Methods for Detecting Unsolvable Planning Instances using Variable Projection

Abstract: In this thesis we study automated planning, a branch of artificialintelligence, which deals with construction of plans. A plan is typically an action sequence that achieves some specific goal. In particular, we study unsolvable planning instances, i.e. there is no plan. Historically, this topic has been neglected by the planning community, and up to recently the International Planning Competition has only evaluated planners on solvable planning instances. For many applications we can know, e.g. by design, that there is a solution, but this cannot be a general assumption. One example is penetration testing in computer security, where a system inconsidered safe if there is no plan for intrusion. Other examples are resource bound planning instances that have insufficient resources to achieve the goal.The main theme of this thesis is to use variable projection to prove unsolvability of planning instances. We implement and evaluate two planners: the first checks variable projections with the goal of finding an unsolvable projection, and the second builds a pattern collection to provide dead-end detection. In addition to comparing the planners to existing planners, we also utilise a large computer cluser to statistically assess whether they can be optimised further. On the benchmarks of planning instances that we used, it turns out that further improvement is likely to come from supplementary techniques rather than optimisation. We pursued this and enhanced variable projections with mutexes, which yielded a very competitive planner. We also inspect whether unsolvable variable projections tend to be composed of variables that play different roles, i.e. they are not 'similar'. We devise a variable similarity measure to rate how similar two variables are on a scale, and statistically analyse it. The measure can differentiate between unsolvable and solvable planning instances quite well, and is integrated into our planners. We also define a binary version of the measure, namely, that two variables are isomorphic if they behave exactly the same in some optimal solution (extremely similar). With the help of isomorphic variables we identified a computationally tractable class of planning instances that meet certain restrictions. There are several special cases of this class that are of practical interest, and this result encompass them.