Learning the Travelling Salesperson Problem Requires Rethinking Generalization

Joshi, Chaitanya K.; Cappart, Quentin; Rousseau, Louis-Martin; Laurent, Thomas

doi:10.48550/arxiv.2006.07054

Cited by 6 publications

(11 citation statements)

References 62 publications

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“…The authors stated that, based on their findings, NCO methods are not robust enough to handle real world situations beyond what they see in training and do not reliably scale to practical sizes. As we will see in what follows, apart from the generalization issue reported by Joshi et al [24], the application of NCO in COPs poses a number of questions that are worth investigating. For that purpose, in this paper we present a broad analysis addressing those concerns.…”

Section: Related Workmentioning

confidence: 98%

“…The model infers the matrix in one go and solutions are then obtained by performing a beamsearch over the probability matrix [23]. (2) Autoregressive methods construct the solutions sequentially, adding one item to the solution in each iteration and updating its current state [24].…”

Section: Related Workmentioning

confidence: 99%

“…Joshi et al [24] analyse the generalization of these architectures to instances larger than those seen in training. The authors stated that, based on their findings, NCO methods are not robust enough to handle real world situations beyond what they see in training and do not reliably scale to practical sizes.…”

Section: Related Workmentioning

confidence: 99%

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Neural Combinatorial Optimization: a New Player in the Field

Garmendia¹,

Ceberio²,

Mendiburu³

2022

Preprint

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Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural architectures for a wide variety of combinatorial problems. However, the incorporation of such algorithms in the conventional optimization framework has raised many questions related to their performance and the experimental comparison with other methods such as exact algorithms, heuristics and metaheuristics. This paper presents a critical analysis on the incorporation of algorithms based on neural networks into the classical combinatorial optimization framework. Subsequently, a comprehensive study is carried out to analyse the fundamental aspects of such algorithms, including performance, transferability, computational cost and generalization to larger-sized instances. To that end, we select the Linear Ordering Problem as a case of study, an NP-hard problem, and develop a Neural Combinatorial Optimization model to optimize it. Finally, we discuss how the analysed aspects apply to a general learning framework, and suggest new directions for future work in the area of Neural Combinatorial Optimization algorithms.

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Section: Related Workmentioning

confidence: 98%

Section: Related Workmentioning

confidence: 99%

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Neural Combinatorial Optimization: a New Player in the Field

Garmendia¹,

Ceberio²,

Mendiburu³

2022

Preprint

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“…Recently several machine learning-based methods such as Joshi et al (2020), Bresson and Laurent (2021), Kool, van Hoof, and Welling (2018) have been developed to address TSP. In these studies, TSP is reformulated as a deep reinforcement learning problem where the actor's policy network is implemented by Graph Neural Network (GNN) or Transformers Vaswani et al (2017) trained using the REINFORCE Williams (1992) method.…”

Section: Related Workmentioning

confidence: 99%

Learning from Drivers to Tackle the Amazon Last Mile Routing Research Challenge

Chen¹,

Yin²,

March³

et al. 2022

Preprint

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The goal of the Amazon Last Mile Routing Research Challenge is to integrate the real-life experience of Amazon drivers into the solution of optimal route planning and optimization. This paper presents our method that tackles this challenge by hierarchically combining machine learning and conventional Traveling Salesperson Problem (TSP) solvers. Our method reaps the benefits from both worlds. On the one hand, our method encodes driver know-how by learning a sequential probability model from historical routes at the zone level, where each zone contains a few parcel stops. It then uses a single step policy iteration method, known as the Rollout algorithm, to generate plausible zone sequences sampled from the learned probability model.On the other hand, our method utilizes proven methods developed in the rich TSP literature to sequence stops within each zone efficiently. The outcome of such a combination appeared to be promising. Our method obtained an evaluation score of 0.0374, which is comparable to what the top three teams have achieved on the official Challenge leaderboard. Moreover, our learning-based method is applicable to driving routes that may exhibit distinct sequential patterns beyond the scope of this Challenge. The source code of our method is publicly available at this GitHub repository † .

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“…For example, a recent study (Tang et al, 2020) has demonstrated the direct benefits of choosing inductive biases that align well with iterative algorithms. Algorithms have also been used to highlight the importance of attention mechanisms (Graves et al, 2014) or to disambiguate various message passing mechanisms for graph neural networks (Richter & Wattenhofer, 2020;Joshi et al, 2020;Veličković et al, 2019).…”

Section: Motivationmentioning

confidence: 99%