Related papers: A Class of Weighted TSPs with Applications
The characterization of strong valid inequalities for integer and mixed-integer programs is more of an artistic task than a systematic methodology, requiring inspiration that can sometimes be elusive. Frequently, this task is facilitated by…
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…
The Quadratic Travelling Salesman Problem (QTSP) is to find a least cost Hamilton cycle in an edge-weighted graph, where costs are defined on all pairs of edges contained in the Hamilton cycle. This is a more general version than the…
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…
In many industrial robotics applications, such as spot-welding, spray-painting or drilling, the robot is required to visit successively multiple targets. The robot travel time among the targets is a significant component of the overall…
Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on…
In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…
This paper considers the application of Model Predictive Control (MPC) to a weighted coverage path planning (WCPP) problem. The problem appears in a wide range of practical applications, including search and rescue (SAR) missions. The basic…
We present a new $(\frac32+\frac1{\mathrm{e}})$-approximation algorithm for the Ordered Traveling Salesperson Problem (Ordered TSP). Ordered TSP is a variant of the classical metric Traveling Salesperson Problem (TSP) where a specified…
The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We study the traveling salesman problem when the positions of the…
We introduce the $L_p$ Traveling Salesman Problem ($L_p$-TSP), given by an origin, a set of destinations, and underlying distances. The objective is to schedule a destination visit sequence for a traveler of unit speed to minimize the…
The $k$-opt algorithm is one of the simplest and most widely used heuristics for solving the traveling salesman problem. Starting from an arbitrary tour, the $k$-opt algorithm improves the current tour in each iteration by exchanging up to…
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 propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
We consider the multiple traveling salesman problem on a weighted tree. In this problem there are $m$ salesmen located at the root initially. Each of them will visit a subset of vertices and return to the root. The goal is to assign a tour…
The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along…
Local search is a widely-employed strategy for finding good solutions to Traveling Salesman Problem. We analyze the problem of determining whether the weight of a given cycle can be decreased by a popular $k$-opt move. Earlier work has…
The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the…
This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once…