Related papers: Efficient Approximations for Many-Visits Multiple …
The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph…
The travelling thief problem (TTP) is a representative of multi-component optimisation problems with interacting components. TTP combines the knapsack problem (KP) and the travelling salesman problem (TSP). A thief performs a cyclic tour…
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…
The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…
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…
Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant on the well-known Christofides' algorithm for the TSP, called the Best-of-Many Christofides' algorithm. The algorithm involves…
Recent systems applying Machine Learning (ML) to solve the Traveling Salesman Problem (TSP) exhibit issues when they try to scale up to real case scenarios with several hundred vertices. The use of Candidate Lists (CLs) has been brought up…
We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…
We present novel path-slicing strategies integrated with quantum local search to optimize solutions for the Traveling Salesman Problem (TSP), addressing the limitations of current Noisy Intermediate-Scale Quantum (NISQ) technologies. Our…
Multimodal Large Language Models (MLLMs) harness comprehensive knowledge spanning text, images, and audio to adeptly tackle complex problems, including zero-shot in-context learning scenarios. This study explores the ability of MLLMs in…
We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal,…
We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…
In the Many-visits Path TSP, we are given a set of $n$ cities along with their pairwise distances (or cost) $c(uv)$, and moreover each city $v$ comes with an associated positive integer request $r(v)$. The goal is to find a minimum-cost…
We present a trajectory optimization algorithm for the traveling salesman problem (TSP) in graphs of convex sets (GCS). Our framework uses an augmented graph of convex sets to encode the TSP specification and solve it exactly as a shortest…
Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep…
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…
The Traveling Salesman Problem is one of the most studied problems in computational complexity and its approximability has been a long standing open question. Currently, the best known inapproximability threshold known is 220/219 due to…
We consider the Travelling Salesman Problem with Neighbourhoods (TSPN) on the Euclidean plane ($\mathbb{R}^2$) and present a Polynomial-Time Approximation Scheme (PTAS) when the neighbourhoods are parallel line segments with lengths between…
The minmax multiple traveling salesman problem involves minimizing the longest tour among a set of tours. The problem is of great practical interest because it can be used to formulate several real-life applications. To solve this…