Solving traveling salesman problems by combining global and local search mechanisms

In this paper an evolutionary algorithm for the traveling salesman problem is proposed. The key idea is to enhance the ability of exploration and exploitation by incorporating global search with local search. A new local search, called the neighbor-join (NJ) operator, is proposed to improve the solution quality of the edge assembly crossover (EAX) considered as a global search mechanism in this paper. Our method is applied to 15 well-known traveling salesman problems with numbers of cities ranging from 101 to 3038 cities. The experimental results indicate that the neighbor-join operator is very competitive with related operators surveyed in this paper. Incorporating the NJ into the EAX significantly outperforms the method incorporating 2-opt into the EAX for some hard problems. For each test instance the average value of solution quality stays within 0.03% from the optimum. For the notorious hard problem att532, it is able to find the optimum solution 23 times in 30 independent runs.