# Optimizing Energy Efficiency in Cloud Data Centers:
## 5 Proposed Reinforcement Learning-Based VM Placement in Cloud Environment Using RF_SOM Classifier
### Baseline Algorithms Form VM Placement
#### 5.3.3 Genetic Algorithms (GAs) for VM Placement  
Genetic algorithms (GAs) are a type of evolutionary algorithm inspired by the process of natural selection and genetics. They are used to solve optimization and search problems by mimicking the process of natural selection.  
Initializing the population: We start by creating an initial population comprising individuals, each representing a potential solution to the VM placement problem. These individuals are characterized by a list of host identifiers for every VM, denoting feasible placement locations.  
Evaluating the population: Subsequently, we evaluate each individual within the population using a designated fitness function. This function enables us to gauge the efficacy of each solution based on factors such as resource utilization and load balancing.  
Selecting the best individuals: We proceed by identifying the highest-performing individuals, those exhibiting superior fitness values, for replication. Various selection strategies, including tournament selection or probability-based approaches, may be employed.  
Crossing over selected individuals: Selected individuals are crossed over to produce new offspring to engender new offspring, thus amalgamating attributes from their parent individuals. Crossover mechanisms, such as single-point or two-point crossover, are employed for this process.  
Mutating the new individuals: To foster genetic diversity, a small sub-set of the newly generated offspring undergoes mutation. This random mutation introduces diversity and helps avoid early convergence to suboptimal results.  
Replacing the population: The new offspring subsequently supplant the existing population, helping the algorithm gradually improve its solutions. Only the most high-performing individuals are retained for each subsequent generation.  
Choosing the best solution: After evaluating all the generations, we select the optimum solution from all the individuals. This solution defines the ideal placement of VMs on the available hosts.  
Constructing the migration map: Based on the optimal solution, we build the migration map, associating each virtual machine with its assigned host.  
Returning the migration map: In the end, we provide the migration map as the result of the genetic algorithm, offering an efficient and balanced VM placement strategy.  
The time complexity of a genetic algorithm (GA) depends on the population size (P), the number of generations (G), and the complexity of the fitness function evaluation (F). Each generation involves evaluating the fitness of all individuals, which is \(O(P\cdot F)\), followed by selection, crossover, and mutation operations, typically \(O(P)\) each. Therefore, the overall time complexity per generation is dominated by the fitness evaluation, making it \(O(P\cdot F)\). For G generations, the total time complexity of the GA is \(O(G\cdot P\cdot F)\). This reflects that the primary computational cost arises from the repeated fitness evaluation across generations. The detailed steps of the GA-based VM placement algorithm are presented in Algorithm 5.
```
1:Inputs: vmsToMigrate, excludedHosts
2:Outputs: migrationMap
3:Initialize a population of populationSize individuals
4:for generation = 1 to maxGenerations do
5: Evaluate the population using a fitness function
6: Select the best individuals for reproduction
7: Cross over selected individuals to create new individuals
8: Mutate new individuals to introduce genetic diversity
9: Replace the population with the new individuals
10:endfor
11:Choose the best individual from the population
12:Build migrationMap for the best solution
13:Return migrationMap
```  
**Algorithm 5** GA for VM placement