An exponentially convergent distributed algorithm for resource allocation problem

Resource allocation problems usually seek to find an optimal allocation of a limited amount of resources to a number of activities. The allocation solutions of different problems usually optimize different objectives under constraints [1, 2]. If the activities and constraints among them are presented as nodes and edges respectively, the resource allocation problem can be modeled as a k-coloring problem with additional optimization objectives [3, 4]. Since the amount of resources is limited, it is common that some of the activities (nodes) cannot obtain a resource (color). Because the importance of the nodes is usually different, let the weight of a node denote the cost if it cannot obtain a resource, then the resource allocation problem can be described by a node-weighted graph G(E,V), where E and V are the edge and node set, respectively. Some of the nodes that cannot obtain a resource will incur cost to the allocation solution. The optimization objective of the resource allocation problem formulated in this paper is to minimize the total cost of all the nodes that do not obtain a resource. If the total cost is zero, the obtained solution is a k-coloring of the graph; otherwise, the obtained solution is a k -coloring of the graph after removing the nodes that do not obtain a resource. So the resource allocation problem is a generalization of the k-coloring problem.

In this paper, a distributed resource allocation problem is investigated based on a continuous-time algorithm in the presence of time-varying communication delays. The considered delays are allowed to take both "large" and "small" delay values in an alternating manner. The "small" delays refer to a class of delays that guarantee the exponential convergence to the optimal solution; otherwise, they are called "large" delays. The existence of "large" delays may affect the behavior of the optimal allocation solution, and the existing algorithms with delays may not be applicable to this kind of "large" delays. To address "large" delay cases, a switched algorithm is first proposed based on switching techniques, and then, such an algorithm is modeled as switched delay systems. Second, by adopting the Lyapunov functional theory, the upper bound of delays is first derived to guarantee the exponential convergence to the optimal solution under "small" delays, and then, a delay-dependent sufficient condition is obtained to ensure exponential convergence of the proposed algorithm based on some restrictions on "large" delays. Finally, we adopt an IEEE 118-bus practical example to show the effectiveness of the proposed algorithm.

Distributed algorithm for resource allocation problems under persistent attacks

In this research work, we present a combination of a memetic algorithm and an immunological algorithm that we call Memetic Immunological Algorithm - MIA. This algorithm has been designed to tackle the resource allocation problem on a communication network. The aim of the problem is to supply all resource requested on a communication network with minimal costs and using a fixed number of providers, everyone with a limited resource quantity to be supplied. The scheduling of several resource allocations is a classical combinatorial problem that finds many applications in real-world problems. MIA incorporates two deterministic approaches: (1) a local search operator, which is based on the exploration of the neighbourhood; and (2) a deterministic approach for the assignment scheme based on the Depth First Search (DFS) algorithm. The results show that the usage of a local search procedure and mainly the DFS algorithm is an effective and efficient approach to better exploring the complex search space of the problem. To evaluate the performances of MIA we have used 28 different instances. The obtained results suggest that MIA is an effective optimization algorithm in terms of the quality of the solution produced and of the computational effort.

Energy-efficiency, high transmission data rates and Quality of Service (QoS) awareness are the major challenges for resource management in the uplink of Visible Light Communication Personal Area Networks (VPANs). This paper investigates the problem of Optical Access Point (OAP) selection and resource allocation in the uplink of VPANs under two different transmission techniques, namely Orthogonal Frequency Division Multiple Access (OFDMA) and Non-Orthogonal Multiple Access (NOMA). Each user is associated with a generic utility function, which represents his perceived satisfaction with respect to the overall resource allocation problem. OAP selection adopts Maximum Gain Selection (MGS) policy, i.e. users select an OAP to connect to based on the highest path gain. A distributed resource allocation problem in VPANs is formulated and solved as an optimization problem. Following this analysis, a decentralized iterative and low-complexity algorithm for determining OAP selection and resource allocation is proposed, while the overall approach’s efficiency is illustrated via modeling and simulation, highlighting and assessing the advantages and drawbacks of each adopted transmission technique, i.e. OFDMA and NOMA.

