Related papers: Characterisation of the probabilistic travelling s…
We introduce a new bounding approach called Continuity* C*, which provides optimality guarantees for the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relaxes the continuity constraints on the agent's tour by partitioning…
In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. (The…
We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
In this work, we consider the problem of finding a set of tours to a traveling salesperson problem (TSP) instance maximizing diversity, while satisfying a given cost constraint. This study aims to investigate the effectiveness of applying…
In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once,…
The maximum traveling salesman problem (Max TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. This problem is APX-hard in the general metric case but admits…
We present a polynomial-time approximation scheme (PTAS) for the min-max multiple TSP problem in Euclidean space, where multiple traveling salesmen are tasked with visiting a set of $n$ points and the objective is to minimize the maximum…
The 2-Opt heuristic is one of the simplest algorithms for finding good solutions to the metric Traveling Salesman Problem. It is the key ingredient to the well-known Lin-Kernighan algorithm and often used in practice. So far, only upper and…
This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling…
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…
Current navigation systems conflate time-to-drive with the true time-to-arrive by ignoring parking search duration and the final walking leg. Such underestimation can significantly affect user experience, mode choice, congestion, and…
We study the Many Visits TSP problem, where given a number $k(v)$ for each of $n$ cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city $v$ exactly $k(v)$ times. The currently…
We study the unit-demand capacitated vehicle routing problem in the random setting of the Euclidean plane. The objective is to visit $n$ random terminals in a square using a set of tours of minimum total length, such that each tour visits…
We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and…
Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local…
Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire sam-…
We initiate the study of online routing problems with predictions, inspired by recent exciting results in the area of learning-augmented algorithms. A learning-augmented online algorithm which incorporates predictions in a black-box manner…
A generalization of the classical TSP is the so-called quadratic travelling salesman problem (QTSP), in which a cost coefficient is associated with the transition in every vertex, i.e. with every pair of edges traversed in succession. In…
We consider the problem of estimating the average tour length of the asymmetric TSP arising from the disk scheduling problem with a linear seek function and a probability distribution on the location of I/O requests. The optimal disk…
The travelling thief problem (TTP) is a well-known multi-component optimisation problem that captures the interdependence between two components: the tour across cities and the packing of items. The packing while travelling problem (PWT) is…