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The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…

The multiple Traveling Salesmen Problem (mTSP) is a general extension of the famous NP-hard Traveling Salesmen Problem (TSP), that there are m (m > 1) salesmen to visit the cities. In this paper, we address the mTSP with both the minsum…

Grover's search algorithm is one of the basic building block in the world of quantum algorithms. Successfully applying it to combinatorial optimization problems is a subtle challenge. As a quadratic speedup is not enough to naively search…

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Metaheuristics are known to be strong in solving large-scale instances of computationally hard problems. However, their efficiency still needs exploration in the context of instance structure, scale and numerical properties for many of…

We propose an end-to-end learning framework based on hierarchical reinforcement learning, called H-TSP, for addressing the large-scale Travelling Salesman Problem (TSP). The proposed H-TSP constructs a solution of a TSP instance starting…

In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…

With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…

This work presents solutions to the Traveling Salesperson Problem with precedence constraints (TSPPC) using Deep Reinforcement Learning (DRL) by adapting recent approaches that work well for regular TSPs. Common to these approaches is the…

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…

Multi-agent path finding (MAPF) is the problem of finding collision-free paths for a team of agents to reach their goal locations. State-of-the-art classical MAPF solvers typically employ heuristic search to find solutions for hundreds of…

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the…

In the last years, there has been a great interest in machine-learning-based heuristics for solving NP-hard combinatorial optimization problems. The developed methods have shown potential on many optimization problems. In this paper, we…

In this work, we provide a systematic analysis of how large language models (LLMs) contribute to solving planning problems. In particular, we examine how LLMs perform when they are used as problem solver, solution verifier, and heuristic…

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…

Recently, deep reinforcement learning (DRL) frameworks have shown potential for solving NP-hard routing problems such as the traveling salesman problem (TSP) without problem-specific expert knowledge. Although DRL can be used to solve…

Integrating combinatorial optimization layers into neural networks has recently attracted significant research interest. However, many existing approaches lack theoretical guarantees or fail to perform adequately when relying on inexact…

Consider a Machine Learning Service Provider (MLSP) designed to rapidly create highly accurate learners for a never-ending stream of new tasks. The challenge is to produce task-specific learners that can be trained from few labeled samples,…

The Travelling Salesman Problem (TSP), finding a minimal weighted Hamilton cycle in a graph, is a typical problem in operation research and combinatorial optimization. In this paper, based on some novel properties on Hamilton graphs, we…