Multi-Objective Optimization Algorithm Using Genetic Algorithm (GA)

Genetic Algorithm (GA) is an optimization method that simulates biological evolution processes, continuously evolving populations through operations like selection, crossover, and mutation to ultimately obtain optimal solutions. Multi-objective optimization problems involve multiple conflicting objective functions, requiring identification of a set of optimal solutions (Pareto optimal set). NSGA-II (Non-dominated Sorting Genetic Algorithm II) is a classic algorithm for solving multi-objective optimization problems, featuring the following core characteristics:

Non-dominated Sorting: Divides the population into different levels based on solution dominance relationships, ensuring priority retention of high-quality solutions during selection. Crowding Distance Calculation: Maintains solution diversity within the same level by calculating crowding distances, preventing result over-concentration. Elitist Preservation Strategy: Combines parent and offspring populations before filtering to prevent loss of excellent individuals and accelerate convergence.

Key implementation steps for NSGA-II in MATLAB include: population initialization, objective function value calculation, non-dominated sorting, selection operations (such as tournament selection), crossover and mutation for offspring generation, and population combination with new generation filtering. By adjusting parameters like population size, crossover probability, and mutation probability, the algorithm's exploration and exploitation capabilities can be balanced.

NSGA-II is widely applied in engineering optimization, scheduling problems, and machine learning fields. Its advantages include efficient handling of complex nonlinear problems and intuitive presentation of Pareto fronts for decision-makers to evaluate trade-offs. For MATLAB users, proper utilization of matrix operations and built-in functions can significantly enhance algorithm efficiency, with key implementation aspects including vectorized fitness calculations and efficient non-dominated sorting routines.