MATLAB Implementation of Genetic Algorithm (GA)

Genetic Algorithm (GA) is an optimization method that simulates biological evolution processes, particularly suitable for solving complex search and optimization problems. Implementing a basic genetic algorithm in MATLAB typically involves key steps such as population initialization, fitness evaluation, selection, crossover, and mutation operations. ### 1. Population Initialization The process begins by randomly generating an initial population where each individual represents a potential solution. In MATLAB, this can be implemented using random number generation functions like `rand` for continuous variables or `randi` for discrete variables. For example, creating a population matrix of size [population_size, chromosome_length] with values within specified bounds using: population = lower_bound + (upper_bound - lower_bound) * rand(pop_size, chrom_len); ### 2. Fitness Evaluation The fitness function assesses the quality of each individual, typically determined by the specific optimization problem. In optimization scenarios, fitness often corresponds to the objective function value or its transformed version. MATLAB implementation involves writing a custom function that evaluates each solution, which can be vectorized for efficiency using array operations: fitness_values = arrayfun(@fitness_func, population); ### 3. Selection Operation Selection mimics natural selection's "survival of the fittest" principle, where individuals with higher fitness have greater chances of being selected. Common selection methods include roulette wheel selection and tournament selection. In MATLAB, roulette wheel selection can be implemented using cumulative probability weights: selected_indices = randsample(1:pop_size, pop_size, true, fitness_probabilities); ### 4. Crossover Operation Crossover (recombination) simulates genetic exchange to create new individuals. Techniques like single-point, multi-point, or uniform crossover can be implemented in MATLAB using indexing operations combined with random number generation. For single-point crossover: crossover_point = randi([1, chrom_len-1]); offspring = [parent1(1:crossover_point), parent2(crossover_point+1:end)]; ### 5. Mutation Operation Mutation introduces random changes to increase population diversity, typically with low probability. This can be achieved by randomly replacing certain genes or adjusting numerical values. MATLAB's random functions control mutation scope and probability: mutation_mask = rand(size(chromosome)) < mutation_rate; mutated_chromosome = chromosome + mutation_mask .* random_changes; ### 6. Iterative Update The algorithm performs selection, crossover, and mutation operations through multiple iterations, gradually optimizing the population until termination conditions are met (e.g., maximum iterations or fitness thresholds). MATLAB implementation typically uses loop structures: for generation = 1:max_generations followed by the sequential application of genetic operators. Genetic algorithm implementation in MATLAB is suitable for both educational demonstrations and engineering optimization problems. By adjusting parameters such as population size, crossover rate, and mutation rate, the algorithm can be adapted to various optimization requirements. The modular structure allows easy customization of individual components for specific applications.