HGADC: Hierarchical Genetic Algorithm with Density-Based Clustering for TSP

Genetic algorithms (GA) are widely used to solve complex combinatorial optimization problems, such as the Traveling Salesman Problem (TSP). However, as the problem being scale-up, the feasible solution space expands extremely large, resulting in a significant decrease in the efficiency of GA. This paper is dedicated to address this challenge on large TSP by proposing an improved Hierarchical Genetic Algorithm with Density-Based Clustering (HGADC). First the Hierarchical Density-Based Clustering (HDBSCAN) algorithm was employed to cluster all cities into clusters. Each cluster will be considered as a sub-problem, by this way we have a hierarchical structure, i.e. low-level intra-cluster sub-problems and high-level inter-clusters problems. For low-level, a novel Elite Ranking strategy GA was proposed. While for high-level, we designed two approaches, one is the Barycenter Method (BM), which condensed the cluster to be an individual city, the other is called Gene Segment Method (GSM), which kept both head and tail of gene segment as a representation of the cluster. Finally, the results of two levels were integrated to form the final solution. HGADC facilitated the preservation of high-quality genes in GA via the clustering method combined with GA, dramatically reduced the problem’s size and computational costs. The experiments showed that the HGADC algorithm exhibits promising performance in solving large TSPs in TSPLIB compared with notable methods such as MMAS, PACO-3OPT, and KIG.