title: Genetic Algorithm for Path Finding - Crossover and Mutation
body: <p>I want to use a Genetic Algorithm for finding the shortest path within an undirected graph. I have two questions about this regarding Crossover and Mutation. I've been researching how crossover can be performed in similar situations to this, and the most popular algorithm out there seems to be PMX, my understanding of this is a partial path is swapped between 2 parent chromosomes to make the offspring. The issue I'm having with this is, there is massive scope for almost all of the offspring to become invalid isn't there? I was wondering if you could confirm this for me, and if I'm wrong, please correct me and explain it.</p>
  
  <p>On separate but relevant note; I did have an idea for how to do this, but I don't know if its a good idea, simply select 2 parents where they share the same node in their path and crossover at that point, so all of the offspring remain valid.</p>
  
  <p>My second issue is with Mutation; I have a general idea for how this can be done; would it be wise to select one node and remove it, and relink the path by an alternative means?</p>
  
  <p>Thanks :)!</p>