Optimization of bounds in temporal flexible planning with dynamic controllability

A temporal flexible planning problem can be formulated as a simple temporal network with uncertainty (STNU), whose links are classified as contingent and requirement links. The problem of constraint satisfaction for STNU has been characterized as controllability, where dynamic controllability is the most interesting and useful controllability property. We study the assignment of bounds allowed on the requirement links in order for the resulting STNU to be dynamically controllable and the total cost over the allowed ranges of the requirement links to be minimized. Since the problem with a linear cost function is NP-hard, we formulate the dynamic controllability of an STNU with a general cost function as constraints in a nonlinear optimization problem. Our approach is flexible because it can incorporate additional constraints, such as resource constraints, in the formulation. Finally, we present methods to reduce the number of constraints in order to make the problem tractable.