arXiv subjects

Daniel Fuertes

Publications and source records attributed to Daniel Fuertes.

7 recordsLinked to original sources

arXiv2026

Geometric Self-Supervised Pre-training for Neural Combinatorial Optimization

Neural Combinatorial Optimization (NCO) techniques have emerged as a highly efficient alternative to traditional exact algorithms for solving routing problems such as the Traveling Salesman Problem (TSP). However, the generalization capabilities of these Reinforcement Learning-based models are severely hindered when scaling to high-dimensional instances. This issue has been mitigated in other domains, like computer vision and natural language processing, by adopting a self-supervised pre-training strategy. Nevertheless, its application to routing graphs, which lack complex topological attributes beyond 2D spatial coordinates, remains a challenge. In this paper, we propose a geometric self-supervised pre-training framework specifically designed to capture spatial invariance and global relative distance distributions. By applying isometric transformations, such as rotations and axial reflections, the model learns robust structural representations prior to the policy optimization phase. Empirical results demonstrate that this strategy consistently outperforms models trained from scratch (baselines), achieving a 7.23\% improvement in tour length for massive zero-shot extrapolation scenarios (TSP1,000). Furthermore, the proposed model exhibits remarkable computational efficiency, delivering speedups of up to two orders of magnitude over the exact solver Concorde at massive scales. The source code and pre-trained models are publicly available at https://github.com/davidaguadocosano/TSP-GeoPretrain.git.

cs.AI↗

arXiv2026

Enhancing Transformer-based Routing by Encoding Distance via Relative Positional Encoding

This paper explores Relative Positional Encoding (RPE) as an additive bias in Transformer architectures to solve the Team Orienteering Problem. By embedding in the attention mechanism pairwise spatial relationships among nodes of the graph that represents the routing problem, the transformer encoder can compute a richer spatial-aware graph embedding that allows the decoder to estimate better routes. Experimental results involving instances up to 100 nodes demonstrate consistent improvements in collected rewards and optimality gaps over vanilla Transformer architectures used by other state-of-the-art works. These findings highlight that explicit relational modeling significantly enhances scalability and generalization for complex combinatorial optimization.

cs.AI↗

arXiv2026

On the Effectiveness of Pretraining for Graph Combinatorial Optimization

This paper introduces a self-supervised pretraining framework for graph combinatorial optimization specifically designed to address the nature of routing problems like the Traveling Salesman Problem. By utilizing graph contrastive learning with geometric augmentations (specifically, rotations and axial reflections) the model is forced to learn invariant structural representations and global relative distance distributions. Results demonstrate that this pretraining strategy outperforms non-pretrained models across various problem scales. Notably, the hybrid strategy (combining rotation and reflection) achieved a 6.57% improvement in tour length for TSP1000, proving that geometric pretraining is an important inductive bias for effectively scaling neural solvers to high-dimensional instances.

cs.AI↗

arXiv2026

Multi-stage Planning for Multi-target Surveillance using Aircrafts Equipped with Synthetic Aperture Radars Aware of Target Visibility

Generating trajectories for synthetic aperture radar (SAR)-equipped aircraft poses significant challenges due to terrain constraints, and the need for straight-flight segments to ensure high-quality imaging. Related works usually focus on trajectory optimization for predefined straight-flight segments that do not adapt to the target visibility, which depends on the 3D terrain and aircraft orientation. In addition, this assumption does not scale well for the multi-target problem, where multiple straight-flight segments that maximize target visibility must be defined for real-time operations. For this purpose, this paper presents a multi-stage planning system. First, the waypoint sequencing to visit all the targets is estimated. Second, straight-flight segments maximizing target visibility according to the 3D terrain are predicted using a novel neural network trained with deep reinforcement learning. Finally, the segments are connected to create a trajectory via optimization that imposes 3D Dubins curves. Evaluations demonstrate the robustness of the system for SAR missions since it ensures high-quality multi-target SAR image acquisition aware of 3D terrain and target visibility, and real-time performance.

cs.RO↗

arXiv2026

NaviFormer: A Deep Reinforcement Learning Transformer-like Model to Holistically Solve the Navigation Problem

Path planning is usually solved by addressing either the (high-level) route planning problem (waypoint sequencing to achieve the final goal) or the (low-level) path planning problem (trajectory prediction between two waypoints avoiding collisions). However, real-world problems usually require simultaneous solutions to the route and path planning subproblems with a holistic and efficient approach. In this paper, we introduce NaviFormer, a deep reinforcement learning model based on a Transformer architecture that solves the global navigation problem by predicting both high-level routes and low-level trajectories. To evaluate NaviFormer, several experiments have been conducted, including comparisons with other algorithms. Results show competitive accuracy from NaviFormer since it can understand the constraints and difficulties of each subproblem and act consequently to improve performance. Moreover, its superior computation speed proves its suitability for real-time missions.

cs.RO↗

arXiv2024

Multi-Agent Environments for Vehicle Routing Problems

Research on Reinforcement Learning (RL) approaches for discrete optimization problems has increased considerably, extending RL to areas classically dominated by Operations Research (OR). Vehicle routing problems are a good example of discrete optimization problems with high practical relevance, for which RL techniques have achieved notable success. Despite these advances, open-source development frameworks remain scarce, hindering both algorithm testing and objective comparison of results. This situation ultimately slows down progress in the field and limits the exchange of ideas between the RL and OR communities. Here, we propose MAEnvs4VRP library, a unified framework for multi-agent vehicle routing environments that supports classical, dynamic, stochastic, and multi-task problem variants within a single modular design. The library, built on PyTorch, provides a flexible and modular architecture design that facilitates customization and the incorporation of new routing problems. It follows the Agent Environment Cycle ("AEC") games model and features an intuitive API, enabling rapid adoption and seamless integration into existing reinforcement learning frameworks. The project source code can be found at https://github.com/ricgama/maenvs4vrp.

cs.LG↗

arXiv2023

TOP-Former: A Multi-Agent Transformer Approach for the Team Orienteering Problem

Route planning for a fleet of vehicles is an important task in applications such as package delivery, surveillance, or transportation, often integrated within larger Intelligent Transportation Systems (ITS). This problem is commonly formulated as a Vehicle Routing Problem (VRP) known as the Team Orienteering Problem (TOP). Existing solvers for this problem primarily rely on either linear programming, which provides accurate solutions but requires computation times that grow with the size of the problem, or heuristic methods, which typically find suboptimal solutions in a shorter time. In this paper, we introduce TOP-Former, a multi-agent route planning neural network designed to efficiently and accurately solve the Team Orienteering Problem. The proposed algorithm is based on a centralized Transformer neural network capable of learning to encode the scenario (modeled as a graph) and analyze the complete context of all agents to deliver fast, precise, and collaborative solutions. Unlike other neural network-based approaches that adopt a more local perspective, TOP-Former is trained to understand the global situation of the vehicle fleet and generate solutions that maximize long-term expected returns. Extensive experiments demonstrate that the presented system outperforms most state-of-the-art methods in terms of both accuracy and computation speed.

cs.AI↗