At what point in the genetic algorithm should a fitness approach be applied?

I am using the fitness sharing method to solve a multimodal problem (2 max). The fitness function finds the maximum number of zeros and the number of ones separately:

f=max(u,(1-u))

      

where u

is the number of units in the genotype. For example, for the genotype 101110

,

f=max(4,2)=4

      

The problem can be solved with a genetic algorithm. A genetic algorithm often has 5 steps:

Initial_Population-> Fitness Evaluation-> Selection-> Crossover-> Mutation-> Fitness Evaluation

To ensure that both peaks in this multimodal fitness landscape are found, a fitness sharing method can be added to the genetic algorithm. However, I don't know where this method is introduced in the previous GA steps. Is it between mutation assessment and fitness? And if that's correct, does the fitness assessment make the raw fitness or the adapted fitness from the sharing method?

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The most intuitive way to use fitness sharing is to give it a fitness rating, using it to tune raw fitness every time you assess fitness.

The inspiration for fitness sharing is that in biology, the amount of competition a given organism faces will have a big impact on its fitness. Organisms that have to compete with many other foods will consume less energy and produce fewer offspring, which means their fitness will be lower. There will be tougher competition between more similar organisms.

Thus, fitness sharing is best perceived as an adjustment to the fitness score - this, in fact, explains the fact that the fitness decision is lower than it appears due to "competition." Of course, in the standard genetic algorithm, this is not traditional resource contention. Instead, this competition is the best choice in this part of the fitness landscape.



A more rigorous way to think about fitness sharing is a process that directly deforms the fitness landscapeas shown in the animation below. Hills of warmer colors represent areas in search space that have a higher physical form. Thus, the population quickly gravitates towards them. However, if fitness sharing is applied, it diminishes the fitness associated with these areas, forcing the population to spread and explore more search space (as most locations are only good if there are multiple solutions). Since the fitness landscape directly determines the fitness associated with each decision, it also suggests that the fitness assessment step is an appropriate place to apply the transformation.

enter image description here

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