Related papers: Edge-wise Topological Divergence Gaps: Guiding Sea…
We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space…
In the maximum traveling salesman problem (Max TSP) we are given a complete undirected graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. We present a fast combinatorial $\frac…
The travelling thief problem (TTP) is a multi-component optimisation problem involving two interdependent NP-hard components: the travelling salesman problem (TSP) and the knapsack problem (KP). Recent state-of-the-art TTP solvers modify…
In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the…
The Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
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 Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…
In recent years, there has been a notable surge in research on machine learning techniques for combinatorial optimization. It has been shown that learning-based methods outperform traditional heuristics and mathematical solvers on the…
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…
Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…
We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
In this article, a heuristic is proposed for a min-max heterogeneous multi-vehicle multi-depot traveling salesman problem (TSP), wherein heterogeneous vehicles start from given depot positions and need to cover a given set of targets. The…
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…
We present an approach for the traveling salesman problem with graph metric based on Steiner cycles. A Steiner cycle is a cycle that is required to contain some specified subset of vertices. For a graph $G$, if we can find a spanning tree…
Multiple-TSP, also abbreviated in the literature as mTSP, is an extension of the Traveling Salesman Problem that lies at the core of many variants of the Vehicle Routing problem of great practical importance. The current paper develops and…
We give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower…
The Asymmetric Traveling Salesperson Path Problem (ATSPP) is one where, given an asymmetric metric space $(V,d)$ with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V.…