Stability analysis of multi-objective planning problems for unmanned aircraft

By performing sensitivity analysis on multi-objective mission planning problems for unmanned aircraft, this paper provides insight into properties of optimal solutions and their robustness with respect to trade-offs between objectives and also perturbations in the objective functions. We consider mission planning for unmanned aircraft in hostile environments, where a trade-off between short mission execution time and low risk must be made. This paper develops a method to compute stability regions for a set of schedules for a prototypical mission for unmanned aircraft, the weighted multi-objective symmetric traveling salesman problem. A stability region associated with an optimal solution is the set of all perturbations to the input parameters for which that solution remains optimal. In particular, this paper studies perturbations to the weights and costs in the objective functions. This work has multiple potential benefits such as providing insight into how robust a solution is with respect to modeling uncertainties, how limited intelligence resources should be allocated, and the influence of each objective on the solution. A numerical example is given to demonstrate the methods developed in this paper.