Differential-Based Multi-Objective Optimization Problem

This article explores differential-based multi-objective optimization problems and presents their formulation using sub-functions. This complex problem requires multiple mathematical tools and techniques for effective resolution. Our research demonstrates that the primary optimization challenge can be decomposed into several sub-problems, each amenable to optimization through differential methods. The implementation typically involves creating separate objective functions that can be optimized using gradient-based algorithms like gradient descent or evolutionary strategies with differential operators. This decomposition approach not only enhances computational efficiency but also provides deeper insights into the problem's fundamental structure. The sub-functions can be implemented as modular code components, allowing for independent optimization and parallel processing. In forthcoming research, we will further investigate the advantages and practical applications of this methodology, including specific code implementations using numerical differentiation techniques and multi-objective optimization frameworks.