# 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
#### 5.3.2 Particle Swarm Optimization (PSO) for VM Placement  
PSO (particle swarm optimization) is a computer optimization technology inspired by the social behavior of birds in flight or fish in schools. In PSO, a population of solution candidates, called particles, moves through the search space. Each individual particle adjusts its position according to its own experience and that of neighboring particles. To adapt PSO to this discrete optimization problem, we can use a binary representation in which each particle represents a possible assignment of virtual machines to hosts. The following steps outline the adaptation process.  
Step 1 (particle initialization): The process starts by defining a specific number of particles for optimization. For each particle, we randomly generate an initial VM placement configuration in our CloudSim environment. Each configuration is represented by a list of maps, associating each VM with a host.  
Step 2 (evaluation of solution quality): a special power consumption-based function to evaluate each VM placement configuration. This function, adapted to our CloudSim environment, is designed to measure the energy consumption of each configuration.  
Step 3 (updating best positions): Each particle keeps in memory the best VM placement configuration found so far (personal best position), based on the results of the energy consumption-based function.  
Step 4 (updating global best position): We find the best VM placement configuration among all the particles (best overall position), which ensures that our proposal comes close to the optimum solution in terms of minimizing energy consumption.  
Step 5 (updating particle velocity and position): This step uses a power consumption-based function to evaluate each configuration. The velocity and position of each particle are then updated based on the personal best and global best positions, following the PSO update equations adapted to our CloudSim environment.  
Step 6 (repeat steps 2 to 5 until convergence): We iterate the process of evaluation, using the standard PSO update equations, adapted to the discrete nature of VM placement in CloudSim.  
Step 7 (obtaining the optimal solution): When the algorithm converges, the best VM placement configuration (i.e., the global best position) represents the optimal or near-optimal solution for minimizing energy consumption in our CloudSim environment, in accordance with our proposal.  
The time complexity of the particle swarm optimization (PSO) algorithm is influenced by the number of particles (P), the number of dimensions (D), and the number of iterations (T). Each iteration involves evaluating the fitness function for each particle, updating their velocities and positions, and adjusting their personal and global bests. The time complexity per iteration is \(O(P\cdot(F+2D))\), where F represents the cost of the fitness function evaluation. Thus, for T iterations, the overall time complexity is \(O(T\cdot P\cdot(F+2D))\), which can often be approximated as \(O(T\cdot P\cdot F)\) if the fitness evaluation is the most computationally expensive operation. The detailed steps of the PSO-based VM placement algorithm are presented in Algorithm 4.
```
1:Input: vmLists, hostLists, nparticles, maxIter
2:Initialize particles randomly
3:for i = 1 to maxIter do
4: Evaluate energy consumption-based function for each particle based on vms and hosts
5: Update personal best positions for each particle
6: Update global best position
7:for each particle do
8: Update velocity and position based on personal and global best positions
9:endfor
10:Return Best VM placement configuration found
11:endfor
```
**Algorithm 4**PSO for VM placement