Real-Coded Genetic Algorithm for Function Maximization

Real-coded genetic algorithms serve as an efficient approach for continuous function optimization problems. Compared to traditional binary encoding methods, they directly use real numbers to represent solutions, eliminating encoding/decoding processes and achieving higher computational efficiency, making them particularly suitable for high-precision numerical optimization scenarios.

Core Methodology: Population Initialization: Randomly generate multiple real-number solutions within the domain to form the initial population, where each solution represents potential coordinates of function extremum points. Fitness Evaluation: Use the target function value as fitness measure to directly assess solution quality (higher function values indicate better solutions for maximization problems). Selection Operation: Implement roulette wheel or tournament selection strategies to prioritize high-fitness individuals, ensuring propagation of superior genetic material. Real-valued Crossover: Generate offspring through arithmetic crossover operations like Simulated Binary Crossover (SBX), blending parental characteristics while maintaining solution feasibility. Mutation Operation: Apply Gaussian or uniform mutation to introduce perturbations near solutions, enhancing population diversity and preventing premature convergence. Elitism Preservation: Directly retain the best solution from each generation without mutation, guaranteeing algorithm convergence.

Key Advantages: Eliminates binary encoding/decoding steps, reducing computational complexity Mutation operators enable fine-tuning directly in real-number space, providing stronger local search capabilities Particularly effective for multidimensional, nonlinear, multimodal function extremum searches

Typical applications include engineering parameter optimization and machine learning hyperparameter tuning where high-precision numerical solutions are required. By simulating natural evolution mechanisms, the algorithm efficiently explores the solution space to locate global or near-optimal solutions. Implementation typically involves defining solution boundaries, setting population size, and calibrating crossover/mutation probabilities based on problem complexity.