The Lagrangian Relaxation based resources allocation methods for air-to-ground operations under uncertainty circumstances

The task of assigning weapons and sensors to targets is a crucial one in the military, and it is a resources allocation problem under uncertainty circumstances. Firstly, the integer program based formal model of resources allocation is put forward. The formulation can be solved using Lagrangian relaxation (LR) to decouple the multi-target problem into many single-target POMDPs, and they are small enough to solve fastly. Then, the POMDP based single target multi-stage optimization, which reflects the uncertainty in task execution output and decision-making, is bring forward to modeling and solving low level sub-problems. And sub-gradients algorithm is used in top-level search processes to offer the marginal resources price for POMDP sub-problems, so as to coordinate the resources consumption of low level problems. Lastly, the method of construction feasible solutions based on the solutions of Lagrangian dual problem is put forward. Simulation results illustrate the validity of our method.