Function Extremum Optimization Using Real-Coded Genetic Algorithm

Real-coded genetic algorithm (RCGA) is an optimization technique that directly utilizes real numbers for gene encoding. Compared with traditional binary encoding methods, RCGA demonstrates superior precision and computational efficiency when solving continuous function optimization problems.

When implementing this algorithm in MATLAB, the core workflow consists of five sequential stages: population initialization, fitness evaluation, selection operation, crossover operation, and mutation operation. During initialization, a set of real-valued vectors is randomly generated to form the initial population, where each vector represents a potential solution in the search space. The fitness evaluation stage calculates each individual's fitness value using the objective function, which quantifies solution quality.

Selection operations typically employ roulette wheel or tournament selection mechanisms to preferentially retain high-fitness individuals. For real-coded representations, specialized crossover techniques like arithmetic crossover or heuristic crossover generate new solutions through linear combinations of parent individuals. Mutation operations maintain population diversity by introducing random perturbations, with common strategies including uniform mutation or Gaussian mutation implemented using MATLAB's random number generation functions.

This algorithm is particularly effective for solving multidimensional continuous optimization problems, such as locating global extrema of complex mathematical functions. In MATLAB implementations, key parameters including population size, crossover probability, and mutation probability can be adjusted to balance convergence speed and solution quality. The algorithm's performance can be monitored through fitness progression plots and statistical analysis of population diversity metrics.