Related papers: Generating subtour elimination constraints for the…
Determining the integrality gap of the linear programming (LP) relaxation of the metric traveling salesman problem (TSP) remains a long-standing open problem. We introduce a transfer principle: when the integer optimum of 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…
For several combinatorial optimization problems over random structures, the theory of local weak convergence from probability and the cavity method from statistical physics can be used to deduce a recursive equation for the distribution of…
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…
In the maximum scatter traveling salesman problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting…
The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by…
We design a $1.49993$-approximation algorithm for the metric traveling salesperson problem (TSP) for instances in which an optimal solution to the subtour linear programming relaxation is half-integral. These instances received significant…
Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in…
In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…
Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and…
This work proposes a novel enumeration algorithm for computing the integrality gap of small instances of the subtour elimination formulation for the Asymmetric Traveling Salesman Problem (ATSP). The core idea is to enumerate pairs of…
Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called "last-mile delivery". In this novel approach, they are deployed alongside…
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…
This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency.…
In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast…
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…
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…
The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with…
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…
The traveling salesman problem (TSP) is a cornerstone of combinatorial optimization and has deeply influenced the development of algorithmic techniques in both exact and approximate settings. Yet, improving on the decades-old bounds for…