I'm trying to solve this problem using genetic algorithms and am having difficulty choosing the fitness function. My problem is a little different than the original Traveling Salesman Problem, since the population and maybe also the win unit do not necessarily contain all the cities.
So, I have 2 values for each unit: the amount of cities he visits, the total time and the order he visits the cities. I tried 2-3 fitness function but they don't give good solutions.
I need an idea of a good fitness function which takes into account the amount of cities he visited and also the total time.
EDIT: more accurate description
The objective of the PTSP is to visit the maximum number of waypoints of the map in the minimum number of time steps. The map takes the form of a two-dimensional board, where ten waypoints are scattered around and multiple obstacles are present. The following image is an example of a map with obstacles and waypoints