Related papers: Learning to Sparsify Travelling Salesman Problem I…

In this paper we discuss the application of Artificial Intelligence (AI) to the exemplary industrial use case of the two-dimensional commissioning problem in a high-bay storage, which essentially can be phrased as an instance of Traveling…

Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…

This thesis introduces stochastic generalized routing problem model and proposes exact and heuristic algorithms to solve it efficiently, in a wide range of problem sizes. At first, the classic routing problem with its common variations in…

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…

Evolving diverse sets of high quality solutions has gained increasing interest in the evolutionary computation literature in recent years. With this paper, we contribute to this area of research by examining evolutionary diversity…

Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep…

Graph Neural Networks (GNNs) have emerged as highly successful tools for graph-related tasks. However, real-world problems involve very large graphs, and the compute resources needed to fit GNNs to those problems grow rapidly. Moreover, the…

In this paper, we consider differential approximability of the traveling salesman problem (TSP). We show that TSP is $3/4$-differential approximable, which improves the currently best known bound $3/4 -O(1/n)$ due to Escoffier and Monnot in…

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…

In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input,…

We present a $1.5$-approximation for the Metric Path Traveling Salesman Problem (Path TSP). All recent improvements on Path TSP crucially exploit a structural property shown by An, Kleinberg, and Shmoys [Journal of the ACM, 2015], namely…

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…

Cutting planes are crucial for the performance of branch-and-cut algorithms for solving mixed-integer programming (MIP) problems, and linear row aggregation has been successfully applied to better leverage the potential of several major…

Combinatorial optimization problems are foundational challenges in fields such as artificial intelligence, logistics, and network design. Traditional algorithms, including greedy methods and dynamic programming, often struggle to balance…

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We…

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…

Deep learning's success has been attributed to the training of large, overparameterized models on massive amounts of data. As this trend continues, model training has become prohibitively costly, requiring access to powerful computing…

Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been…

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient…

Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance…