Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization

The Non-dominated Sorting Genetic Algorithm (NSGA-II) represents a classical multi-objective optimization approach that simulates natural selection and genetic mechanisms to identify optimal solution sets. This algorithm is particularly effective for optimization problems involving multiple conflicting objectives, generating a set of approximate optimal solutions in a single run rather than a single solution.

The core concepts of NSGA-II involve non-dominated sorting and crowding distance calculation. Non-dominated sorting hierarchically classifies population individuals based on dominance relationships, ensuring superior solutions are prioritized for retention. Crowding distance measurement maintains population diversity, preventing premature convergence to local optima. The resulting solution set distributes along the Pareto front, achieving optimal trade-offs among multiple objectives.

When implementing NSGA-II in MATLAB, developers typically need to define objective functions, encoding schemes (such as real-value encoding or binary encoding), and genetic operations including selection, crossover, and mutation. Key adjustable parameters include population size, crossover probability, and mutation probability, which users can modify to balance convergence speed and global exploration capabilities according to specific problem requirements. The algorithm flow involves initial population generation, fitness evaluation, non-dominated sorting with O(MN²) complexity, crowding distance computation, and elitist selection.

NSGA-II finds applications across various domains including engineering optimization, economic dispatch, and hyperparameter tuning in machine learning. By customizing objective functions and constraint conditions, users can flexibly adapt NSGA-II to diverse multi-objective optimization scenarios, obtaining practically meaningful solution sets that facilitate informed decision-making.