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This is my genetic algorithm, step by step:

  1. Generate two initial population's randomly, and select the fittest tour from both.

  2. Perform an ordered crossover, which selects a random portion of the first fit tour and fills in the rest from the second, in order.

  3. Mutates this tour by randomly swapping two cities if the tour is only 1.3 times as good as the top 10% tour in the initial population (which I have literally just done by induction, singling out poor tours that are produced) - I would love to change this but can't think of a better way.

    • The mutation is selected from a population of several mutations.

  4. Returns the tour produced.

The mutation, however is almost ALWAYS worse, if not the same as the crossover.

I'd greatly appreciate some help. Thanks!

sam price
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  • Don't do the crossover. It's not necessary. – Ray Dec 06 '17 at 19:12
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    The crossover actually improves upon that which is selected from the initial population (the parents) - but doesn't produce the best possible tour. – sam price Dec 06 '17 at 19:18
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    Crossover and mutation doesn't make better genes; they make different genes. Selecting makes things better. And crossover is a needless complication. – Ray Dec 06 '17 at 19:22
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    That's what I though as well but take out crossover and mutation and all you have is brute force. I need to design a genetic algorithm. – sam price Dec 06 '17 at 19:49
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    You still do mutation. Randomly "select" among the top genes & mutate it. It's not brute force, it's stochastic. And it's genetic because your mutating "genes". – Ray Dec 07 '17 at 01:01
  • So you're saying your algorithm is to brute force a decent solution and then randomly mutate it and hope it improves? I don't see how this would ever work well. I do appreciate the comments, though. – sam price Dec 07 '17 at 12:51
  • You don't "hope it improves"; you literally select the the best ones to mutate. Selection is the most important part. That's how evolution works. And again, as in natural evolution, crossover is optional. – Ray Dec 07 '17 at 21:12
  • I know you select the best one to mutate, but if you mutate the best one in the way I have, which is just randomly swapping cities, then you will always get a worse solution. I still don't understand why you'd take a good solution and then perform a function that will most likely make it a worse solution. – sam price Dec 08 '17 at 13:05
  • Mutation won't "always get a worse solution". Again, crossover does NOT create better solutions it also makes worse solutions just like mutation. – Ray Dec 08 '17 at 18:07
  • Also, other genetic algorithms that solve tsp, just use mutation. You can look them up on YouTube. – Ray Dec 08 '17 at 18:09

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A problem in GA's is narrowing your search space too quickly and reaching a local maxima solution. You need to ensure that you are not leading your solution in any way other than in the selection/fitness function. So when you say,

why would you take a good solution and then perform a function that will most likely make it a worse solution

,the reason is that you WANT a chance for the solution to take a step back, it will likely need to get worse before it gets better. So really you should remove any judgement logic from your genetic operators, leave this to the selection process.

Also, crossover and mutation should be seen as 2 different ways of generating a child individual, you should use one or the other. In practice, this means you have a chance of performing either a mutation of a single parent or a crossover between 2 parents. Usually the mutation chance is only 5% with crossover being used to generate the other 95%.

A crossover keeps the genetic information from both parents (children are mirror images), so one child will be worse than the parents and the other better (or both the same). So in this sense with crossover, if there is a change, you will always get a better individual.

Mutation on the other hand offers no guarantee of a better individual, yet it exists for the purpose of introducing new data, helping to move the GA from the local maxima scenario. If the mutation fails to improve the individual and makes it worse, then it has less chance of being selected for parenting a child anyway (i.e. you don't need this logic in the mutation operator itself).

you select the best one to mutate

This is not strictly true, good individuals should have a higher CHANCE of being selected. In here there is a subtle difference that BAD individuals may also be selected for parents. Again this helps reduce the chance of reaching a local maxima solution. This also means that the best individual for a generation could (and often does) actually get worse. To solve this we usually implement 'elitism', whereby the best individual is always copied to the next generation (at it is/undergoing no operations).

It would also be beneficial if I could comment on which genetic operators you are using. I have found cycle crossover and inversion mutation to work well in my experience.

M. Mansell
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