Solving Delete Free Planning with Relaxed Decision Diagram Based Heuristics

Abstract

We investigate the use of relaxed decision diagrams (DDs) for computing admissible heuristics for the cost-optimal delete-free planning (DFP) problem. Our main contributions are the introduction of two novel DD encodings for a DFP task: a multivalued decision diagram that includes the sequencing aspect of the problem and a binary decision diagram representation of its sequential relaxation. We present construction algorithms for each DD that leverage these different perspectives of the DFP task and provide theoretical and empirical analyses of the associated heuristics. We further show that relaxed DDs can be used beyond heuristic computation to extract delete-free plans, find action landmarks, and identify redundant actions. Our empirical analysis shows that while DD-based heuristics trail the state of the art, even small relaxed DDs are competitive with the linear programming heuristic for the DFP task, thus, revealing novel ways of designing admissible heuristics.

Efficient Encoding of Cost Optimal Delete-Free Planning as SAT

“…Imai and Fukunaga (2015) compute the value of h + by solving a Mixed Integer and Linear Programming (MILP) formulation of delete-free planning problems. Another notable work is computing h + by using relaxed Decision Diagram based heuristics (Castro et al 2020).…”

“…The current state-of-the-art methods for finding exact value of h + are based on Integer and Linear Programming (IP/LP) (Haslum, Slaney, and Thiébaux 2012;Imai and Fukunaga 2015;Castro et al 2020). Because propositional satisfiability has a limited expressive power compared to that of LP and IP, using it for computing h + might seem counter-intuitive.…”

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

“…Similarly, Maschler and Raidl (2018) studied the DD bound quality for a prize-collecting sequencing problem and compared the bounds given by a top-down and an iterative refinement construction scheme. Lastly, Castro et al (2018Castro et al ( , 2019Castro et al ( , 2020b) explored different DDbased relaxations for AI planning problems and show encouraging results when comparing the DD dual bounds with those from an LP relaxation.…”

“…However, larger relaxed DDs require more computational resources, i.e., memory and time for compilation. Further, empirical results show that bound improvements decrease as the DD width increases (Bergman et al 2014c, Castro et al 2020b. The question of which DD width will lead to computationally efficient relaxed DDs that provide informative dual bounds is still open.…”

“…DD bounds can also be integrated into other search procedures, such as a standard branch-and-bound (Cire and van Hoeve 2013, Kinable et al 2017, Castro et al 2020b, Tjandraatmadja and van Hoeve 2020. The main disadvantage is that the search algorithm might not leverage the DD structure as the specialized DD-based branch-and-bound does.…”