Combinatorial optimization (CO) is fundamental to several realworld applications, from logistics and scheduling to hardware design and resource allocation.Deep reinforcement learning (RL) has recently shown significant benefits in solving CO problems, reducing reliance on domain expertise and improving computational efficiency.However, the absence of a unified benchmarking framework leads to inconsistent evaluations, limits reproducibility, and increases engineering overhead, raising barriers to adoption for new researchers.To address these challenges, we introduce RL4CO, a unified and extensive benchmark with in-depth library coverage of 27 CO problem environments and 23 state-of-the-art baselines.Built on efficient software libraries and best practices in implementation, RL4CO features modularized implementation and flexible configurations of diverse environments, policy architectures, RL algorithms, and utilities with extensive documentation.RL4CO helps researchers build on existing successes while exploring and developing their own designs, facilitating the entire research process by decoupling science from heavy engineering.We finally provide extensive benchmark studies to inspire new insights and future work.RL4CO has already attracted numerous researchers in the community and is open-sourced at https://github.com/ai4co/rl4co 1 .

We introduce PyVRP, a Python package that implements hybrid genetic search in a state-of-the-art vehicle routing problem (VRP) solver. The package is designed for the VRP with time windows (VRPTW) but can be easily extended to support other VRP variants. PyVRP combines the flexibility of Python with the performance of C++ by implementing (only) performance-critical parts of the algorithm in C++ while being fully customizable at the Python level. PyVRP is a polished implementation of the algorithm that ranked first in the 2021 DIMACS VRPTW challenge and, after improvements, ranked first on the static variant of the EURO meets NeurIPS 2022 vehicle routing competition. The code follows good software engineering practices and is well documented and unit tested. PyVRP is freely available under the liberal MIT license. Through numerical experiments, we show that PyVRP achieves state-of-the-art results on the VRPTW and capacitated VRP. We hope that PyVRP enables researchers and practitioners to easily and quickly build on a state-of-the-art VRP solver. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: Funding was provided by TKI Dinalog, Topsector Logistics, and the Dutch Ministry of Economic Affairs and Climate Policy. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0055 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0055 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ . There is a video associated with this paper. Click here to view the Video Overview . To save the file, right click and choose “Save Link As” from the menu.

The Gumbel-max trick is a method to draw a sample from a categorical distribution, given by its unnormalized (log-)probabilities. Over the past years, the machine learning community has proposed several extensions of this trick to facilitate, e.g., drawing multiple samples, sampling from structured domains, or gradient estimation for error backpropagation in neural network optimization. The goal of this survey article is to present background about the Gumbel-max trick, and to provide a structured overview of its extensions to ease algorithm selection. Moreover, it presents a comprehensive outline of (machine learning) literature in which Gumbel-based algorithms have been leveraged, reviews commonly-made design choices, and sketches a future perspective.

We develop ancestral Gumbel-Top-$k$ sampling: a generic and efficient method for sampling without replacement from discrete-valued Bayesian networks, which includes multivariate discrete distributions, Markov chains and sequence models. The method uses an extension of the Gumbel-Max trick to sample without replacement by finding the top $k$ of perturbed log-probabilities among all possible configurations of a Bayesian network. Despite the exponentially large domain, the algorithm has a complexity linear in the number of variables and sample size $k$. Our algorithm allows to set the number of parallel processors $m$, to trade off the number of iterations versus the total cost (iterations times $m$) of running the algorithm. For $m = 1$ the algorithm has minimum total cost, whereas for $m = k$ the number of iterations is minimized, and the resulting algorithm is known as Stochastic Beam Search. We provide extensions of the algorithm and discuss a number of related algorithms. We analyze the properties of ancestral Gumbel-Top-$k$ sampling and compare against alternatives on randomly generated Bayesian networks with different levels of connectivity. In the context of (deep) sequence models, we show its use as a method to generate diverse but high-quality translations and statistical estimates of translation quality and entropy.

The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample $k$ elements without replacement. We show how to implicitly apply this ’Gumbel-Top-$k$’ trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Search. Even for exponentially large domains, the number of model evaluations grows only linear in $k$ and the maximum sampled sequence length. The algorithm creates a theoretical connection between sampling and (deterministic) beam search and can be used as a principled intermediate alternative. In a translation task, the proposed method compares favourably against alternatives to obtain diverse yet good quality translations. We show that sequences sampled without replacement can be used to construct low-variance estimators for expected sentence-level BLEU score and model entropy.