Advanced Mathematical Modeling AND Optimization Techniques FOR Solving Complex Engineering Problems
DOI:
https://doi.org/10.29284/8k920742Keywords:
Mathematical Modeling, Nonlinear Systems, Optimization Techniques, Metaheuristics, Multi-objective Optimization, Engineering Systems, Computational Methods.Abstract
Complex engineering systems increasingly demand robust mathematical modeling frameworks capable of addressing nonlinear dynamics, uncertainty, multi-scale interactions, and high-dimensional decision spaces. Traditional analytical techniques often fail to capture the coupled physical, economic, and operational constraints inherent in modern engineering challenges. This paper presents a comprehensive review and synthesis of advanced mathematical modeling and optimization techniques used to solve complex engineering problems across mechanical, civil, electrical, aerospace, and industrial domains. The study explores nonlinear differential equation modeling, stochastic processes, multi-objective optimization, metaheuristic algorithms, convex optimization, and hybrid AI-driven optimization frameworks. Emphasis is placed on practical implementation, computational trade-offs, convergence behavior, and scalability. The paper proposes an integrated modeling–optimization framework that combines deterministic, probabilistic, and data-driven approaches to enhance robustness and solution quality. Applications in structural design, energy systems, supply chain networks, and control engineering are discussed to illustrate real-world relevance. The findings highlight the critical role of advanced optimization in improving efficiency, sustainability, reliability, and cost-effectiveness in engineering systems.
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This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
