Algorithm For Resource Allocation Problem Research Articles

Distributed Adaptive Algorithm for Resource Allocation Problem Over Weight-Unbalanced Graphs

Distributed Adaptive Algorithm for Resource Allocation Problem Over Weight-Unbalanced Graphs

Distributed stochastic mirror descent algorithm for resource allocation problem

In this paper, we consider a distributed resource allocation problem of minimizing a global convex function formed by a sum of local convex functions with coupling constraints. Based on neighbor communication and stochastic gradient, a distributed stochastic mirror descent algorithm is designed for the distributed resource allocation problem. Sublinear convergence to an optimal solution of the proposed algorithm is given when the second moments of the gradient noises are summable. A numerical example is also given to illustrate the effectiveness of the proposed algorithm.

Distributed algorithm for resource allocation problems under persistent attacks

This paper explores the ability of a distributed resource allocation algorithm under attacks to identify the optimal solution in the framework of hybrid dynamical systems. Since the attacks can result in time-varying topologies, differential inclusions are used to model attack modes and an average dwell-time automaton and time-ratio monitor are employed to constrain attacks. To address the effect induced by such attacks, a switched algorithm is considered. Then, to analyze stability, the switched algorithm is first modeled as a hybrid system and then a Lyapunov function is constructed to prove that the distributed algorithm under attacks is able to converge to the optimal solution of the resource allocation problem. Moreover, based on automaton and monitor constraints, an inequality condition is provided to guarantee exponential stability of the optimal solution. Finally, an example is presented to verify the theoretical result.

An exponentially convergent distributed algorithm for resource allocation problem

AbstractIn this paper, the distributed resource allocation problem over undirected networks, considering box constraints and demand–supply constraints, is studied. Furthermore, each agent has one private cost function that is only known by itself. The aim is to minimize the sum of all local cost functions in a distributed manner while meeting the constraints. To solve the dispatch problem, a continuous‐time distributed algorithm with fixed step‐size is proposed. After that, a modified distributed algorithm of discrete‐time multi‐agent system is provided. Moreover, the proposed algorithms obtain the global optimal solution with an exponential convergence speed by the conventional Lyapunov methods. Finally, several simulations of IEEE‐14 bus are presented to validate and illustrate the proposed designed algorithm.

Near Optimal Online Algorithms and Fast Approximation Algorithms for Resource Allocation Problems

We present prior robust algorithms for a large class of resource allocation problems where requests arrive one-by-one (online), drawn independently from an unknown distribution at every step. We design a single algorithm that, for every possible underlying distribution, obtains a 1−ϵ fraction of the profit obtained by an algorithm that knows the entire request sequence ahead of time. The factor ϵ approaches 0 when no single request consumes/contributes a significant fraction of the global consumption/contribution by all requests together. We show that the tradeoff we obtain here that determines how fast ϵ approaches 0, is near optimal: We give a nearly matching lower bound showing that the tradeoff cannot be improved much beyond what we obtain. Going beyond the model of a static underlying distribution, we introduce the adversarial stochastic input model, where an adversary, possibly in an adaptive manner, controls the distributions from which the requests are drawn at each step. Placing no restriction on the adversary, we design an algorithm that obtains a 1−ϵ fraction of the optimal profit obtainable w.r.t. the worst distribution in the adversarial sequence. Further, if the algorithm is given one number per distribution, namely the optimal profit possible for each of the adversary’s distribution, then we design an algorithm that achieves a 1−ϵ fraction of the weighted average of the optimal profit of each distribution the adversary picks. In the offline setting we give a fast algorithm to solve very large linear programs (LPs) with both packing and covering constraints. We give algorithms to approximately solve (within a factor of 1+ϵ) the mixed packing-covering problem with O (γ m log ( n /δ)/ϵ 2 ) oracle calls where the constraint matrix of this LP has dimension n × m , the success probability of the algorithm is 1−δ, and γ quantifies how significant a single request is when compared to the sum total of all requests. We discuss implications of our results to several special cases including online combinatorial auctions, network routing, and the adwords problem.

Improved Algorithm for Resource Allocation Problems

We consider the problem of allocating a set of resources for performing a given collection of jobs. Each of the jobs has specific resource requirement for its execution. Each resource has specific start time, finish time and associated cost per unit usage. The objective is to execute the jobs while incurring minimum cost. The problem is NP-hard. We improve known four-approximation to a three-approximation algorithm. Our algorithm implies better approximation for two other related problems.

Approximation Algorithm for Resource Allocation Problems with Time Dependent Penalties

The Resource Allocation Problem with Time Dependent Penalties (RAPTP) is a variant of uncapacitated resource allocation problems generally referred as uncapacitated facility allocation problems or uncapacitated facility location problem (UFLP). Work done in this paper is motivated by the work of Du, Lu and Xu [7] in which authors considered facility location problems with submodular penalties and presented a 3-approximation primal dual algorithm. This paper considers that each unallocated demand point adds to penalty that increases as time passes and is thus represented by function [Formula: see text] where [Formula: see text] and [Formula: see text] are elapse time and priority of demand point [Formula: see text]. As this problem has been considered for emergency service allocation, all demand points should be allocated to some facility or resource within some stipulated time limit beyond which it may lose its purpose. Thus penalty incurred by a demand point is considered till that threshold value only. Thus it is assumed that penalty contribution by a demand point remains constant after a specified threshold value. By exploiting the properties of time dependent penalties, a 4-approximation primal-dual algorithm is proposed which is based on LP framework, and is the first constant-factor approximation algorithm for RAPTP.

Distributed Continuous-Time Algorithms for Resource Allocation Problems Over Weight-Balanced Digraphs.

In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms.

A Memetic Algorithm for Resource Allocation Problem Based on Node-Weighted Graphs [Application Notes

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.