Investigating TSP Heuristics for Location-Based Services

Abstract

Travel planning is one of the important issues in the location-based services (LBS). Traveling salesman problem (TSP) is to find the optimal tour that traverses points exactly once in the minimum total distance. Given the hardness of TSP (NP-hard), TSP query for a given set of points, Q, is not widely studied for online LBS, and the nearest-neighbor heuristic is the only heuristic adapted to find TSP-like tours with additional constraints for LBS. The questions to ask are: Is the nearest-neighbor the best in terms of accuracy? Which heuristics among many should we use to process TSP queries online for LBS? In the literature, TSPLIB benchmarks are designed for special cases where the number of points used is large, and the existing synthetic datasets are based on uniform/normal distributions. Both do not reflect the real datasets used in real applications. Therefore, the best heuristics suggested by the TSPLIB and the existing benchmarks need to be reconsidered for LBS setting. In this work, we investigate 22 heuristics and show that the best heuristics in terms of accuracy for LBS are not the ones suggested by the existing work, and identify several heuristics by extensive performance studies over real datasets, TSPLIB benchmarks, the existing synthetic datasets and our new synthetic datasets. Among many issues, we also show that it is possible to get high-quality TSP by precomputing/indexing, even though it is hard to prove by theorem.