Applicability of Neural Combinatorial Optimization: A Critical View

Abstract

Neural Combinatorial Optimization has emerged as a new paradigm in the optimization area. It attempts to solve optimization problems by means of neural networks and reinforcement learning. In the last few years, due to their novelty and presumably good performance, many research papers have been published introducing new neural architectures for a variety of combinatorial problems. However, the incorporation of such models in the conventional optimization portfolio raises many questions related to their performance compared to other existing methods, such as exact algorithms, heuristics or metaheuristics. This paper aims to present a critical view of these new proposals, discussing their benefits and drawbacks with respect to the tools and algorithms already present in the optimization field. For this purpose, a comprehensive study is carried out to analyse the fundamental aspects of such methods, including performance, computational cost, transferability and reusability of the trained model. Moreover, this discussion is accompanied by the design and validation of a new neural combinatorial optimization algorithm on two well-known combinatorial problems, the Linear Ordering Problem and the Permutation Flowshop Scheduling Problem. Finally, new directions for future work in the area of Neural Combinatorial Optimization algorithms are suggested.