I am trying to solve the problem of optimization (VRP) with genetic algorithm and quantum computing in the platform IBM Q Experience. But I am unable to advance on this. How can I do it? According to my understanding of quantum computing, we cannot apply the two processes of crossover and mutation in their classic sense.
Please have a look at this paper: Ising formulations of many NP problems. It deals with binary optimization on quantum annealers (e.g. D-Wave). As mentioned in comments, quantum annealers are more suitable for optimization tasks in comparison with gate-based universal quantum computers like IBM Q.
Here you can find something more about D-Wave, how it works and how it can be programmed.