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you just randomly generate N solutions in your search space

then you evaluate your objective function for these N solutions ... and the fireflies start to shine accordingly

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if you have an educated guess for the location of the optimum, you may generate your solutions at random "around" this location, of course

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For most of the optimization algorithms, the initial population will be randomly generated.

A very common way is the usage of:

x = low_bound + (upper_bound - low_bound) * rand

where x is the position of the firefly, low_bound and upper_bound are the lower and highest values that the decision variable can take and rand is a random number between (0,1)

As mentioned above (in the previous answers), randomization is the most frequent way to initialize your population.

I agree with Alexandros. The initial population is calculated using the formula:

x = LB + rand · (UB − LB), where x is the firefly position that can be determined by the objective function set in the algorithm.  For your reference, I recommend you to read  from https://www.degruyter.com/view/j/bpasts.2012.60.issue-2/v10175-012-0049-y/v10175-012-0049-y.xml

Dear contributors,

your explanation remains incomplete unless you specify the number of those fireflies.  Without a prescription for this number your explanations are indistinguishable from those describing Monte Carlo procedures.

Based on Mr Gutowski's answer, I can assume that Ervin is seeking for the optimal initial number of population. Not the way to produce it.

If this is correct, then my answer in this is ...parameter tuning.

Usually, such algorithms are defined of a standard initial population (e.g. 50 agents or fireflies). Although, trying different number of populations, will eventually lead to the population that helps the algorithm converge fast without trapping the solutions in local optimas.

There is no standard value, but keep in mind that you want so many agents (to achieve high exploration at the begging) as many they must be to interact with each other to achieve exploitation also (search around good solutions).

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here is a link to a limited empirical research in the firefly parameter tuning

http://zeus.inf.ucv.cl/~bcrawford/MII-748-METAHEURISTICAS/Papers_BinaryMH/Optimal%20Choice%20of%20Parameters%20for%20Firefly%20Algorithm.pdf

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thank you for the explanation, it is very helpful