Solving a new type of TSP using Genetic Algorithm

In this paper, a new type of TSP, i.e. PTSP (Polymorphic Traveling Salesman Problem) is proposed. The problem is discovered from the research of scan field route optimization. As for PTSP, every node is polymorphic, which means each node can have several states, but obtains only a determined state in a determined loop, moreover a path which connects a pair of nodes can be different and have different distances when either of the node is in a different state in this pair of nodes. Aiming at the particularity of PTSP, hierarchical mapping operator is proposed. By reasonable partition, PTSP weight matrix can be translated to TSP weight matrix formally. A combination of hierarchical mapping operator with classical TSP algorithms is a valid way to solve PTSP. To optimize the search process of GA(genetic algorithm), the select operator of GA is improved. In this paper, a combination of hierarchical mapping operator with improved genetic algorithm is used. Finally, four types of select operators are compared to evaluate their convergent results and performances.