A METHOD FOR DISTRIBUTED OPTIMIZATION FOR TASK ALLOCATION Sheng Zhao, Baisravan HomChaudhuri and Manish Kumar Dept. of Mechanical Engineering University of Cincinnati Cincinnati, Oh, 45221 zhaose@email.uc.edu ABSTRACT Allocation of a large number of resources to tasks in a complex environment is often a very challenging problem. This is primarily due to the fact that a large number of resources to be allocated results into an optimization problem that involves a large number of decision variables. Most of the optimization algorithms suffer from this issue of non-scalability. Further, the uncertainties and dynamic nature of environment make the optimization problem quite challenging. One of the techniques to overcome the issue of scalability that have been considered recently is to carry out the optimization in a distributed or decentralized manner. Such techniques make use of local information to carry out global optimization. However, such techniques tend to get stuck in local minima. Further, the connectivity graph that governs the sharing of information plays a role in the performance of algorithms in terms of time taken to obtain the solution, and quality of the solution with respect to the global solution. In this paper, we propose a distributed greedy algorithm inspired by market based concepts to optimize a cost function. This paper studies the effectiveness of the proposed distributed algorithm in obtaining global solutions and the phase transition phenomenon with regard to the connectivity metrics of the graph that underlies the network of information exchange. A case study involving resource allocation in wildland firefighting is provided to demonstrate our algorithm. INTRODUCTION The allocation of resources is encountered in various domains such as manufacturing, operation management, firefighting, disaster management, and multi-robot cooperation [1-3]. They often represent complex decision making problems. To effectively use and allocate a large number of resources to different tasks, so that the overall objective is achieved in an optimal manner, is a very challenging problem. This is primarily due to the complexity that arises from a large number of decision variables. Furthermore, dynamic and uncertain nature of environment makes optimization problem more challenging. Additionally, in a complex and dynamic environment, the volume of information needed to reach the global solution could be huge, and obtaining an optimal solution could be computationally prohibitive. This paper proposes a distributed greedy optimization method to reduce computational load and hence shorten response time. A lot of effort has been made to address the task allocation problem in the Distributed Artificial Intelligence community [7, 8]. There are many auction-based algorithms for the multi-robot task allocation problem such as M+ [4] and MURDOCH [5]. The comparison of computational complexity between those methods can be found in paper [6]. Market-based algorithm is one of the promising ways to allocate resources [9]. Market-based algorithm is inspired from the field of economy where each resource is a self-interested individual whose only purpose is to maximize its benefit. Through a careful design of reward and cost for each task, the actions by the self-interested agents can help obtain an optimal solution that is close to the global one. Auction is a commonly used method in market-based algorithms to help the agents negotiate with each other and allocate themselves to different tasks. One of the most popular market-based architectures is Hoplites [10]. In this architecture, there are two types of coordination: passive coordination and active coordination. The agents passively coordinate with each other until the best profit they can get is not acceptable due to the existence of constraints. Then they start actively generating team