Related papers: Nonexistence of a Universal Algorithm for Travelin…
The Multiple Traveling Salesman Problem (MTSP) extends the traveling salesman problem by assigning multiple salesmen to visit a set of targets from a common depot, with each target visited exactly once while minimizing total tour length. A…
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 Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
The input to the unrooted traveling repairman problem is an undirected metric graph and a subset of nodes, each of which has a time window of unit length. Given that a repairman can start at any location, the goal is to plan a route that…
In this study, we consider the guidance control problem of the sheepdog system, which involves the guidance of the flock using the characteristics of the sheepdog and sheep. Sheepdog systems require a strategy to guide sheep agents to a…
In this paper we schedule the travel path of a set of drones across a graph where the nodes need to be visited multiple times at pre-defined points in time. This is an extension of the well-known multiple traveling salesman problem. The…
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…
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…
In this paper a highly abstracted view on the historical development of Genetic Algorithms for the Traveling Salesman Problem is given. In a meta-data analysis three phases in the development can be distinguished. First exponential growth…
While there are optimal TSP solvers, as well as recent learning-based approaches, the generalization of the TSP to the Multiple Traveling Salesmen Problem is much less studied. Here, we design a neural network solution that treats the…
We propose a new optimization method based on a demagnetization procedure well known in magnetism. We show how this procedure can be applied as a general tool to search for optimal solutions in any system where the configuration space is…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and V\'egh. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus…
In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q larger than 1, the objective function sums the costs for…
The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and…
In many real-world routing problems, decision makers must optimise over sparse graphs such as transportation networks with non-metric costs on the edges that do not obey the triangle inequality. Motivated by finding a sufficiently long…
We present a self-learning approach that combines deep reinforcement learning and Monte Carlo tree search to solve the traveling salesman problem. The proposed approach has two advantages. First, it adopts deep reinforcement learning to…
If one places N cities randomly on a lattice of size L, we find that the normalized optimal travel distances per city in the Euclidean and Manhattan metrics vary monotonically with the city concentration p. We have studied such optimal…
Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. We…
We study the random link traveling salesman problem, where lengths l_ij between city i and city j are taken to be independent, identically distributed random variables. We discuss a theoretical approach, the cavity method, that has been…