Open AccessPosted Content
How to Evaluate Machine Learning Approaches for Combinatorial Optimization: Application to the Travelling Salesman Problem.
Reads0
Chats0
TLDR
A new metric, ratio of optimal decisions (ROD), is proposed, based on a fair comparison with a parametrized oracle, mimicking a ML model with a controlled accuracy, and made open-source in order to ease future research in the field.Abstract:
Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve combinatorial optimization problems, such as the well-known Travelling Salesman Problem (TSP). Based on deep (reinforcement) learning, new models and architecture for the TSP have been successively developed and have gained increasing performances. At the time of writing, state-of-the-art models provide solutions to TSP instances of 100 cities that are roughly 1.33% away from optimal solutions. However, despite these apparently positive results, the performances remain far from those that can be achieved using a specialized search procedure. In this paper, we address the limitations of ML approaches for solving the TSP and investigate two fundamental questions: (1) how can we measure the level of accuracy of the pure ML component of such methods; and (2) what is the impact of a search procedure plugged inside a ML model on the performances? To answer these questions, we propose a new metric, ratio of optimal decisions (ROD), based on a fair comparison with a parametrized oracle, mimicking a ML model with a controlled accuracy. All the experiments are carried out on four state-of-the-art ML approaches dedicated to solve the TSP. Finally, we made ROD open-source in order to ease future research in the field.read more
Citations
More filters
Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Posted Content
Learning TSP Requires Rethinking Generalization
TL;DR: This paper identifies inductive biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training, revealing that extrapolating beyond training data requires rethinking the entire neural combinatorial optimization pipeline.
Posted Content
Combinatorial optimization and reasoning with graph neural networks
Quentin Cappart,Didier Chételat,Elias B. Khalil,Andrea Lodi,Christopher Morris,Petar Veličković +5 more
TL;DR: A conceptual review of recent key advancements in this emerging field, aiming at researchers in both optimization and machine learning, can be found in this article, where the inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity.
Journal ArticleDOI
A machine learning-based branch and price algorithm for a sampled vehicle routing problem
TL;DR: In this article, a branch and price framework is proposed to predict the value of binary decision variables in the optimal solution and to predict branching scores for fractional variables based on full strong branching.
Proceedings ArticleDOI
Learning to Optimise Routing Problems using Policy Optimisation
TL;DR: This article proposed an entropy regularised reinforcement learning (ERRL) method that supports exploration by providing more stochastic policies, improving optimisation, which can find better and faster solutions in most test cases than the state-of-the-art algorithms.
References
More filters
Journal ArticleDOI
Gradient-based learning applied to document recognition
Yann LeCun,Léon Bottou,Léon Bottou,Yoshua Bengio,Yoshua Bengio,Yoshua Bengio,Patrick Haffner +6 more
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Journal ArticleDOI
Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Book
Reinforcement Learning: An Introduction
TL;DR: This book provides a clear and simple account of the key ideas and algorithms of reinforcement learning, which ranges from the history of the field's intellectual foundations to the most recent developments and applications.
Book
Pattern Recognition and Machine Learning
TL;DR: Probability Distributions, linear models for Regression, Linear Models for Classification, Neural Networks, Graphical Models, Mixture Models and EM, Sampling Methods, Continuous Latent Variables, Sequential Data are studied.
Proceedings ArticleDOI
Bleu: a Method for Automatic Evaluation of Machine Translation
TL;DR: This paper proposed a method of automatic machine translation evaluation that is quick, inexpensive, and language-independent, that correlates highly with human evaluation, and that has little marginal cost per run.