Oversubscription planning termed by D. Smith (2004), also referred to as OSP, deals with achieving a state with a high utility value, given a budget on total action cost. This formulation allows us to handle situations with under-constrained resources, which do not allow us to achieve all possible goal facts. OSP objective differs from classical planning objective, in which the objective is to find a cheap plan which achieves all goal facts. In optimal OSP and optimal classical planning, the tasks are further constrained to finding a path which achieves a state with maximal utility, and, to finding the cheapest cost path which achieves the goal, respectively.
Over the years, the theory and practice of classical planning have been studied and advanced much more intensively compared to OSP. Recent work (Mirkis & Domshlak 2013,2014; Domshlak & Mirkis 2015) made several contributions aiming at improving the scalability of OSP solvers. In particular, they developed a planner which exploits standard landmark discovery tools of classical planning, as well as abstractions for solving OSP problems. They showed how standard goal-reachability landmarks of certain classical planning tasks could be generated to represent achievements of valuable facts of the original OSP task. These landmarks compiled into the original OSP task to obtain an equivalent OSP task with a lower cost allowance, and thus with a smaller effective search space. In this research, we investigate approximation methods for OSP, aiming at extending the scope of the landmark-based approximations for OSP, as well as on improving the scalability of the state-space search driven by these approximations. We propose techniques which allow us to discover more informative landmarks than previous methods. Furthermore, our techniques are applicable for OSP tasks generalized to additive utility setting.
Starting with the most basic question of what additive utility function in OSP problem is, we point out the challenges in multi-valued planning tasks with additive utility setting. We discuss the relationships between state variables and different value assignments to a variable in successive states along a plan. We closely consider negative interactions between state variables with multi-valued (non-zero binary) utility setting, and we show how these negative interactions could occur in tasks with non-negative utility setting. We introduce a novel heuristic search approach to address additive utility OSP tasks which differs from the traditional automated action planning approach in the sense of interpretation of the objective of planning for valuable facts. With our focus on improving state-variables rather than on collecting valuable facts, we define the utility of actions. Investigation of planning tasks and their utility structure with the utility of action definition in hand allowed us to discover properties of optimal plans on the level of actions and sequences of actions. A synergistic combination of these properties allows handling OSP additive utility functions over multi-valued variables.