In 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.

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time (1+varepsilon )-approximation algorithm that yields an (e+varepsilon )-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with optimal cost at 1+varepsilon speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most log n many classes. This algorithm allows the jobs even to have up to log n many distinct release dates. All proposed quasi-polynomial time algorithms require the input data to be quasi-polynomially bounded.

Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by emerging applications in smart grid and distributed sparse regression, this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints. We consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions. To solve this problem in a distributed manner, we propose a consensus-based distributed primal-dual perturbation (PDP) algorithm. In the algorithm, agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors, and meanwhile use a local primal-dual perturbed subgradient method to approach a global optimum. The proposed PDP method not only can handle smooth inequality constraints but also non-smooth constraints such as some sparsity promoting constraints arising in sparse optimization. We prove that the proposed PDP algorithm converges to an optimal primal-dual solution of the original problem, under standard problem and network assumptions. Numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented.

We study the distributed nonconvex resource allocation with Limited Communication Data Rate (LCDR) over a communication network. Each node in the network has its own private cost function and determines the optimal resource allocation through interactions solely with its neighboring nodes. The nodes need to cooperatively minimize the total cost function to achieve the optimal resource allocation under the constraint of constant total resources. First, we consider exact communication. By Lagrange dual method, we propose a successive convex approximation-based distributed dual gradient tracking algorithm to solve the distributed nonconvex resource allocation problems. Then, we consider the case of digital communication among nodes based on LCDR. The information transmission among nodes is based on the Dynamic Encoding and Decoding (DED) with finite-level uniform quantization. We propose a successive convex approximation-based distributed dual gradient tracking algorithm with LCDR and conduct numerical simulations. The numerical results show that the algorithm converges based on merely one-bit quantizers when appropriate step sizes and scaling functions are chosen.

The economic dispatch problem in smart grids is studied in this paper. A discrete predefined-time distributed optimization algorithm is proposed based on predefined-time convergence, which can make reasonable decisions on power generation for each generator within a predefined time. In the optimization algorithm designed in this paper, information exchanged between generators in the communication network is only the information of auxiliary variables, which avoids the problem of privacy data leakage. Finally, a set of numerical simulations is provided to verify the feasibility of the proposed algorithm.

The distributed optimal coordinated control problem of heterogeneous linear multi-agent systems is studied in this paper. Specifically, each agent in the system under consideration has a local private cost function, which is assumed to be strongly convex with a Lipschitz continuous gradient. The agents aim to achieve output consensus on the optimal solution of a global cost function, which is the sum of local cost functions. The communication topology among agents is assumed to be a weight-unbalanced and strongly connected directed graph. To solve such a control problem, a tracking-based approach is suggested and utilized, where an auxiliary system is designed to seek the optimal solution. Based on the output regulation technique, distributed tracking control inputs are proposed for the agents, which ensure that the outputs of the agents track the trajectories generated by the auxiliary system. Under the assumptions on the local cost functions, the communication topology and system matrices, it is proved that with the proposed control scheme, the outputs of all agents can achieve consensus on the optimal solution. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed tracking control scheme.

In this paper, we consider the problem of multi-agent systems where each agent aims to establish a line formation in a distributed manner. In constructing an efficient line formation, finding a line with the closest total distance from every agent is essential. We propose a formation control using least squares estimation (LSE) performed by each agent with only the local information that consists of the corresponding agent’s and neighbors’ positions. Each agent calculates the local cost function, which is the squared distance from the LSE line to the related agent’s and its neighbors’ positions. Our goal is to minimize the global cost function, which is the sum of these local cost functions. To achieve this, we employ distributed optimization to the global cost function of the overall system using the subgradient method performed by each agent locally. We evaluate our proposed method using numerical simulation, and the result complies with our goal of this paper

