Related papers: Report on article The Travelling Salesman Problem:…
In this work we focus on the well-known Euclidean Traveling Salesperson Problem (TSP) and two highly competitive inexact heuristic TSP solvers, EAX and LKH, in the context of per-instance algorithm selection (AS). We evolve instances with…
This paper presents a new method for integrated time-optimal routing and trajectory optimization of multirotor unmanned aerial vehicles (UAVs). Our approach extends the well-known Traveling Salesman Problem by accounting for the limited…
The $k-$traveling salesman problem ($k$-TSP) seeks a tour of minimal length that visits a subset of $k\leq n$ points. The traveling repairman problem (TRP) seeks a complete tour with minimal latency. This paper provides constant-factor…
In math.CO/0111309, we used admissible permutations and a variant of the Floyd-Warshall Algorithm to obtain an optimal solution to the Assignment Problem and an approximate solution to the Traveling Salesman Problem. Here we give a large,…
In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an…
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking…
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…
While traditional optimization problems were often studied in isolation, many real-world problems today require interdependence among multiple optimization components. The traveling thief problem (TTP) is a multi-component problem that has…
Traditional Learning-To-Rank (LETOR) approaches, including pairwise methods like RankNet and LambdaMART, often fall short by solely focusing on pairwise comparisons, leading to sub-optimal global rankings. Conversely, deep learning based…
This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes.…
We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed…
We propose a new transformer model for the Traveling Salesman Problem (TSP) called CycleFormer. We identified distinctive characteristics that need to be considered when applying a conventional transformer model to TSP and aimed to fully…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the metric Travelling Salesman Problem (TSP) has been an open problem for over thirty years, with little progress made. It is known that $4/3 \leq \alpha \leq 3/2$, and a…
The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient…
Investigation of detailed and complex optimisation problem formulations that reflect realistic scenarios is a burgeoning field of research. A growing body of work exists for the Travelling Thief Problem, including multi-objective…
We consider the Travelling Salesman Problem with Vertex Requisitions, where for each position of the tour at most two possible vertices are given. It is known that the problem is strongly NP-hard. The proposed algorithm for this problem has…
In the Traveling Salesperson Problem (TSP) we are given a list of locations and the distances between each pair of them. The goal is to find the shortest possible tour that visits each location exactly once and returns to the starting…
Yatsenko gives a polynomial-time algorithm for solving the traveling salesman problem. We examine the correctness of the algorithm and its construction. We also comment on Yatsenko's evaluation of the algorithm.
The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by…