Why does adding Crossover to my Genetic Algorithm gives me worse results?

Question

I have implemented a Genetic Algorithm to solve the Traveling Salesman Problem (TSP). When I use only mutation, I find better solutions than when I add in crossover. I know that normal crossover methods do not work for TSP, so I implemented both the Ordered Crossover and the PMX Crossover methods, and both suffer from bad results.

Here are the other parameters I'm using:

Mutation: Single Swap Mutation or Inverted Subsequence Mutation (as described by Tiendil here) with mutation rates tested between 1% and 25%.

Selection: Roulette Wheel Selection

Fitness function: 1 / distance of tour

Population size: Tested 100, 200, 500, I also run the GA 5 times so that I have a variety of starting populations.

Stop Condition: 2500 generations

With the same dataset of 26 points, I usually get results of about 500-600 distance using purely mutation with high mutation rates. When adding crossover my results are usually in the 800 distance range. The other confusing thing is that I have also implemented a very simple Hill-Climbing algorithm to solve the problem and when I run that 1000 times (faster than running the GA 5 times) I get results around 410-450 distance, and I would expect to get better results using a GA.

Any ideas as to why my GA performing worse when I add crossover? And why is it performing much worse than a simple Hill-Climb algorithm which should get stuck on local maxima as it has no way of exploring once it finds a local max?

Answer 1

It looks like your crossover operator is introducing too much randomness into the new generations, so you are losing your computational effort trying to improve bad solutions. Imagine that the Hill-Climb algorithm can improve a given solution to the best of its neighborhood, but your Genetic Algorithm can only make limited improvements to almost random population (solutions).

It is also worth to say that GA is not the best tool to solve the TSP. Anyway, you should look like at some examples of how to implement it. e.g. http://www.lalena.com/AI/Tsp/