A generalized model and a heuristic algorithm for the large-scale covering tour problem

The covering tour problem (CTP) is defined on a graph, where there exist two types of vertices. One is called visited vertex , which can be visited. The other is called covered vertex , which must be covered but cannot be visited. Each visited vertex covers a subset of covered vertices, and the costs of edges between visited vertices are given. The objective of the CTP is to obtain a minimum cost tour on a subset of visited vertices while covering all covered vertices. In this paper, we deal with the large-scale CTPs, which are composed of tens of thousands of vertices; in the previous studies, the scales of the instances in the experiments are at most a few hundred vertices. We propose a heuristic algorithm using local search techniques for the large-scale CTP. With computational experiments, we show that our algorithm outperforms the existing methods.