Genetic Algorithm Implementation in MATLAB with Prufer Encoding for Minimum Spanning Tree Problems

Genetic algorithm is an optimization technique based on natural selection and genetic mechanisms that can be applied to various problems, including minimum spanning tree (MST) problems. Specifically, this implementation utilizes a data structure called Prufer encoding to represent and solve MST problems. Prufer encoding provides a compact and efficient tree representation method that facilitates genetic algorithm operations such as crossover and mutation by converting trees into numerical sequences. When implementing this in MATLAB, key functions would include: population initialization using Prufer sequences, fitness evaluation based on tree weights, crossover operations that maintain valid Prufer codes, and mutation procedures that ensure feasible solutions. The algorithm typically follows these steps: generating initial population of Prufer-encoded trees, calculating fitness values based on edge weights, selecting parents using roulette wheel or tournament selection, performing crossover to create offspring, applying mutation operators, and replacing the population while maintaining elitism. By combining genetic algorithms with Prufer encoding, this approach effectively solves MST problems and achieves satisfactory optimization results while leveraging MATLAB's matrix operations for efficient population handling and fitness calculations.