Abstract—Desirable goals for grid task scheduling algorithms would shorten average delay, maximize system utilization and fulfill user constraints. In this work, an agent-based grid management infrastructure coupled with Mean Field Annealing (MFA) scheduling algorithm has been proposed. An agent in grid utilizes a neural network algorithm to manage and schedule tasks. The Hopfield Neural Network is good at finding optimal solution with multi-constraints and can be fast to converge to the result. However, it is often trapped in a local minimum. Stochastic simulated annealing algorithm has an advantage in finding the optimal solution and escaping from the local minimum. Both significant characteristics of Hopfield neural network structure and stochastic simulated annealing algorithm are combined together to yield a mean field annealing scheme. A modified cooling procedure to accelerate reaching equilibrium for normalized mean field annealing has been applied to this scheme. The simulation results show that the scheduling algorithm of MFA works effectively. I. INTRODUCTION ASK scheduling is an integral part of parallel and distributed computing. Extensive research has been conducted in this area leading to significant theoretical and practical results. However, with the emergence of the computational Grid, new scheduling algorithms are in demand for addressing concerns originating from the Grid infrastructure. The Grid is coordinated resource sharing and problem solving in dynamic, multi-institutional virtual organizations [2]. How to solve the dynamic and heterogeneous properties is the main difficulty. Many traditional distributed algorithms [3] and Grid scheduling algorithms [6] have some features in common, that are performed in multiple steps to solve the problem to match application needs with resource availability and providing quality of service. Currently available scheduling models include AppLes, Nimrod, Condor, etc. The scheduling algorithm in AppLeS focuses on efficient co-location of data and adaptive scheduling. The scheduling in Nimrod is based on deadlines and Grid economy model. Condor is designed for high throughput computing in a controlled local network Manuscript received Dec 1, 2007. Guixiang Xue, Zheng Zhao, and Shuang Liu were with the School of Computer Science and Technology, Tianjin University, Tianjin, 300072, China (Phone: +86-22-27402264; e-mail: xueguixiang@gmail.com, zhengzh@tju.edu.cn) Maode Ma was with the School of Electrical and Engineering, Nanyang Technological University, Singapore, Singapore (e-mail: emdma@ntu.edu.sg). Tonghua Su and Tianwen Zhang were with the School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China ( e-mail: tonghuasu@hit.edu.cn, twzhang@hit.edu.cn). environment. Its matchmaker scheduler targets only single processor tasks which are scheduled independently. In grid, two major challenges that must be addressed are scalability and adaptability. Effective management and scheduling has to be achieved in an intelligent and autonomous way. Software agents have been accepted to be a powerful high-level abstraction for modeling of a complex software system [5]. In this paper, an agent is responsible for task scheduling and resource management in a local grid. The agent couples neural network scheduling algorithms to dynamically minimize task delay and host idle time while meeting the deadline requirements of each task. Here, we consider independent task scheduling instance of the grid utilizing MFA based on agent. The Hopfield Neural Network (HNN) model provides a method to solve optimization problems with multiple constraints. Intrinsically, Hopfield neural network is good at finding optimal solution with multi-constraints and can be fast convergent to the result. However, it often traps to a local minimum. Stochastic simulated annealing algorithm has an advantage in finding the optimal solution. It can provide a chance to escape from the local minimum. Both significant characteristics of Hopfield neural network structure and stochastic simulated annealing algorithm are combined together to yield a so called MFA scheme. Several metrics are considered to measure the performance of the algorithm. One is the average delay. The other is the tardy rate. We compare our approach to other algorithms. The rest of the paper is organized as follows: In section 2, the agent-based task scheduling with neural network technique and the MFA scheme to solve sophisticated instance of scheduling problem will be presented. In section 3, the simulation environment will be described and results from a case study concerning a small grid environment are presented. And at last in section 4, we conclude the paper with a summary. II. GRID SCHEDULING ALGORITHMS A. Energy Function We consider an N tasks and M processors grid for scheduling in this paper. We assume that the execution time for each task is determined in advance, which can not be sliced to schedule at different time. And no idle time exists for any processor before task is finished. Also, we limit each task can only be executed at one processor. Subject to the assumptions that preemptive tasks with deadline and limited number of non-preemptive processors are interested, thus our goal of multi-tasks on multi-processors scheduling problems Task Scheduling by Mean Field Annealing Algorithm in Grid Computing Guixiang Xue, Zheng Zhao, Maode Ma, Tonghua Su, Tianwen Zhang and Shuang Liu T 783 978-1-4244-1823-7/08/$25.00 c 2008 IEEE