A Constrained Optimal Task Scheduling Problem in Multi-Agent System

In our previous works, based on characteristics of emergency systems such as quick response to emergencies, a polynomial time algorithm was proposed to solve task schedulable problem. However, the above mentioned task scheduling method did not consider importance and urgency differences among tasks in selecting task to accomplish. In order to make the task scheduling be more close to actual process of emergencies, the constrained optimal task scheduling problem (COTSP) which considering the implementation sequence of tasks is proposed. Then, the flow network model with cost is built based on instance of COTSP, and it is proved that COTSP can be solved in polynomial time by using minimum cost flow theory on the flow network model. Finally, Iterative Minimum Cost Flow Algorithm (IMCA) is designed to solve COTSP, and IMCA is proved be able to actually derive the optimal solution of COTSP by analyzing the process of IMCA.