OPTIMIZATION OF BOUNDS IN TEMPORAL FLEXIBLE PLANS WITH DYNAMIC CONTROLLABILITY

Abstract

A temporal flexible planning problem that involves contingent and requirement events can be formulated as a simple temporal network with uncertainty (STNU). An STNU is controllable when there is a strategy for executing the requirement events (or actions) in such a way that all the conditions involving contingent events can be satisfied in all situations. The most interesting and useful controllability property is dynamic controllability in which the remaining actions in an STNU can always be scheduled under all possible feasible durations of future contingent events when all the past contingent events are known. In this paper, we propose and study a novel problem of assigning bounds on the duration of each requirement link in order for the resulting STNU to be dynamically controllable and to minimize the total cost over the allowed durations of all requirement links. We first prove the NP hardness of the problem with a linear cost function. We then formulate the dynamic controllability of an STNU as the constraints in a nonlinear optimization problem. Finally, we present methods for reducing the number of constraints in order to make the problem tractable and to demonstrate the computational performance of our methods.