A multi-objective Covering Salesman Problem with 2-coverage

Abstract

In a wide range of contexts including military operations, environment monitoring, surveillance in border areas, health care, public safety [1, 2], disaster management, humanitarian relief and blood supply chain, a robust solution of the Covering Salesman Problem (CSP) is necessary. These applications require more than one facilities to cover a given customer (region of interest (ROI)). In this paper, we consider the coverage radius to be fixed and same for each node. Then we propose a multi-objective algorithm based on NSGA-II, in which minimization of tour length and maximization of number of nodes with 2-coverage are considered as the objectives. For implementing the algorithm, an individual chromosome is represented using a one-dimensional array with variable length, and developed a new crossover and a new mutation operator based on the problem and variable length chromosome representation. Numerical examples taken from TSP instances (TSPLIB [3]) with number of nodes ranging from 51 to 150 are solved using the algorithm. For each numerical example, the tour corresponding to the solution with 2-coverage of customer nodes is presented, which shows that the proposed algorithm is effective. Finally, a potential future research direction of this problem is discussed.