Dantzig-Wolfe Decomposition for Cost Partitioning

Abstract

Optimal cost partitioning can produce high quality heuristic estimates even from small abstractions. It can be computed with a linear program (LP) but the size of this LP often makes this impractical. Recent work used Lagrangian decomposition to speed up the computation. Here we use a different decomposition technique called Dantzig-Wolfe decomposition to tackle the problem. This gives new insights into optimal cost partitioning and has several advantages over Lagrangian decomposition: our method detects when a cost partition is optimal; it can deal with general cost functions; and it does not consider abstractions in the linear program that do not contribute to the heuristic value. We also show the advantage of the method empirically and investigate several improvements that are useful for all cost partitioning methods.

Sensitivity Analysis for Saturated Post-Hoc Optimization in Classical Planning

“…To evaluate if our theoretical results transfer into practice, we implemented the lazy SPhO heuristic with all four cover rules and the offline SPhO heuristic in the Scorpion planner [25], which is an extension of Fast Downward 22.12 [10] and contains an implementation of the eager SPhO heuristic [26]. In our experiments, we run A * searches [8] with all SPhO heuristic variants over pattern database heuristics [6] using patterns of sizes 1 and 2 that are interesting [20,19] for general cost partitioning [18]. We use CPLEX 20.1 to solve the linear programs and evaluate the different approaches on the 1827 benchmark tasks without conditional effects from the optimal tracks of the 1998-2018 International Planning Competitions (IPCs).…”

“…As a result, previous research has leveraged state sampling either before [14,27,25,5,19] or during [22] the search. These sampled states serve as a basis for computing cost partitioning heuristics, which are then maximized over during the search process.…”