In this talk, we first give an introduction to modern PC architectures and the GPU, and survey the literature on GPU-based solution methods in discrete optimization that currently consists of some 100 papers. Many of them describe GPU implementations of well-known metaheuristics and report impressive speedups relative to a sequential version. As for applications and problems studied, 26 papers describe research on routing problems of which 9 focus on the Shortest Path Problem, 15 discuss the Travelling Salesman Problem, and only 2 study the Vehicle Routing Problem.
In the second part of this talk we present a GPU-based TSP solver which is inspired by the highly successful and leading TSP solver LKH2 of Keld Helsgaun. To our knowledge this is the first GPU based TSP-solver that provides a competitive solution quality for large sized TSP problems. During the development of the GPU solver we examined two different ways of adapting the Lin-Kernighan heuristic to the data-parallelism of the GPU. In contrast to LKH2, one of these approaches leads to fewer random restarts, but with more heavy and involved local searches. The other version uses the same number of restarts as in LKH2, but with a different distribution into the two kinds of restarts in LKH2. For a selected number of large-scale instances we will present numerical results.