MATLAB Implementation of Adaptive Genetic Algorithm with Code Descriptions

Adaptive Genetic Algorithm (AGA) is an enhanced version of traditional genetic algorithms where crossover and mutation probabilities dynamically adjust based on individual fitness values, thereby improving convergence speed and solution accuracy. In MATLAB implementation, the key considerations include designing appropriate fitness functions and establishing mechanisms for automatic probability adjustments based on fitness evaluations. ### Core Algorithm Concepts Fitness Calculation: Each individual's fitness value is determined by the objective function, where higher fitness indicates better solution quality. MATLAB implementation typically involves vectorized fitness function calculations using function handles for efficient population evaluation. Adaptive Crossover Probability: High-fitness individuals receive lower crossover probabilities to preserve quality gene combinations, while low-fitness individuals get higher crossover rates to enhance population diversity. This can be implemented using linear scaling functions like: Pc = Pc_max - (Pc_max - Pc_min) * (fitness - min_fitness)/(max_fitness - min_fitness) Adaptive Mutation Probability: To prevent local optima convergence, mutation probability inversely correlates with fitness. High-fitness individuals have lower mutation rates, while low-fitness individuals get higher mutation probabilities for better global exploration, implemented as: Pm = Pm_min + (Pm_max - Pm_min) * (max_fitness - fitness)/(max_fitness - min_fitness) ### Implementation Key Points Crossover Probability Adjustment: Typically implemented using linear or nonlinear mapping functions that convert fitness values to predefined probability ranges (0.6-0.9). MATLAB code can utilize interpolation functions or custom mapping equations. Mutation Probability Adjustment: Similarly dynamic adjustment using inverse relationships, where lower fitness triggers higher mutation rates. Boundary checks ensure probabilities stay within valid ranges (0.001-0.1). Parameter Boundary Control: Essential to maintain probabilities within effective operational ranges using MATLAB's min/max functions or conditional statements to clamp values. ### Algorithm Advantages Adaptive Genetic Algorithm effectively balances global and local search capabilities, preventing premature convergence, making it suitable for complex optimization problems. In MATLAB, vectorized operations and built-in optimization functions (like ga with custom options) can further enhance computational efficiency through parallel processing and optimized memory management.