Transformer-based placement heuristic for online 2D strip packing problem
This paper addresses the online 2D Strip Packing Problem (2D-SPP), where rectangular items must be packed sequentially into a strip of fixed width, with the objective of minimizing the total height of packing. We propose a novel reinforcement learning (RL) approach based on a transformer encoder–dec...
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| Vydáno v: | Computers & industrial engineering Ročník 210; s. 111464 |
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| Jazyk: | angličtina |
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01.12.2025
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| ISSN: | 0360-8352 |
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| Abstract | This paper addresses the online 2D Strip Packing Problem (2D-SPP), where rectangular items must be packed sequentially into a strip of fixed width, with the objective of minimizing the total height of packing. We propose a novel reinforcement learning (RL) approach based on a transformer encoder–decoder architecture, optimized using Proximal Policy Optimization (PPO). Unlike traditional heuristic methods, which often lack adaptability, our model dynamically selects candidate placements by analyzing spatial relationships between packed items and available free spaces, represented using variants of the MaxRects heuristic. This design enables the agent to generalize across different problem instances with varying lengths. Extensive experiments on a variety of synthetic and real-world datasets, including NGCUT and recursive slicing scenarios, demonstrate that our model consistently outperforms classic heuristics such as MaxRectsBL, MaxRectsBSSF, MaxRectsBAF, and MaxRectsBLSF. In particular, our method achieves up to 73% improvement in packing efficiency on longer episodes and maintains high performance even in generalization settings. The study also introduces the Algorithm Selection Problem to the 2D-SPP domain, showing that transformer-based RL agents can effectively learn heuristic strategies for online combinatorial optimization.
•RL agent uses transformer to solve online 2D strip packing efficiently.•Learns dynamic placement via MaxRects-inspired representations.•Outperforms classic MaxRects variants by up to 73% in long episodes.•Trained with PPO, handles variable input without positional embeddings.•Addresses Algorithm Selection Problem in 2D-SPP with learned strategies. |
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| AbstractList | This paper addresses the online 2D Strip Packing Problem (2D-SPP), where rectangular items must be packed sequentially into a strip of fixed width, with the objective of minimizing the total height of packing. We propose a novel reinforcement learning (RL) approach based on a transformer encoder–decoder architecture, optimized using Proximal Policy Optimization (PPO). Unlike traditional heuristic methods, which often lack adaptability, our model dynamically selects candidate placements by analyzing spatial relationships between packed items and available free spaces, represented using variants of the MaxRects heuristic. This design enables the agent to generalize across different problem instances with varying lengths. Extensive experiments on a variety of synthetic and real-world datasets, including NGCUT and recursive slicing scenarios, demonstrate that our model consistently outperforms classic heuristics such as MaxRectsBL, MaxRectsBSSF, MaxRectsBAF, and MaxRectsBLSF. In particular, our method achieves up to 73% improvement in packing efficiency on longer episodes and maintains high performance even in generalization settings. The study also introduces the Algorithm Selection Problem to the 2D-SPP domain, showing that transformer-based RL agents can effectively learn heuristic strategies for online combinatorial optimization.
•RL agent uses transformer to solve online 2D strip packing efficiently.•Learns dynamic placement via MaxRects-inspired representations.•Outperforms classic MaxRects variants by up to 73% in long episodes.•Trained with PPO, handles variable input without positional embeddings.•Addresses Algorithm Selection Problem in 2D-SPP with learned strategies. |
| ArticleNumber | 111464 |
| Author | Kołodziejczyk, Waldemar Zoltowska, Izabela Kaleta, Mariusz |
| Author_xml | – sequence: 1 givenname: Mariusz orcidid: 0000-0002-2225-8956 surname: Kaleta fullname: Kaleta, Mariusz email: mariusz.kaleta@pw.edu.pl – sequence: 2 givenname: Waldemar orcidid: 0000-0002-2031-4264 surname: Kołodziejczyk fullname: Kołodziejczyk, Waldemar – sequence: 3 givenname: Izabela orcidid: 0000-0002-6563-099X surname: Zoltowska fullname: Zoltowska, Izabela |
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| Cites_doi | 10.1016/j.cor.2020.104959 10.1287/opre.48.2.256.12386 10.3390/math12203223 10.1590/0101-7438.2016.036.02.0197 10.3390/systems11090457 10.1007/978-981-97-4752-8 10.1007/s10100-016-0455-6 10.1145/3056461 10.3934/jimo.2022088 10.1007/s10878-007-9125-x 10.1016/j.cie.2020.106687 10.3390/s24165370 10.1016/j.ejor.2015.08.018 10.1016/S0377-2217(02)00123-6 10.1109/LRA.2024.3468161 10.1016/S0065-2458(08)60520-3 10.5784/36-2-686 10.1016/j.ejor.2020.07.027 10.1016/j.ejor.2008.08.020 10.1016/j.eswa.2022.119153 10.1137/0209064 10.1016/j.apm.2019.01.022 10.1016/j.knosys.2021.107683 10.1016/j.ejor.2020.06.050 10.1287/ijoc.1070.0250 10.1016/j.disopt.2008.11.002 10.1016/S0377-2217(00)00263-0 |
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| Keywords | Proximal Policy Optimization (PPO) Algorithm Selection Problem Reinforcement learning Online packing 2D strip packing problem MaxRects heuristic Transformer architecture |
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| SubjectTerms | 2D strip packing problem Algorithm Selection Problem MaxRects heuristic Online packing Proximal Policy Optimization (PPO) Reinforcement learning Transformer architecture |
| Title | Transformer-based placement heuristic for online 2D strip packing problem |
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