi-agent systems and can flexibly scale without changing the model structure even in a dynamic environment. Furthermore, the cooperation between CAM and multi-head self-attention (MHSA) in DADR improves the representation learning ability of DRL and offers better optimization direction for the DRL model to maximize the energy-efficient and data transmission reliability. Simulation results demonstrate that the proposed DADR algorithm outperforms the existing resource allocation algorithms and MARL models in terms of network lifetime, transmission reliability, and network stability, respectively.

An Asynchronous Gradient Descent Based Method for Distributed Resource Allocation With Bounded Variables

This article considers the distributed resource allocation problem over a network of n agents with individual optimization functions and coupled resource constraints. The optimization variables are bounded for each agent. We propose an asynchronous distributed gradient descent based method, which is able to tackle time-varying communication networks and communication problems. The main ideas are twofold. First, the degree of freedom of the network is reduced to deal with the global constraint. Second, we utilize delay compensation to counteract the delay of asynchronous communication. We prove that the convergence rate is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(\frac{1}{k})$</tex-math></inline-formula> and analyze both the communication complexity and the time complexity. This method is applied into the parallel pump control problem in HVAC system and shows good numerical results.

Synthesis of Cost-Optimal Multi-Agent Systems for Resource Allocation

Multi-agent systems for resource allocation (MRAs) have been introduced as a concept for modelling competitive resource allocation problems in distributed computing. An MRA is composed of a set of agents and a set of resources. Each agent has goals in terms of allocating certain resources. For MRAs it is typically of importance that they are designed in a way such that there exists a strategy that guarantees that all agents will achieve their goals. The corresponding model checking problem is to determine whether such a winning strategy exists or not, and the synthesis problem is to actually build the strategy. While winning strategies ensure that all goals will be achieved, following such strategies does not necessarily involve an optimal use of resources. In this paper, we present a technique that allows to synthesise cost-optimal solutions to distributed resource allocation problems. We consider a scenario where system components such as agents and resources involve costs. A multi-agent system shall be designed that is cost-minimal but still capable of accomplishing a given set of goals. Our approach synthesises a winning strategy that minimises the cumulative costs of the components that are required for achieving the goals. The technique is based on a propositional logic encoding and a reduction of the synthesis problem to the maximum satisfiability problem (Max-SAT). Hence, a Max-SAT solver can be used to perform the synthesis. From a truth assignment that maximises the number of satisfied clauses of the encoding a cost-optimal winning strategy as well as a cost-optimal system can be immediately derived.

A Distributed Resource Allocation Algorithm for the General Linear Multiagent Systems

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.

Robust Utility Design in Distributed Resource Allocation Problems with Defective Agents

Robust Utility Design in Distributed Resource Allocation Problems with Defective Agents

Distributed algorithm design for constrained resource allocation problems with high-order multi-agent systems

This paper studies distributed resource allocation problems of multi-agent systems, where the decisions of agents are subject to inequality network resource constraints and local inequality constraints. Compared with well-known resource allocation problems, our problem considers the high-order dynamics of agents. Without involving the control of high-order dynamics, existing distributed resource allocation algorithms cannot deal with our problem. Meanwhile, the high-order dynamics together with the inequality constraints makes it difficult to design and analyze distributed resource allocation algorithms, because the outputs of agents cannot be decided by their inputs directly and the optimal decisions of agents must satisfy the inequality constraints. In order to control the high-order agents to accomplish the resource allocation tasks autonomously, a distributed algorithm is designed by state feedback, gradient descent and primal–dual methods. Moreover, the convergence of the algorithm is analyzed by convex analysis and Lyapunov stability theory. With the algorithm, the high-order agents converge to the optimal allocation. Finally, numerical simulations verify the effectiveness of the algorithm.

Free2Shard

In this paper, we formulate and study a new, but basic, distributed resource allocation problem arising in scaling blockchain performance. While distributed resource allocation is a well-studied problem in networking, the blockchain setting additionally requires the solution to be resilient to adversarial behavior from a fraction of nodes. Scaling blockchain performance is a basic research topic; a plethora of solutions (under the umbrella of sharding) have been proposed in recent years. Although the various sharding solutions share a common thread (they cryptographically stitch together multiple parallel chains), architectural differences lead to differing resource allocation problems. In this paper we make three main contributions: (a) we categorize the different sharding proposals under a common architectural framework, allowing for the emergence of a new, uniformly improved, uni-consensus sharding architecture. (b) We formulate and exactly solve a core resource allocation problem in the uni-consensus sharding architecture -- our solution, Free2shard, is adversary-resistant and achieves optimal throughput. The key technical contribution is a mathematical connection to the classical work of Blackwell approachability in dynamic game theory. (c) We implement the sharding architecture atop a full-stack blockchain in 3000 lines of code in Rust -- we achieve a throughput of more than 250,000 transactions per second with 6 shards, a vast improvement over state-of-the-art.

Distributed resource allocation algorithm for second-order multi-agent systems with external disturbances

This paper focuses on the distributed resource allocation problem of a second-order multi-agent system with external disturbances. The global network resource equality constraint is considered. A distributed algorithm with an exponential convergence rate is proposed based on an internal model for a known bounded disturbance. By using the active disturbance approach to design a reduced-order extended state observer, the proposed algorithm is modified to reject an unknown external disturbance. Moreover, exponential convergence is achieved through the Lyapunov theory when the disturbance is constant. When the differential of the disturbance is bounded, by adjusting the control parameter of the observer, the proposed algorithm converges to an arbitrarily small neighbourhood of the optimal solution. Finally, our simulation results demonstrate the effectiveness of our proposed algorithm.

