In the next generation of heterogeneous wireless networks (HWNs), a large number of different radio access technologies (RATs) will be integrated into a common network. In this type of networks, selecting the most optimal and promising access network (AN) is an important consideration for overall networks stability, resource utilization, user satisfaction, and quality of service (QoS) provisioning. This paper proposes a general scheme to solve the access network selection (ANS) problem in the HWN. The proposed scheme has been used to present and design a general multicriteria software assistant (SA) that can consider the user, operator, and/or the QoS view points. Combined fuzzy logic (FL) and genetic algorithms (GAs) have been used to give the proposed scheme the required scalability, flexibility, and simplicity. The simulation results show that the proposed scheme and SA have better and more robust performance over the random-based selection.