I am using a genetic algorithm to solve a multivariable optimization problem. The difficulty in exploring all the solutions is that the permissible set of each variable of the solution is of the form {0} U [a,b], where 0 < a < b (the magnitudes are around a=4 and b=15). "Solutions" that do not satisfy the constraints get a low fitness. So when the genetic explores the search space, it is difficult that it tries solutions with one variable at 0 (zero). I can try to enlarge the interval around 0 and to modify the fitness of variables close to zero. Does anybody know how to treat this kind of constraints? By the way I am using the DEAP genetic algorithms, more precisely this one: http://deap.gel.ulaval.ca/doc/default/examples/ga_onemax.html.
Since the single value zero has a insignificant "length" much shorter than any interval [a,b], it is hardly that a solution may contain the value zero based on probabilities.
I suggest that you may re-write the codes of GA operators, and make a solution contain the value at some bigger probabilities in the Population Initialization, like the following code:
1: r=rand();
2: if(r
Thank you MengChang, it is a good option. What do you think about this one:
1: x=rand(0,b)
2: if x < a/2:
3: x=0
4: elseif x in (a/2, a):
5: x.fitness = low rate
6: endif
hi Hector Marañón-Ledesma
To optimize a multivariable problem with constraints of the form `{0} ∪ [a, b]` using a genetic algorithm, consider implementing custom mutation and crossover functions that increase the likelihood of variables taking on a value of zero, and adjust the fitness function to impose penalties for values within the non-desirable range `(0, a)`. You can also employ a two-part variable representation to handle zeros and non-zeros distinctly, initialize the population with a higher frequency of zeros, or use adaptive fitness scaling to dynamically value solutions with zeros more favorably. Lastly, specialized selection mechanisms can be designed to favor individuals that meet the constraints, ensuring the genetic algorithm efficiently explores and exploits the desired search space within the DEAP framework.
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