In this chapter, we focus on introducing a distributed online optimization problem for a set of nodes communicating on a time-varying unbalanced directed network, while considering the problem of how to preserve the privacy of their local cost functions. The main goal of this set of nodes is to cooperatively minimize the sum of all locally known convex cost functions (global cost function). We propose a differentially private distributed stochastic subgradient-push algorithm, named DP-DSSP, to solve such an optimization problem in a collaborative and distributed manner. The algorithm ensures that nodes interact with their in-neighbors and collectively optimize the global cost function. Unlike most existing distributed algorithms that do not consider privacy issues, DP-DSSP successfully protects the privacy of participating nodes through a differential privacy strategy, which is more practical in applications involving sensitive information, such as military affairs or medical treatment. An important feature of DP-DSSP is that it handles distributed online optimization problems in the context of time-varying unbalanced directed networks. Theoretical analysis shows that DP-DSSP can effectively protect differential privacy and can achieve sublinear regret. The tradeoff between the level of privacy and accuracy of DP-DSSP is also revealed. Moreover, DP-DSSP is able to handle arbitrarily large but uniformly bounded delays in the communication link. Finally, simulation experiments confirm the usefulness of DP-DSSP and the findings of this chapter.KeywordsDistributed online optimizationDifferential privacyStochastic subgradient-push algorithmTime-varying directed networksCommunication delays

Population growth and fast urban expansion in the last century generated a metropolitan agglom- eration that caused numerous social and economics impacts. The high demand for mobility has resulted in a growing number of vehicles on the roads, leading to longer travel times, which has caused traffic congestion, increased accident rates, and increased pollution. Intelligent Transportation Systems (ITS) have the potential to revolutionize the transportation and urban mobility to reduce traffic accidents, mitigate congestion and traffic jams. The communication between vehicles allows negotiation and cooperation that can be used in various contexts such as crossing intersections, on-ramp merge and lane change. Resolving conflicts between vehicles is a challenging task due to the higher density of vehicles and limited maneuverability, often limited to only speed changes. A significant number of studies focus on solutions rely on centralized methods that have a heavy dependency on the infrastructure. Additionally, there is limited research on decentralized negotiation methods that take into account multi-objective systems where each vehicle has its own private cost function and also there is a lack of work in generalized solutions that tackles different dynamic scenarios with traffic flow using the same approach. This thesis proposes a method for resolving conflicts between vehicles that have the ability to communicate in a decentralized manner that can be used in multiple dynamic scenarios, such as: crossing intersections, on-ramp merging and changing lanes. We also considered vehicles with different characteristics, dimensions and private cost functions. The proposed approach aims to improve the flow of vehicles and reduce travel time that can be translated into a reduction in the emission of pollutants. To evaluate our proposal, we use a simulation tool to create various test scenarios and compare our results with existing methods using metrics commonly used in the literature. In addition, it was also necessary to adapt the simulation tool to include features such as trajectory calculation, collision detection and vehicle management in relation to the decision-making process. In every scenario, significant improvements were achieved in terms of vehicle flow, resulting in a decrease in travel time and an increase in average speed when compared to the benchmarks used.

This article addresses a resilient exponential distributed convex optimization problem for a heterogeneous linear multiagent system under Denial-of-Service (DoS) attacks over random digraphs. The random digraphs are caused by unreliable networks and the DoS attacks, allowed to occur aperiodically, refer to an interruption of the communication channels carried out by the intelligent adversaries. In contrast to many existing distributed convex optimization works over a perfect communication network, the global optimal solution might not be sought under the adverse influences that result in performance degradations or even failures of optimization algorithms. The aforementioned setting poses certain technical challenges to optimization algorithm design and exponential convergence analysis. In this work, several resilient algorithms are presented such that a team of agents minimizes a sum of local nonquadratic cost functions in a safe and reliable manner with the global exponential convergence. Numerical simulation results are further presented to validate the effectiveness of the proposed distributed approaches.