# Why GA convergence curves continue as two parallel lines?

I'm working on a optimization problem and using GA algorithm (in MATLAB, ga function).

As you know MATLAB plots GA result with two curves, one for the best values and other to show the mean values and when this two curves touch each others it means algorithm has been converged.

On my cause these two curves don't get along and continue as two parallel lines until the end of max Generations number and finally a premature convergence,What makes it happen?

I have tested with other parameters value but same result. On pre-processing I used Missing value,Normalized and smoothing and tested data set belongs to UCI.

GA Parameters:

MutationFcn      : @mutationadaptfeasible: 0.03
CrossoverFcn     : @crossoverheuristic : 1.2
maxGenerations   : 200;
populationSize   : 180;
Chromosome length: 33
Test Instances   : 71


• Is there a theorem which proves that these two curves must always converge to same value ? I suspect there is no such result. – cfdlab Nov 24 '19 at 14:18
• @cpraveen you mean it can be a normal thing? – motevalizadeh Nov 24 '19 at 15:11
• I dont know enough to answer that. If there is no convergence theorem, then this may happen. In GA, there will be some variability in the different members of the population due to mutations, right ? Why would all members in the population converge to the exact same solution ? – cfdlab Nov 25 '19 at 5:08
• In particular, I can see that there would be no convergence to a single line if you had a problem with local minima. I strongly suspect that it depends on the objective function you are trying to minimize. – Wolfgang Bangerth Nov 25 '19 at 15:42