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

Faculty of Business and Commerce, Kansai University, 564-8680 Osaka Prefecture, Suita, Japan.

^* Corresponding author: kmura@kansai-u.ac.jp

Received: 1 May 2017
Accepted: 17 December 2017

Abstract

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.