Genetic Algorithm Main Program Implementation

This document presents fga.m as the core implementation of the genetic algorithm. The algorithm employs binary Gray coding for individual representation, which reduces Hamming distance between consecutive integers and improves convergence. The selection process utilizes a nonlinear ranking approach based on the roulette wheel method, where fitness values are mapped to selection probabilities through exponential ranking. For crossover operations, the implementation uses uniform crossover that exchanges bits between parent chromosomes with equal probability at each position, maintaining genetic diversity effectively. The mutation operator introduces random bit flips with controlled probability, while the specialized inversion operation reverses subsequences of chromosomes to enhance exploration capabilities in the solution space. Through the integrated application of these strategies, the algorithm efficiently navigates the problem's solution space, balancing exploration and exploitation to improve overall optimization performance. Key functions include population initialization with Gray encoding, fitness scaling for selection pressure control, and adaptive operator probabilities for dynamic search behavior.