---
title: "Solving QNP and FOND+ with Generating, Testing and Forbidding"
authors:
  - "Zheyuan Shi"
  - "Hao Dong"
  - "Yongmei Liu"
doi: "10.24963/ijcai.2025/961"
url: "https://ijcai.org/proceedings/2025/961"
pdf: "https://ijcai.org/proceedings/2025/0961.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "8644-8651"
track: "Main Track"
keywords:
  - "Planning and Scheduling: PS: Planning under uncertainty"
  - "Planning and Scheduling: PS: Planning algorithms"
---

# Solving QNP and FOND+ with Generating, Testing and Forbidding

Zheyuan Shi, Hao Dong, Yongmei Liu

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 8644-8651. DOI: [10.24963/ijcai.2025/961](https://doi.org/10.24963/ijcai.2025/961)

## Abstract

Qualitative Numerical Planning (QNP) extends classical planning with numerical variables that can be changed by arbitrary amounts. FOND+ extends Fully Observable Non-Deterministic (FOND) planning by introducing explicit fairness assumptions, resulting in a more expressive model that can also capture QNP as a special case. However, existing QNP and FOND+ solvers still face significant scalability challenges. To address this, we propose a novel framework for solving QNP and FOND+ by generating strong cyclic solutions of the associated FOND problem, testing their validity, and forbidding non-solutions in conducting further searches. For this, we propose a procedure called SIEVE*, which generalizes the QNP termination testing algorithm SIEVE to determine whether a strong cyclic solution is a FOND+ solution. Additionally, we propose several optimization techniques to further improve the performance of our basic framework. We implemented our approach based on the advanced FOND solver PRP; experimental results show that our solver shows superior scalability over the existing QNP and FOND+ solvers.