Genetic Algorithm Steps: Understanding the Application Order

A Genetic Algorithm (GA) is a method for solving optimization problems based on natural selection. It mimics the process of evolution to find the best solution. Applying a GA involves several key steps that need to be performed in a specific sequence to ensure the algorithm works correctly.

Calculating Fitness: The Starting Point

The first crucial step in applying a Genetic Algorithm is to evaluate how good each potential solution (or 'individual') in the current population is. This is known as calculating the fitness of each member.

• Step C: Calculate fitness of each member of the population. This step assigns a score to each individual, indicating its suitability or quality concerning the problem being solved. Without fitness values, the algorithm cannot determine which individuals are better than others.

Selection: Choosing Parents for the Next Generation

Once the fitness of all individuals is known, the algorithm needs to select which individuals will become parents for the next generation. Better individuals (those with higher fitness) usually have a higher chance of being selected.

• Step A: Select a pair of parents from the population. This selection is typically based on the fitness values calculated in the previous step. Various selection methods exist, like roulette wheel selection or tournament selection.

Crossover: Creating Offspring

The selected parents are then combined to create new potential solutions, called offspring. This process aims to combine desirable traits from the parents.

• Step D: Apply crossover with probability $p_c$ to form offsprings. Crossover involves swapping parts of the parent solutions to create one or more offspring. The probability $p_c$ controls how often this operation occurs. If crossover doesn't happen for a selected pair, the parents might pass directly to the next generation (or copies of them).

Mutation: Introducing Variation

After crossover, the newly created offspring might undergo mutation. Mutation introduces small, random changes into the offspring's genetic material.

• Step B: Apply mutation at each locus with probability $p_m$. Mutation helps maintain diversity in the population and prevents the algorithm from getting stuck in a local optimum. The probability $p_m$ determines the likelihood of a mutation occurring at any specific point (locus) within an individual's representation.

Correct Sequence Summary

Based on the standard workflow of a Genetic Algorithm, the correct order of the given steps is:

1. C: Calculate fitness of each member of the population.
2. A: Select a pair of parents from the population.
3. D: Apply crossover with probability $p_c$ to form offsprings.
4. B: Apply mutation at each locus with probability $p_m$.

Therefore, the correct sequence is C $\rightarrow$ A $\rightarrow$ D $\rightarrow$ B.