Constraints on locational optimization problems

Abstract

This paper discusses a clustering approach to locational optimization in the context of UAV (unmanned air vehicles) mission planning. In particular, the deterministic annealing (DA) algorithm from the data compression literature is adapted to address such problems, which bears a strong analogy to the statistical physics formulation of the annealing process (i.e. material transformation under a decreasing temperature schedule). The mission planning domain motivates several extensions to DA to handle the case of heterogeneous UAVs, multiple resource types, and fungible and non-fungible resource types. These extensions introduce constraints on the basic optimization problem. Algorithmically, these are addressed by modifications to the free energy of the DA algorithm. An analysis of the algorithm shows that the iterations at a given temperature are of the form of a decent method, which motivates scaling principles which tend to accelerate convergence. Finally, an application of the algorithm to the UAV prepositioning problem is discussed.