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Neural networks have advanced combinatorial optimization, with Transformer-based solvers achieving near-optimal solutions on the Traveling Salesman Problem (TSP) in milliseconds. However, these models operate as black boxes, providing no…

Most neural solvers for the Traveling Salesperson Problem (TSP) are trained to output a single solution, even though practitioners rarely stop there: at test time, they routinely spend extra compute on sampling or post-hoc search. This…

Traditional solvers for tackling combinatorial optimization (CO) problems are usually designed by human experts. Recently, there has been a surge of interest in utilizing deep learning, especially deep reinforcement learning, to…

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with…

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…

The primary paradigm in Neural Combinatorial Optimization (NCO) are construction methods, where a neural network is trained to sequentially add one solution component at a time until a complete solution is constructed. We observe that the…

Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for…

The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…

Neural combinatorial optimization (NCO) has achieved remarkable performance, yet its learned model representations and decision rationale remain a black box. This impedes both academic research and practical deployment, since researchers…

Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been…

End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with…

The Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation…

In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…

There has been a growing number of machine learning methods for approximately solving the travelling salesman problem. However, these methods often require solved instances for training or use complex reinforcement learning approaches that…

Diffusion-based Neural Combinatorial Optimization (NCO) has demonstrated effectiveness in solving NP-complete (NPC) problems by learning discrete diffusion models for solution generation, eliminating hand-crafted domain knowledge. Despite…

Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are…

Neural Combinatorial Optimization (NCO) has emerged as a promising approach for NP-hard problems. However, prevailing RL-based methods suffer from low sample efficiency due to sparse rewards and underused solutions. We propose Best-anchored…

For NP-hard combinatorial optimization problems, it is usually difficult to find high-quality solutions in polynomial time. The design of either an exact algorithm or an approximate algorithm for these problems often requires significantly…

Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant…

Recent advancements in neural combinatorial optimization (NCO) methods have shown promising results in generating near-optimal solutions without the need for expert-crafted heuristics. However, high performance of these approaches often…