Machine Learning-based heuristics have recently shown impressive performance in solving a variety of hard combinatorial optimization problems (COPs). However they generally rely on a separate neural model, specialized and trained for each single problem. Any variation of a problem requires adjustment of its model and re-training from scratch. In this paper, we propose GOAL (for Generalist combinatorial Optimization Agent Learner), a generalist model capable of efficiently solving multiple COPs and which can be fine-tuned to solve new COPs. GOAL consists of a single backbone plus light-weight problem-specific adapters for input and output processing. The backbone is based on a new form of mixed-attention blocks which allows to handle problems defined on graphs with arbitrary combinations of node, edge and instance-level features. Additionally, problems which involve heterogeneous types of nodes or edges are handled through a novel multi-type transformer architecture, where the attention blocks are duplicated to attend the meaningful combinations of types while relying on the same shared parameters. We train GOAL on a set of routing, scheduling and classic graph problems and show that it is only slightly inferior to the specialized baselines while being the first multi-task model that solves a wide range of COPs. Finally we showcase the strong transfer learning capacity of GOAL by fine-tuning it on several new problems. Our code is available at https://github.com/naver/goal-co .

We consider a large-scale data center where a fleet of heterogeneous mobile robots and human workers collaborate to handle various installation and maintenance tasks. We focus on the underlying multi-agent task assignment problem which is crucial to optimize the overall system. We formalize the problem as a Markov Decision Process and propose an end-to-end learning approach to solve it. We demonstrate the effectiveness of our approach in simulation with realistic data and in the presence of uncertainty.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure. Our code is available at: [link](https://github.com/naver/bq-nco).

We study the problem of finding bi-criteria Pareto optimal journeys in public transit networks. We extend the Trip-Based Public Transit Routing (TB) approach [Sascha Witt, 2015] to allow for users to select modes of interest at query time. As a first step, we modify the preprocessing of the TB method for it to be correct for any set of selected modes. Then, we change the bi-criteria earliest arrival time queries, and propose a similar algorithm for latest departure time queries, that can handle the definition of the allowed mode set at query time. Experiments are run on 3 networks of different sizes to evaluate the cost of allowing for mode personalization. They show that although preprocessing times are increased, query times are similar when all modes are allowed and lower when some part of the network is removed by mode selection.