Neural combinatorial optimization: A tutorial

Recent advancements in deep reinforcement learning have sparked a growing interest in the application of this approach to solve combinatorial optimization (CO) problems. This paper presents neural combinatorial optimization (NCO) as a framework for constructing functions that work as heuristics for...

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Veröffentlicht in:Computers & operations research Jg. 182; S. 107102
Hauptverfasser: Angioni, Davide, Archetti, Claudia, Speranza, M. Grazia
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.10.2025
Schlagworte:
Deep neural networks
Neural Combinatorial Optimization
Reinforcement learning
Traveling salesman problem
Traveling salesman problem
Deep neural networks
Neural Combinatorial Optimization
Reinforcement learning
ISSN:0305-0548
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Zusammenfassung:Recent advancements in deep reinforcement learning have sparked a growing interest in the application of this approach to solve combinatorial optimization (CO) problems. This paper presents neural combinatorial optimization (NCO) as a framework for constructing functions that work as heuristics for CO problems. Given the rapid expansion of the field and the increasing interest in the topic, this tutorial introduces the main techniques utilized in NCO and explores the current open issues in the field. We define key terms and concepts related to NCO and present the latest developments, using the Knapsack Problem as a running example to complement theoretical explanations. Finally, we analyze prominent works in the field of NCO, with a focus on their application to the Traveling Salesman Problem, which serves as the most extensively studied problem in this domain. •We provide a tutorial on NCO.•We give an example on the TSP and the KP.•We provide a short code for a basic version of NCO.•We discuss some pros and cons of NCO.
ISSN:0305-0548
DOI:10.1016/j.cor.2025.107102