Introducing Preferences in Planning as Satisfiability

Abstract

Planning as Satisfiability is one of the most well-known and effective techniques for classical planning: satplan has been the winning system in the deterministic track for optimal planners in the 4th International Planning Competition (IPC) and a cowinner in the 5th IPC. Given a planning problem Π and a makespan n, the approach based on satisfiability (a.k.a. SAT-based) simply works by (i) constructing a SAT formula Π n and (ii) checking Π n for satisfiability: if there is a model for Π n then we have found a plan, otherwise n is increased. The approach guarantees that the makespan is optimal, i.e. minimum. In this article we extend the Planning as Satisfiability approach in order to handle preferences and satplan in order to solve problems with simple preferences. This allows, e.g. to take into consideration 'plan quality' issues other than makespan, like number of actions and 'soft' goals. The basic idea is to explore the search space of possible plans in accordance with the given partially ordered preferences. We first prove that, at fixed makespan, our approach returns an 'optimal' plan, if any. Then, considering both classical planning problems and problems coming from IPC-5, we show that satplan extended in order to deal with preferences: (i) returns optimal plans that are often of considerable better quality, i.e. with fewer actions or with a better plan metric on soft goals, than satplan; and (ii) is overall competitive, in terms of plan quality, with sgplan, the winning system in the 'SimplePreferences' category of the IPC-5. Notably, such results are often obtained without sacrificing efficiency.

Planning as satisfiability with IPC simple preferences and action costs

“…the winners of the "SimplePreferences" track of the IPC-5 and of all optimizations tracks of the IPC-6, and the previous SAT-based proposal SAT-PLAN(P) [GM11]. Differently from our proposal and [GM11], SGPLAN and GAMER can find sequential plans with unbounded horizon, but they were the clear winners of the competition tracks of interest, and thus are used as references. Our analysis shows that our approach is competitive and helps to widen the set of benchmarks that can be dealt with efficiently using SAT-based technology, at the same time relying on a more natural representation of the planning problem at hand.…”

“…The approach described in [GM07,GM11] is completely based on a compilation into a SAT problem: non-uniform weights, described by a non-constant function w, are dealt by reducing w to a SAT formula by using the encoding in [War98], to be conjoined with the SAT-based encoding of classical planning explained before.…”

“…The second and third columns of Table 1 report the number of variables and clauses of the resulting PB formula as defined in the previous section. We can note that, in general, the new encodings are not that much smaller than those in [GM11]: the size of the added formula depends on how many variables are involved in w, and on the coefficients. Several benchmarks are described by a function w having relatively few actions and goals involved, and with relatively low coefficients.…”

“…improved encodings [RHN06,CHXZ09,RGPS09,HCZ10] and the exceptions to this trend are limited to particular forms of preferences and plan quality measures (e.g., soft goals with uniform costs [GM07], minimum-length plans [BR05], action costs [RG07,CLH08]). In this context the recent extension of the planning as satisfiability framework to include preferences [GM07,GM11] is nowadays considered the reference approach to compute "optimal" plans in SAT-based planning, which includes reasoning about soft goals and plan length as (part of the features) introduced in IPC-5 and IPC-6. 3 It helped to enhance the applicability of the SAT-based approach in planning, by allowing to deal with plan quality issues other than the makespan, outside the "traditional" domains of SAT-based technologies.…”

“…Then, we implement our ideas in SATPLAN and run a wide experimental analysis on planning problems from IPC-5 and IPC-6, taking as references the state-of-the-art planners SG-PLAN [HWHC06,HWHC07] and GAMER [EK09], i.e. the winners of the "SimplePreferences" track of the IPC-5 and of all optimizations tracks of the IPC-6, and the previous SAT-based proposal SAT-PLAN(P) [GM11]. Differently from our proposal and [GM11], SGPLAN and GAMER can find sequential plans with unbounded horizon, but they were the clear winners of the competition tracks of interest, and thus are used as references.…”