Basic Genetic Algorithm (GA) Implementation

Genetic Algorithm (GA) is an optimization algorithm that simulates natural selection and genetic mechanisms, widely applied to solve complex optimization problems. Its core concept involves mimicking biological evolution processes through selection, crossover, and mutation operations to progressively search for optimal solutions.

Basic Workflow 1. Population Initialization: Randomly generate a set of candidate solutions (chromosomes) to form the initial population. In MATLAB implementation, this typically involves using rand() or randi() functions to create population matrices. 2. Fitness Evaluation: Calculate fitness values for each individual to measure their quality. This requires designing a fitness function (e.g., fitness = 1/(1+objective_function)) that converts problem objectives into maximization values. 3. Selection Operation: Use methods like roulette wheel selection or tournament selection based on fitness values to choose superior individuals for the next generation. Code implementation often involves cumulative probability calculations and random number comparisons. 4. Crossover Operation: Simulate genetic recombination by exchanging partial genes between two parent individuals to generate new offspring. Common techniques include single-point crossover (using randperm() for crossover point selection) and uniform crossover. 5. Mutation Operation: Randomly alter certain genes with a small probability to increase population diversity. In binary encoding, this can be implemented using bit-flipping operations with rand() < mutation_rate conditions. 6. Termination Criteria: Stop when maximum iterations are reached or fitness convergence is achieved, then output the optimal solution. Convergence detection can be implemented through fitness variance thresholds or best-value stagnation checks.

MATLAB Implementation Key Points - Encoding Methods: Represent solution space using binary, real-valued, or other encoding formats. Binary encoding uses logical operations while real-valued encoding requires boundary handling. - Fitness Function Design: Must be adjusted according to specific problems to ensure guidance toward optimal solutions. The function should be vectorized for efficient population evaluation. - Parameter Tuning: Crossover rate and mutation rate significantly impact algorithm efficiency, requiring experimental adjustment. Typical ranges are 0.6-0.9 for crossover and 0.001-0.1 for mutation rates.

Genetic Algorithm's advantage lies in its strong global search capability, making it suitable for nonlinear, multi-peak problems. However, it is sensitive to parameter settings. Improvement methods like elitism preservation (keeping best individuals unchanged) and adaptive parameters (dynamically adjusting rates) can further enhance performance.