# Deep Belief Networks (DBN) with IoT-Based Alzheimer's Disease Detection and Classification
## 3 Proposed System
### Maufty Optimization Algorithm
#### 3.5.3 Mating Procedure  
The crossover operator is used to model the mayfly mating behavior described below. One male and one female are picked from each set to be the parents, just as males are attracted to specific females. Winner selection can be based either on chance or on the objective function. For each group, the fittest females mate with the fittest males, the second-fittest females with the second-fittest males, and so on. With the help of the following equation, we can foresee the offspring of the crossover. \[\alpha 1=\beta\times male+(1-\beta)\times female \tag{17}\]  
\[\alpha 2=\beta\times female+(1-\beta)\times male \tag{18}\]  
The first and second generations of this family are denoted here as \(\alpha 1\) and \(\alpha 2\). The third element, \"\(\beta\)\" is a random number within a specified interval. In addition, males and females represent biological parents. Note that a child is assumed to have no initial velocity (Algorithm 1). ```
Inputs: - Population size (N) - Maximum number of iterations (max_iter) - Objective function (obj_func) Outputs: - Best solution found (best_solution)
1. Initialization: * Initialize a population of N female mayflies with random positions and velocities * Initialize a population of male mayflies with random velocities
2. Evaluate initial solutions: * Evaluate the fitness of each female mayfly using the objective function * Set the global best solution (gbest) to be the female mayfly with the highest fitness
3. While stopping criteria are not met do: * Update velocities and solutions: * Update the velocities of male and female mayflies using Equation (1) and (2), respectively * Update the positions of male and female mayflies using Equation (3) and (4), respectively * Evaluate solutions * Evaluate the fitness of each female mayfly using the objective function * Rank the mayflies: * Rank the female mayflies in order of fitness from best to worst * State the mayflies: * Select pairs of female mayflies for mating using a tournament selection approach * Generate offspring using Equation (5) and (6) * Evaluate offspring: * Evaluate the fitness of each offspring using the objective function * Evaluate offspring to male and female randomly: * For each offspring, randomly assign it to be a male or female mayfly G. Replace worst solutions with the best new ones: * Replace the worst female mayflies with the best offspring, maintaining the population size of N * Update the global best solution (gbest) if a better solution is found H. Update personal and global best solutions: * Update the personal best solution (gbest) for each female mayfly if it is better than its current pbest * Update the gbest if a better solution is found * Increment the iteration counter
4. End While
5. Return the best solution found (best_solution), which is the position of the female mayfly with the highest fitness (gbest). ```  
**Algorithm 1** **Mayfly Optimization Algorithm**  
The Mayfly Optimization Algorithm is a metaheuristic optimization algorithm that is inspired by the mating behavior of mayflies. The algorithm begins with an initialization step where a population of female and male mayflies are randomly generated with initial positions and velocities. The fitness of each female mayfly is evaluated using an objective function, and the global best solution is set as the female mayfly with the highest fitness. The algorithm then iterates through a series of steps where the positions and velocities of male and female mayflies are updated using a set of equations. The fitness of each female mayfly is evaluated again, and the female mayflies are ranked based on their fitness. Pairs of female mayflies are selected for mating using a tournament selection approach, and offspring are generated using a set of equations. The fitness of each offspring is evaluated, and they are randomly assigned to be either male or female mayflies. The worst female mayflies are replaced with the best offspring, and the personal and global best solutions are updated accordingly.