Rethinking the parallelization of random-restart hill climbing: a case study in optimizing a 2-opt TSP solver for GPU execution

Random-restart hill climbing is a common approach to combinatorial optimization problems such as the traveling salesman problem (TSP). We present and evaluate an implementation of random-restart hill climbing with 2-opt local search applied to TSP. Our implementation is capable of addressing large problem sizes at high throughput. It is based on the key insight that the GPU’s hierarchical hardware parallelism is best exploited with a hierarchical implementation strategy, where independent climbs are parallelized between blocks and the 2-opt evaluations are parallelized across the threads within a block. We analyze the performance impact of this and other optimizations on our heuristic TSP solver and compare its performance to existing GPU-based 2-opt TSP solvers as well as a parallel CPU implementation. Our code outperforms the existing implementations by up to 3X, evaluating up to 60 billion 2-opt moves per second on a single K40 GPU. It also outperforms an OpenMP implementation run on 20 CPU cores by up to 8X.