{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:54:36Z","timestamp":1777128876502,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"MUR PRIN-2020 project RIPER","award":["20203FFYLK"],"award-info":[{"award-number":["20203FFYLK"]}]},{"name":"PNRR MUR project","award":["PE0000013-FAIR,"],"award-info":[{"award-number":["PE0000013-FAIR,"]}]},{"name":"PNRR MUR project SERICS","award":["PE00000014"],"award-info":[{"award-number":["PE00000014"]}]},{"name":"Climate Change AI project","award":["IG-2023-174"],"award-info":[{"award-number":["IG-2023-174"]}]},{"name":"EU H2020 project AIPlan4EU","award":["GA 101016442"],"award-info":[{"award-number":["GA 101016442"]}]},{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Italian Ministry of University and Research"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>This paper introduces LeapNP (Learning and Planning Framework for Numeric Problems), a lightweight, Python-native framework engineered to support both classical and numeric planning tasks. Designed with a fully modular interface, it specifically aims to facilitate the seamless integration of deep learning methodologies. The design philosophy of LeapNP stems from the observation that traditional planners, while highly efficient, lack the necessary flexibility for experimental research, particularly at the intersection of learning and planning. Most state-of-the-art engines are built as highly optimized, rigid executables that are resistant to internal modification. LeapNP disrupts this paradigm by offering a framework where the entire planning stack is accessible and mutable. Users can seamlessly plug in custom implementations for grounding, define novel state representations, or design bespoke search strategies, thereby enabling a level of integration with learning models that is currently impractical with standard tools. By significantly lowering the engineering barrier, our planner fosters rapid experimentation and accelerates research in neuro-symbolic planning. We also present a comprehensive suite of search algorithms, designed to evaluate different properties of learned heuristics. These include two algorithms designed to exploit batching to maximize inference throughput, and a greedy algorithm meant to test the intrinsic robustness of the learned models, running them as general policies.<\/jats:p>","DOI":"10.3390\/fi18020093","type":"journal-article","created":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T13:25:49Z","timestamp":1770816349000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["LeapNP: A Modular Python Framework for Benchmarking Learned Heuristics in Numeric Planning"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-3833-4654","authenticated-orcid":false,"given":"Valerio","family":"Borelli","sequence":"first","affiliation":[{"name":"Department of Information Engineering, Universit\u00e0 Degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy"},{"name":"Department of Computer, Control and Management Engineering, Sapienza Universit\u00e0 di Roma, Via Ariosto 25, 00185, Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9008-6386","authenticated-orcid":false,"given":"Alfonso Emilio","family":"Gerevini","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Universit\u00e0 Degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2274-875X","authenticated-orcid":false,"given":"Enrico","family":"Scala","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Universit\u00e0 Degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7785-9492","authenticated-orcid":false,"given":"Ivan","family":"Serina","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Universit\u00e0 Degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102012","DOI":"10.1016\/j.softx.2024.102012","article-title":"Unified Planning: Modeling, manipulating and solving AI planning problems in Python","volume":"29","author":"Micheli","year":"2025","journal-title":"SoftwareX"},{"key":"ref_2","unstructured":"Alkhazraji, Y., Frorath, M., Gr\u00fctzner, M., Helmert, M., Liebetraut, T., Mattm\u00fcller, R., Ortlieb, M., Seipp, J., Springenberg, T., and Stahl, P. 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