Best fitness refers to the fitness of the best individual in your current population (or sometimes, the fitness of the best individual you have found so far till the current iteration).

However, the average fitness is simply the mean of the fitness values across the entire population. Each generation, the population changes and you get a new average population fitness.

What we generally see in a typical GA run is that best fitness tends to get better as the iterations proceed. This happens quickly at first, and then slowing down-- as the algorithm finds better and better solutions that are harder to improve upon.

The average fitness is always less than (or equal to) the best fitness, and the difference between the two goes on decreasing over time (until the algorithm completely converges, and the population will containing N copies of the same "best" individual).

You may refer to the answer in the link below (from where I have drawn heavily).

http://programmers.stackexchange.com/questions/177474/matlab-best-fitness-vs-mean-fitness-initial-range

Best fitness refers to the fitness of the best individual in your current population (or sometimes, the fitness of the best individual you have found so far till the current iteration).

However, the average fitness is simply the mean of the fitness values across the entire population. Each generation, the population changes and you get a new average population fitness.

What we generally see in a typical GA run is that best fitness tends to get better as the iterations proceed. This happens quickly at first, and then slowing down-- as the algorithm finds better and better solutions that are harder to improve upon.

The average fitness is always less than (or equal to) the best fitness, and the difference between the two goes on decreasing over time (until the algorithm completely converges, and the population will containing N copies of the same "best" individual).

You may refer to the answer in the link below (from where I have drawn heavily).

http://programmers.stackexchange.com/questions/177474/matlab-best-fitness-vs-mean-fitness-initial-range

Thank you sir..

can you tell me how an ideal best fitness vs no. of generation curve shape should be?

and also for the average fitness vs. no. of generation curve?

is it important to find the average fitness and plot them against no. of generations ?

Ideally, the best/average fitness vs no. of generations curve should be monotonically non-decreasing. The best fitness curve will always be "above" the average fitness curve. If the fitness vs no. of generations curve decreases, then this generally means that the Genetic Algorithm is probably not exploring the solution space adequately and this is typically due to inappropriate mutation and cross-over operations.

You have to save at each iteration the best and the average fitness of the population in a vector or list. Once the GA has finished you will have the info to plot the best and average fitness at each iteration.

Matlab has options to do it automatically.

you have to run 30 time at least and easily u can find all Best , average, worst and standard deviation etc.

for plot u have to save the average of all population in a variable and in the last u have to plot it with iteration. 

For some nice examples of average and best fitness you may refer to the link below.

Necessity of the average fitness plot: If you are working on development of the GA tool, the average fitness plot will of course carry some significant meaning; otherwise (for application of GA to some particular kind of problem) the best solutions after several iterations will usually suffice... in that case the plots (particularly the average fitness) seems a bit redundant to me.

www.whitman.edu/mathematics/SeniorProjectArchive/2014/carrjk.pdf

Lets say you have a population to test fitness on.

For each individual in the population:

When you have finished iterating through the population, divide the running total of all individuals' fitness by the number of individuals to find the average fitness.

With this, you'll have the average fitness and the max fitness for this generation. If you are doing comparisons of multiple generations, add these to some container to compare them against future generations.

Depending on your implementation of crossover and mutation, you may find that some generations have a lower max fitness and/or average fitness than the prior generation, but the general trend tends to maximize the fitness function.

I implemented a GA for a graduate course, feel free to check out my report on it in the attachment; there are many charts comparing average and best fitness against number of generations.

Dear Professors,

Genetic Algorithm is one type of evolutionary algorithms based on Charles Darwin's Theory of Evolution. I have problems when I want to analyze the performances of this method by average fitness value and Standard Deviation? Does somebody have references that can share and support me to deal with this or give me some suggestions about other indexes to analyze the performance of the Genetic Algorithm?

Many thanks and regards,