Antoine François

Bio: Antoine François is an academic researcher. The author has contributed to research in topics: Travelling salesman problem & Combinatorial optimization. The author has an hindex of 1, co-authored 1 publications receiving 6 citations.

How to Evaluate Machine Learning Approaches for Combinatorial Optimization: Application to the Travelling Salesman Problem.

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.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Learning TSP Requires Rethinking Generalization

Abstract: End-to-end training of neural network solvers for combinatorial optimization problems such as the Travelling Salesman Problem is intractable and inefficient beyond a few hundreds of nodes. While state-of-the-art Machine Learning approaches perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances of practical scales. Towards leveraging transfer learning to solve large-scale TSPs, this paper identifies inductive biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training. Our controlled experiments provide the first principled investigation into such zero-shot generalization, revealing that extrapolating beyond training data requires rethinking the neural combinatorial optimization pipeline, from network layers and learning paradigms to evaluation protocols.

Combinatorial optimization and reasoning with graph neural networks

Abstract: Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring the fact that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by enhancing exact solvers. The inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at researchers in both optimization and machine learning.

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

Abstract: Planning of operations, such as routing of vehicles, is often performed repetitively in rea-world settings, either by humans or algorithms solving mathematical problems. While humans build experience over multiple executions of such planning tasks and are able to recognize common patterns in different problem instances, classical optimization algorithms solve every instance independently. Machine learning (ML) can be seen as a computational counterpart to the human ability to recognize patterns based on experience. We consider variants of the classical Vehicle Routing Problem with Time Windows and Capacitated Vehicle Routing Problem, which are based on the assumption that problem instances follow specific common patterns. For this problem, we propose a ML-based branch and price framework which explicitly utilizes those patterns. In this context, the ML models are used in two ways: (a) to predict the value of binary decision variables in the optimal solution and (b) to predict branching scores for fractional variables based on full strong branching. The prediction of decision variables is then integrated in a node selection policy, while a predicted branching score is used within a variable selection policy. These ML-based approaches for node and variable selection are integrated in a reliability-based branching algorithm that assesses their quality and allows for replacing ML approaches by other (classical) better performing approaches at the level of specific variables in each specific instance. Computational results show that our algorithms outperform benchmark branching strategies. Further, we demonstrate that our approach is robust with respect to small changes in instance sizes.

Learning to Optimise Routing Problems using Policy Optimisation

Abstract: Deep reinforcement learning (DRL) has demonstrated promising performance to learn effective heuristics to solve complex combinatorial optimisation problems via policy networks. However, traditional reinforcement learning (RL) suffers from insufficient exploration, which often results in pre-convergence to poor policies and many challenges the performance of DRL. To prevent this, we propose an Entropy Regularised Reinforcement Learning (ERRL) method that supports exploration by providing more stochastic policies, improving optimisation. The ERRL method incorporates an entropy term, defined over the policy network's outputs, into the loss function of the policy network. Hence, policy exploration can be explicitly advocated subjected to a balance to maximise the reward. As a result, the risk of pre-convergence to inferior policies can be reduced. We implement the ERRL method based on two existing DRL algorithms. We have compared the performances of our implementations with the two DRL algorithms along with several state-of-the-art heuristic-based non-RL approaches for three categories of routing problems, i.e., travelling salesman problem (TSP), capacitated vehicle routing problem (CVRP) and multiple routing with fixed fleet problems (MRPFF). Experimental results show that the proposed method can find better and faster solutions in most test cases than the state-of-the-art algorithms.