In this paper, we present a Hybrid Genetic Algorithm (HGA) for the TSP. We propose two new crossover operators based on the Minimal Spanning Tree Algorithm (MST), which allows exploiting problem information. Both operators work under the idea of transmitting good chromosomes segments. We propose a parameterized method, which exploits problem information in order to create individuals. A mutation operator based on swap mutation was also proposed. Genetic operators are driven by a fuzzy logic control, which allows reducing computational effort. We used a tool for scientific visualization in order to build a visual environment, which allows seeing how HGA is working. Latest experiments allowed us to find better solutions than current solutions for some TSP instances.