Expressive Optimal Temporal Planning via Optimization Modulo Theory

Temporal Planning is the problem of synthesizing a course of actions given a predictive model of a system subject to temporal constraints. This kind of planning finds natural applications in the automation of industrial processes and in robotics when the timing and deadlines are important. Finding any plan in temporal planning is often not enough as it is sometimes needed to optimize a certain objective function: particularly interesting are the minimization of the makespan and the optimization of the costs of actions. Despite the importance of the problem, only few works in the literature tackled the problem of optimal temporal planning because of the complicated intermix of planning and scheduling. In this paper, we address the problem of optimal temporal planning for a very expressive class of problems using a reduction of the bounded planning problem to Optimization Modulo Theory (OMT) a powerful discrete/continuous optimization framework. We theoretically and empirically show the expressive power of this approach and we set a baseline for future research in this area.