Which Evolutionary Algorithm for optimization of binary problems?

Question

In our program we use a genetic algorithm since years to sole problems for n variables, each having a fixed set of m possible values. This typically works well for ~1,000 variables and 10 possibilities.

Now i have a new task where only two possibilities (on/off) exist for each variable, but i'll probably need to solve systems with 10,000 or more variables. The existing GA does work but the solution improves only very slowly.

All the EA i find are designed rather for continuous or integer/float problems. Which one is best suited for binary problems?

Answer 1

Like DonAndre said, canonical GA was pretty much designed for binary problems.

However...

No evolutionary algorithm is in itself a magic bullet (unless it has billions of years runtime). What matters most is your representation, and how that interacts with your mutation and crossover operators: together, these define the 'intelligence' of what is essentially a heuristic search in disguise. The aim is for each operator to have a fair chance of producing offspring with similar fitness to the parents, so if you have domain-specific knowledge that allows you to do better than randomly flipping bits or splicing bitstrings, then use this.

Roulette and tournament selection and elitism are good ideas (maybe preserving more than 1, it's a black art, who can say...). You may also benefit from adaptive mutation. The old rule of thumb is that 1/5 of offspring should be better than the parents - keep track of this quantity and vary the mutation rate appropriately. If offspring are coming out worse then mutate less; if offspring are consistently better then mutate more. But the mutation rate needs an inertia component so it doesn't adapt too rapidly, and as with any metaparameter, setting this is something of a black art. Good luck!

Answer 2

Well, the Genetic Algorithm in its canonical form is among the best suited metaheuristics for binary decision problems. The default configuration that I would try is such a genetic algorithm that uses 1-elitism and that is configured with roulette-wheel selection, single point crossover (100% crossover rate) and bit flip mutation (e.g. 5% mutation probability). I would suggest you try this combination with a modest population size (100-200). If this does not work well, I would suggest to increase the population size, but also change the selection scheme to a tournament selection scheme (start with binary tournament selction and increase the tournament group size if you need even more selection pressure). The reason is that with a higher population size, the fitness-proportional selection scheme might not excert the necessary amount of selection pressure to drive the search towards the optimal region.

As an alternative, we have developed an advanced version of the GA and termed it Offspring Selection Genetic Algorithm. You can also consider trying to solve this problem with a trajectory-based algorithm like Tabu Search or Simulated Annealing that just uses mutation to move from one solution to another by just making small changes.

We have a GUI-driven software (HeuristicLab) that allows you to experiment with a number of metaheuristics on several problems. Your problem is unfortunately not included, but it's GPL licensed and you can implement your own problem there (through just the GUI even, there's a howto for that).

Answer 3

Why not try a linear/integer program?