MATLAB Code Implementation of Genetic Algorithm for Multidimensional Parameter Optimization

Genetic algorithm is an optimization method that simulates natural selection mechanisms, particularly suitable for solving complex multidimensional parameter problems. When implementing in MATLAB, using floating-point real-value encoding enables more natural handling of continuous parameter spaces compared to binary encoding, reducing encoding/decoding complexity significantly.

The core implementation typically consists of the following modules:

Population Initialization Generating a set of random real-value vectors as the initial population, where each vector represents a potential solution. For multidimensional problems, the vector dimension corresponds to the number of parameters. In MATLAB code, this is typically implemented using rand(nPopulation, nDimensions) to create initial candidates within specified bounds.

Adaptive Fitness Function Designing objective functions to evaluate solution quality, with dynamic adjustment of evaluation weights based on problem requirements. For example, in matrix parameter optimization, one can compute the error norm between matrix operation results and expected values. The implementation often uses vectorized operations like norm(A*x - b) for efficient computation.

Selection Operation Employing tournament selection or roulette wheel strategies to preferentially retain high-fitness individuals. To prevent premature convergence, linear ranking selection mechanisms can be introduced to balance exploration and exploitation. Code implementation might include tournamentSelect function with adjustable tournament size parameter.

Real-value Crossover and Mutation Crossover: Implementing simulated binary crossover (SBX) or arithmetic crossover, where parent vectors exchange dimension values probabilistically. The SBX operator in MATLAB code uses distribution indices to control offspring spread around parents. Mutation: Applying Gaussian mutation or polynomial mutation to introduce small perturbations in certain dimensions, maintaining population diversity. Mutation functions typically use randn for Gaussian noise with adaptable standard deviation.

Elitism Strategy Preserving several optimal individuals directly into the next generation during each iteration to prevent loss of quality solutions. This is implemented by storing top performers in an elite pool using sorting functions like sort based on fitness values.

The adaptive mechanism manifests in dynamic adjustment of crossover/mutation probabilities—increasing mutation probability when population diversity decreases, and raising crossover probability when convergence stagnates. The implementation outputs the optimal solution from the final generation as the optimized result for multidimensional matrix parameters. This approach overcomes traditional genetic algorithms' drawback of requiring manual parameter tuning, making it suitable for engineering applications.