Combining ant colony optimization algorithm and dynamic programming technique for solving the covering salesman problem

The covering salesman problem (CSP) is an extension of the well-known traveling salesman problem in which we are allowed to leave some vertices unvisited. The goal of the CSP is to construct a minimum length Hamiltonian cycle over a subset of vertices where those vertices not visited by the tour need to be within a pre-determined distance from at least one visited vertex. In this paper, we propose a mathematical formulation and a hybrid heuristic algorithm by combining ant colony optimization algorithm and dynamic programming technique to obtain high quality solutions. Comparing the results of the proposed algorithm with available methods in the literature clearly indicates the effectiveness of our proposed heuristic algorithm.