Related papers: LP-Based Approximation Algorithms for Traveling Sa…
We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…
The Traveling Salesman Problem is one of the most studied problems in computational complexity and its approximability has been a long standing open question. Currently, the best known inapproximability threshold known is 220/219 due to…
We consider some generalizations of the Asymmetric Traveling Salesman Path problem. Suppose we have an asymmetric metric G = (V,A) with two distinguished nodes s,t. We are also given a positive integer k. The goal is to find k paths of…
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…
The Travelling Salesman and its variations are some of the most well known NP hard optimisation problems. This paper looks to use both centralised and decentralised implementations of Evolutionary Algorithms (EA) to solve a dynamic variant…
The paper has been merged into math/0503283
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 ATSP polytope can be expressed by asymmetric polynomial size linear program.
The Multiple Traveling Salesman Problem (mTSP) extends the Traveling Salesman Problem to m tours that start and end at a common depot and jointly visit all customers exactly once. In the min-max variant, the objective is to minimize the…
This letter concerns optimal power transmission line inspection formulated as a proposed generalization of the traveling salesman problem for a multi-route one-depot scenario. The problem is formulated for an inspection vehicle with a…
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…
A well known N P-hard problem called the Generalized Traveling Salesman Problem (GTSP) is considered. In GTSP the nodes of a complete undirected graph are partitioned into clusters. The objective is to find a minimum cost tour passing…
We consider the Travelling Salesman Problem with Neighbourhoods (TSPN) on the Euclidean plane ($\mathbb{R}^2$) and present a Polynomial-Time Approximation Scheme (PTAS) when the neighbourhoods are parallel line segments with lengths between…
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…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
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…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer.
We consider the integrality gap of the subtour LP relaxation of the Traveling Salesman Problem restricted to circulant instances. De Klerk and Dobre conjectured that the value of the optimal solution to the subtour LP on these instances is…
We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several…