Implementation of Genetic Algorithm Using MATLAB Code

Genetic Algorithm (GA) is an intelligent optimization algorithm that mimics biological evolution processes, particularly suitable for solving multi-dimensional parameter optimization problems. Below are the core concepts for implementing a real-valued floating-point encoded genetic algorithm in MATLAB:

Population Initialization The algorithm uses floating-point encoding to directly generate initial solutions, where each individual represents a set of parameters to be optimized. Population size is determined based on problem complexity, typically ranging from 50 to 200 individuals. In MATLAB implementation, this can be achieved using functions like rand() or randn() to create random matrices representing the initial population.

Adaptive Crossover and Mutation - Adaptive Crossover Probability: Dynamically adjusts crossover rates based on individual fitness values, preserving genes from high-quality individuals while increasing crossover probability for inferior ones. This can be implemented using conditional statements that modify crossover rates according to fitness rankings. - Non-uniform Mutation: Gradually reduces mutation step sizes during later iterations to balance global exploration and local refinement. This is typically implemented through generation-dependent mutation parameters that decrease linearly or exponentially over time.

Fitness Function Design The objective function is transformed into fitness values, where minimization problems commonly use reciprocal or negative value conversions. For multi-dimensional matrix parameters, vectorization techniques are employed to enhance computational efficiency. MATLAB's vector operations and matrix functions can significantly speed up fitness calculations compared to loop-based implementations.

Selection Mechanism Combines roulette wheel selection with elitism strategy to ensure superior individuals progress to the next generation while maintaining population diversity. The implementation involves calculating selection probabilities proportional to fitness values and preserving top-performing individuals unchanged.

Termination Conditions Sets maximum iteration limits or fitness thresholds, with early termination triggered when optimal solutions show no significant improvement over consecutive generations. Convergence criteria can be monitored through difference checks between generation best fitness values.

Implementation Key Points: - Uses matrix operations instead of loops to accelerate MATLAB execution - Employs fitness value normalization to prevent premature convergence - Includes visualization modules to track optimal solution evolution curves - The implementation follows modular design (initialization, selection, crossover, mutation sub-functions) for readability and can be directly extended to higher-dimensional parameter optimization scenarios.

Code structure typically includes main function coordinating the evolutionary process, with separate functions handling population generation, fitness evaluation, genetic operators, and results visualization using MATLAB's plotting capabilities.