This paper demonstrates that a robust genetic algorithm for the traveling salesman problem (TSP) should preserve and add good edges efficiently, and at the same time, maintain the population diversity well. We analyzed the strengths and limitations of several well-known genetic operators for TSPs by the experiments. To evaluate these factors, we propose a new genetic algorithm integrating two genetic operators and a heterogeneous pairing selection. The former can preserve and add good edges efficiently and the later will be able to keep the population diversity. The proposed approach was evaluated on 15 well-known TSPs whose numbers of cities range from 101 to 13509. Experimental results indicated that our approach, somewhat slower, performs very robustly and is very competitive with other approaches in our best surveys. We believe that a genetic algorithm can be a stable approach for TSPs if its operators can preserve and add edges efficiently and it maintains population diversity.