In this paper we develop a problem with potential applications in humanitarian relief transportation and telecommunication networks. Given a set of vertices including the depot, facility and customer vertices, the goal is to construct a minimum length cycle over a subset of facilities while covering a given number of customers. Essentially, a customer is covered when it is located within a pre-specified distance of a visited facility on the tour. We propose two node-based and flow-based mathematical models and two metaheuristic algorithms including memetic algorithm and a variable neighborhood search for the problem. Computational tests on a set of randomly generated instances and on set of benchmark data indicate the effectiveness of the proposed algorithms. 
The generalized covering traveling salesman problem