MATLAB Implementation for Multi-Objective Optimization Problems

In this example, we implement a genetic algorithm to solve multi-objective optimization problems. The algorithm progressively reduces the number of offspring individuals through generations, ultimately stabilizing at a population of 10 chromosomal individuals. This optimization strategy employs a dynamic population sizing technique where the offspring count decreases according to a predefined schedule, allowing for more focused exploration of the solution space in later generations. Key implementation aspects include: - Utilization of MATLAB's Global Optimization Toolbox functions - Implementation of non-dominated sorting for Pareto front identification - Custom crossover and mutation operators tailored for multi-objective optimization - Adaptive population sizing mechanism with generation-based reduction criteria Through this optimization methodology, we achieve improved solution quality by balancing exploration and exploitation phases, effectively satisfying multiple competing objectives while maintaining computational efficiency. The stabilization at 10 individuals represents an optimal trade-off between solution diversity and convergence precision for this specific problem class.