Question

I think different machine has different answer for this, let me assume this test is performed in same machine.

Actually I am thinking is it worth to implement Genetic algorithm to one of my problem which I assume it has combination/permutation about 20! (! is factoria, it is not really 20, it could be more or less).

If the number is within an allowable scope, I will use brute force (loop through all the possiblity) instread of using Genetic algorithm, because to design GA and the possibility factor (crossover, mutation rate) are not easy.

How am I going to determine whether GA is suitable for the problem domain?

Answer 1

Good question. There’s no precise answer, it depends on a few “rules of thumb” plus a bit of logic.

My suggestions:

• Do the maths to work out how long an exhaustive search will take. This is relatively straightforward, so it’s worth estimating this up-front. If the search space is large (and 20! is probably large enough….) then an exhaustive search is likely to be impractical – e.g. if each solution takes only 1millisecond to evaluate, then doing 20! will still take you 77 million years. Even running a parallel serach with 1000 cores will take 77 thousand years.
• Remember that GAs don’t usually find the optimal solution – they will often converge to a “local minima” in complex problems. You’ll need to determine whether this is “good enough” for your needs (it often is).
• Consider that GAs are relatively better when the evaluation function is computationally expensive (e.g. you have to run a small simulation to evaluate each solution). This is because the expensive evaluation makes the overhead of the GA algorithm itself basically irrelevant, and it is worth it because it avoids the evaluation of huge numbers of unfit solutions in the search space.
• As you noted GAs are tricky to set up and fine-tune – in particular the choise of a good genotype representation and crossover / mutation operators will often make a huge difference to how effective your algorithm will be. You also need to be concious of how you maintain diversity in the population, how big you make each generation etc. It’s a fair project in itself to make a GA run well – there’s quite a lot of “black magic” involved that you will only learn with experience.

Of course, it’s quite possible that neither exhaustive search nor GAs are right for your problem. Some problems are much better addressed by other approaches, and if you can find a smart algorithm that uses either dynamic programming or divide-and-conquer to solve your specific problem then you may find that your 77 million year exhaustive search can actually be solved in a millisecond. A better algorithm will always beat raw computational power once the problem becomes large enough.