Related papers: Continuous Relaxations for the Traveling Salesman …
We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are different from the existing benchmark sets. In particular, we focus on small instances which prove to be challenging for one or more…
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…
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of…
This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the…
In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the…
The convex hull cheapest insertion heuristic is a well-known method that efficiently generates good solutions to the Traveling Salesperson Problem. However, this heuristic has not been adapted to account for precedence constraints that…
In the Traveling Salesman Problem (TSP), a list of cities and the distances between them are given. The goal is to find the shortest possible route that visits each city exactly once and returns to the original city. The TSP has a wide…
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…
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…
The Multi-Traveling Salesman Problem (MTSP) is a commonly used mathematical model for multi-agent task allocation. However, as the number of agents and task targets increases, existing optimization-based methods often incur prohibitive…
This article explores the integration of deep learning models into combinatorial optimization pipelines, specifically targeting NP-hard problems. Traditional exact algorithms for such problems often rely on heuristic criteria to guide the…
The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…
In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman…
The Travelling Salesman Problem (TSP) is one of the most popular Combinatorial Optimization Problem. It is well solicited for the large variety of applications that it can solve, but also for its difficulty to find optimal solutions. One of…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…
When trying to find approximate solutions for the Traveling Salesman Problem with heuristic optimization algorithms, small moves called Lin-$k$-Opts are often used. In our paper, we provide exact formulas for the numbers of possible tours…
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…
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 characterize the optimal cycle for every convex and increasing…
The ML-Constructive heuristic is a recently presented method and the first hybrid method capable of scaling up to real scale traveling salesman problems. It combines machine learning techniques and classic optimization techniques. In this…