Multiagent Dynamic Task Assignment Based on Forest Fire Point Model

Abstract

Multiagent dynamic task assignment of forest fires is a complicated optimization problem because it requires the consideration of multiple factors, such as the spread speed of fires, firefighting speed of agents, the movement speed of agents, and the number of deployed agents. In this article, we investigate multiagent dynamic task assignment based on a forest fire point model, the objective of which is to minimize task completion time. First, we establish a model for the spread of fire and dynamic task assignments. Second, we prove that the optimal static task assignment always makes all task completion times the same under certain assumptions. Furthermore, we calculate the optimal solution to the static task assignment problem assuming no travel time for the agents, which provides the theoretical basis for the initial deployment and dynamic deployment. Third, we propose a dynamic task assignment scheme based on the global information, which ensures that every reassignment reduces the task completion time and makes all task completion times close to each other. Finally, the simulation is carried out on the MATLAB platform to verify the performance of the proposed dynamic task assignment scheme by comparing with a multistage global auction algorithm. We hope that this work provides insight for decision-makers designing reasonable assignment strategies based on the model and solving assignment optimization problem in different situations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to practitioners</i> —The forest firefighting problem considered in this article is a typical multitask and multistage optimization problem. Many searching algorithms for multistage optimization problem are available in the existing literature. However, one of the main challenges is that the time of searching increases exponentially with the number of stages. This work first proves that the tasks are completed in the minimum amount of time, under the constraint of one-shot assignment. This finding helps us to evaluate the gap between the searching algorithm and the optimal solution. In addition, in practice, if the underlying dynamic process can be modeled or partially modeled, then we can predict the behavior of future stages and reduce the searching domain. If a model is available, then we can also adjust the assignment scheme dynamically based on the principle that each adjustment would reduce the total time of tasks completion. In this article, we establish a dynamical fire-spreading model and propose a model-based solution to the multistage optimization problems. The findings in this work can serve as a supplement to the existing optimization algorithms.