A Critical Look at the Abstraction Based on Macro-Operators

Abstraction can be an effective technique for dealing with the complexity of planning tasks. This paper is aimed at assessing and identifying in which cases abstraction can actually speed-up the overall search. In fact, it is well known that the impact of abstraction on the time spent to search for a solution of a planning problem can be positive or negative, depending on several factors -including the number of objects defined in the domain, the branching factor, and the plan length. Experimental results highlight the role of such aspects on the overall performance of an algorithm that performs the search at the ground-level only, and compares them with the ones obtained by enforcing abstraction

Hybrid STAN: Identifying and managing combinatorial optimisation sub-problems in planning

It is well-known that planning is hard but it is less well-known how to approach the hard parts of a problem instance effectively. Using static domain analysis techniques we can identify and abstract certain combinatorial sub-problems from a planning instance, and deploy specialised technology to solve these sub-problems in a way that is integrated with the broader planning activities. We have developed a hybrid planning system (STAN4) which brings together alternative planning strategies and specialised algorithms and selects them according to the structure of the planning domain. STAN4 participated successfully in the AIPS-2000 planning competition. We describe how sub-problem abstraction is done, with particular reference to route-planning abstraction, and present some of the competition data to demonstrate the potential power of the hybrid approach

Magnifying Lens Abstraction for Stochastic Games with Discounted and Long-run Average Objectives

Turn-based stochastic games and its important subclass Markov decision processes (MDPs) provide models for systems with both probabilistic and nondeterministic behaviors. We consider turn-based stochastic games with two classical quantitative objectives: discounted-sum and long-run average objectives. The game models and the quantitative objectives are widely used in probabilistic verification, planning, optimal inventory control, network protocol and performance analysis. Games and MDPs that model realistic systems often have very large state spaces, and probabilistic abstraction techniques are necessary to handle the state-space explosion. The commonly used full-abstraction techniques do not yield space-savings for systems that have many states with similar value, but does not necessarily have similar transition structure. A semi-abstraction technique, namely Magnifying-lens abstractions (MLA), that clusters states based on value only, disregarding differences in their transition relation was proposed for qualitative objectives (reachability and safety objectives). In this paper we extend the MLA technique to solve stochastic games with discounted-sum and long-run average objectives. We present the MLA technique based abstraction-refinement algorithm for stochastic games and MDPs with discounted-sum objectives. For long-run average objectives, our solution works for all MDPs and a sub-class of stochastic games where every state has the same value