The continuous selective generalized traveling salesman problem: An efficient ant colony system

The Generalized Traveling Salesman Problem (GTSP) extends the classical Traveling Salesman Problem (TSP) and has many interesting applications. In this paper we propose a Continuous Selective Generalized Traveling Salesman Problem (CSGTSP), and the existing GTSP is only a special case of the CSGTSP. To solving it effectively, we extend the ant colony system method from TSP to CSGTSP. Meanwhile, to speed up the convergence and improve the quality of solution, a constrained local searching technique is introduced into this method according to the characteristic of the CSGTSP. Experimental results on numerous TSPLIB instances show that the proposed method can deal with the CSGTSP fairly well, and the developed local searching technique is significantly effective.