Distributed Fixed-Time Resource Allocation Algorithm for the General Linear Multi-Agent Systems

This brief focuses on the distributed resource allocation problem (RAP) for a general linear heterogeneous multi-agent system (MAS), in which each agent adopts different structure parameters. By means of multi-agent consensus approach and symbolic-function-based fixed-time control theory, an initialization-free distributed resource allocation algorithm is designed. Moreover, the equality constraint is solved based on the proportional-integral (PI) control idea and the output of all agents tracks to the optimal solution within fixed-time. Finally, we reveal the effectiveness and fast convergence performance of our proposed algorithm by a simulation example.

Parametric Optimal Design System of Construction System Based on Distributed Optimal Algorithm

With the rapid development of science and technology and the continuous expansion of network scale, traditional centralized control and optimization techniques have been difficult to solve large-scale complex network problems, and distributed optimization algorithms with more robustness and flexibility have attracted more and more attention. In view of the irreplaceable advantages of multi-intelligent systems in distributed computing, many researchers have used them as carriers of distributed optimization for theoretical research and application promotion. For the distributed optimization problem in the undirected network environment, this article outlines and summarizes the existing gradient-based distributed simultaneous optimization algorithms, based on which a novel distributed simultaneous momentum acceleration optimization algorithm is proposed. Under the premise that the local objective function is strongly convex and Lipschitz continuous, the algorithm uses heterogeneous steps to precisely drive each node to converge asymptotically to the global optimal solution, and we reduce or compensate the effect of the original error on the pairwise error by introducing an adjustable symmetric matrix. The distributed resource allocation problem under undirected graphs is studied, in which the local cost function of the intelligences is unknown. Using sinusoidal signal excitation, the input and output of the cost function are utilized, and the first-order and second-order polar search algorithms are designed, respectively. In addition, the algorithm innovatively introduces the dual acceleration mechanism combining the Nesterov gradient method and the Heavy-Ball method to greatly improve the convergence speed of the algorithm. Based on the interrelationship of the agreement error, the optimal distance, the state difference, and the tracking error, the step size and the range of the momentum parameters for the linear convergence of the algorithm to the optimal solution are analyzed using the linear matrix inequality technique.

Free2Shard

In this paper, we study a canonical distributed resource allocation problem arising in blockchains. While distributed resource allocation is a well-studied problem in networking, the blockchain setting additionally requires the solution to be resilient to adversarial behavior from a fraction of nodes. Scaling blockchain performance is a basic research topic; a plethora of solutions (under the umbrella of sharding ) have been proposed in recent years. Although the various sharding solutions share a common thread (they cryptographically stitch together multiple parallel chains), architectural differences lead to differing resource allocation problems. In this paper we make three main contributions: (a) we categorize the different sharding proposals under a common architectural framework, allowing for the emergence of a new, uniformly improved, uni-consensus sharding architecture. (b) We formulate and exactly solve a core resource allocation problem in the uni-consensus sharding architecture -- our solution, Free2shard, is adversary-resistant and achieves optimal throughput. The key technical contribution is a mathematical connection to the classical work of Blackwell approachability in dynamic game theory. (c) We implement the sharding architecture atop a full-stack blockchain in 3000 lines of code in Rust -- we achieve a throughput of more than 250,000 transactions per second with 6 shards, a vast improvement over state-of-the-art.

Distributed continuous-time algorithm for resource allocation over unbalanced directed networks

The problem we aim to solve in this study is the distributed resource allocation problem (DRAP) over unbalanced directed networks, in which the local inequality constraint and global equality constraint are considered. On the basis of the fixed-time projection method, a distributed gradient algorithm is developed. The corresponding eigenvalue is obtained within fixed-time by tapping the row-stochastic or column-stochastic Laplacian matrix to overcome the unbalance of directed weights. Therefore, the optimal solution can be obtained asymptotically. Moreover, the proposed algorithm is initialization-free and its control parameters are constant. Finally, the effectiveness is illustrated by several case studies.

Distributed resource allocation via multi-agent systems under time-varying networks

In this paper, the problem of distributed resource allocation with coupled equality, nonlinear inequality and convex set constraints is studied. Each agent only has access to the information associated with its own cost function, inequality constraints, convex set constraint, and a local block of the coupled equality constraints. To address such problem, a new distributed primal–dual algorithm is proposed for a continuous-time multi-agent system under a time-varying graph. In the proposed algorithm, two consensus strategies are employed. One is used to estimate the coupled equality constraint function, and the other one is used to estimate corresponding optimal dual variable. Furthermore, a novel Lyapunov function is constructed based on a strongly convex function to analyze convergence of the algorithm. The results show that if the time-varying graph is balanced and the union in a certain period is strongly connected, the algorithm asymptotically converges, and the convergence state is the solution to the distributed resource allocation problem. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.

Distributed Algorithm Design for Resource Allocation Problems of Second-Order Multiagent Systems Over Weight-Balanced Digraphs

This paper studies two distributed resource allocation problems of second-order systems over weight-balanced communication networks. In the first problem, the decisions of agents are coupled by network resource constraints, and in the second problem, the decisions of agents are constrained by local constraints and network resource constraints. Compared with many existing resource allocation problems, the formulation involves the dynamics of agents. The second-order dynamics of agents induce the difficult in algorithm design and analysis, since the decisions of agents could not be directly decided by their control inputs. In order to optimally allocate the network resource, two distributed algorithms are designed via state feedback and gradient descent for the two problems, respectively. Besides, the convergence of the two algorithms are analyzed. By the two algorithms, the second-order agents converge to the optimal allocation of the two problems, respectively. Finally, two examples about economic dispatch problems verify the two algorithms.