A new heuristic method for solving the bi-objective period trav- eling salesman problem with tour balancing

In the single objective period traveling salesman problem (SOPTSP), each of given n cities has to be visited by the traveling salesman a fixed number of times according to some allowable day combinations over a given m day planning period with the objective to minimize the total traveling distance over the whole period. The existing solution methods for the SOPTSP always generate a set of unbalanced length of tours that violate most real-world applications, so we expand the SOPTSP to the bi-objective period traveling salesman problem (BOPTSP) by minimizing simultaneously the total traveling time and the difference between the long est and the shortest tours. In this paper, we propose a new heuristic method based on the artificial immune system to solve the BOPTSP with tour balancing, and a test problem taken from literature with 50 cities and 5 day planning period is solved and the s-metric is applied to evidence the effectiveness of the proposed heuristic method .