A Method for Distributed Optimization for Task Allocation

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.