Genetic Algorithms (GA) is a new learning paradigm that models a natural evolution mechanism. The framework of GA straightly corresponds to an optimization problem. They are classified into functional optimization and combinatorial one, and have been studied in different manners. GA can be applied to both types of problems and moreover their combinations. According to generations, GA will discover and accumulate building blocks in the form of schemata, and find the global solution as their combinations. It is said GA can find the global solution rapidly if the population holds sufficient varieties. However, this expectation has not been confirmed rigidly. Indeed, there are some problems pointed out such as the early convergence problem in functional optimization, and the encode/decode-crossover problem in combinatorial one. In this paper, we give a solution to the encode/decode-crossover problem for traveling salesman problems (TSP) with a character-preserving GA. In section 2, we define the encode/decode-crossover problem. The encode-decode problem is to define a correspondence between GA space and problem space. The crossover problem is to define a crossover method in GA space. They are closely related to the performance of GA. We point out some problems with conventional approaches for TSP. We propose three criteria to define better encode/decode ; the completeness, soundness and non-redundancy. We also propose a criterion to define better crossover ; character-preservingness. In section 3, we propose a character-preserving GA. In TSP, good subtours are worth preserving for descendants. We propose a subtour exchange crossover, that will not break subtours as possible. We also propose a compress method to improve efficiency. In section 4, we design an experiment to confirm usefulness of our character-preserving GA. We use a double-circled TSP in which the same numbers of cities are placed on two concentrated circles. There are two kinds of local solutions ; "C"-type and "O"-type. The ratio between outer and inner radius determines which is the optimum solution. We vary the radius ratio and see how much optimal solutions are obtained. In the result, character-preserving GA finds optimal solutions effectively.