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This question is basically clone of . I am reposting it here because in my opinion it is more appropriate site and because I didn't actually see answer itself.

Quote from there:

I understand the reasoning behind it: crossover allows the strengths of two individuals to be combined into one individual. But to me that's like saying we can mate a scientist and a jaguar to get a smart and fast hybrid.

My part of the question:

I think you will agree that the only thing that differs GA from classic searches (gradient-like or pseudo gradient searches with some combination with anti-local optimum perturbations like simulated annealing) is crossover operation.

So that is the reason of doing crossover for example on Knapsack problem (on which as I heard GA doing good job) or any other example of GA you like?

Additional question:

Also is there any theoretical approach which shows crossover efficiency?

Note: Question is seemed to be complex (not only for me as for newbie) please answer your best do not try give precisely write answer.

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  • $\begingroup$ A Particle Swam Optimiser (PSO) can (i think) be expressed as a particularly specific GA crossover and mutation function (It is a real stretch of the definitions though). PSO's have a proof of convergence (under certain constraints). If I recall correctly it is in a paper by Miller (but I could be getting confused). $\endgroup$ Commented Sep 29, 2015 at 14:10
  • $\begingroup$ Could you please unfold the abbreviations (I am not specialist)? $\endgroup$ Commented Sep 29, 2015 at 14:12
  • $\begingroup$ Done. PSO = Particle Swarm Optimiser. en.wikipedia.org/wiki/Particle_swarm_optimization The "Cross-over" is to breed each particle with the Global Best particle (Storing the position as a "gene"). The "Mutation" is to move according to the motion rules, using both the local best and global best "genes", and mutating all individuals every step. $\endgroup$ Commented Sep 29, 2015 at 14:14
  • $\begingroup$ PSO reminds me random search, such case there you don't have gradient and have to simulate it. $\endgroup$ Commented Sep 29, 2015 at 14:21

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