Optimality Certificates for Classical Planning

Abstract

Algorithms are usually shown to be correct on paper, but bugs in their implementations can still lead to incorrect results. In the case of classical planning, it is fortunately straightforward to check whether a computed plan is correct. For optimal planning however, plans are additionally required to have minimal cost, which is significantly more difficult to verify. While some domain-specific approaches exists, we lack a general tool to verify optimality for arbitrary problems. We bridge this gap and introduce two approaches based on the principle of certifying algorithms, which provide a computer-verifiable certificate of correctness alongside their answer. We show that both approaches are sound and complete, analyze whether they can be generated and verified efficiently, and show how to apply them to concrete planning algorithms. The experimental evaluation shows that verifying optimality comes with a cost but is still practically feasible. Furthermore it confirms that the tested planner configurations provide optimal plans on the given instances, as all certificates were verified successfully.

Unifying and Certifying Top-Quality Planning

“…Proof: P is a solution to the top-quality planning problem if and only if (a) ∀π ∈ P , cost(π) ≤ q, and (b) Π P has no plans of cost smaller or equal to q. That means that we can certify top-quality planning solutions for Π by certifying optimality for the transformed task Π P (Mugdan, Christen, and Eriksson 2023).…”

“…The natural next step is to check whether a set of plans is a solution to the problem. We follow the existing work on certificates of unsolvability (Eriksson, Röger, and Helmert 2017) and of optimality (Mugdan, Christen, and Eriksson 2023) and propose certifying top-quality planning solutions. We show how to certify top-quality for the unified definition, exploiting existing tools that can certify optimality (Mugdan, Christen, and Eriksson 2023).…”

“…We follow the existing work on certificates of unsolvability (Eriksson, Röger, and Helmert 2017) and of optimality (Mugdan, Christen, and Eriksson 2023) and propose certifying top-quality planning solutions. We show how to certify top-quality for the unified definition, exploiting existing tools that can certify optimality (Mugdan, Christen, and Eriksson 2023). Further, for the computational problems of unordered top-quality planning and subset top-quality planning, the existing in the literature task transformations (Katz, Sohrabi, and Udrea 2020;Katz and Sohrabi 2022) can be used for efficient certification.…”