Optimisation Techniques in Engineering: A Mathematical Perspective

This literature review provides a comprehensive examination of optimization techniques in engineering from a mathematical perspective, highlighting their foundational theories, classifications, multi-objective approaches, constraint handling methods, and hybrid techniques. The rapid advancement and adoption of meta-heuristic algorithms, particularly those inspired by biological and natural phenomena, underscore their effectiveness in solving complex engineering problems. The review discusses the mathematical underpinnings that facilitate the implementation of various optimization strategies, including multiparametric programming and differential geometry, which enhance problem-solving capabilities under uncertainty. Additionally, it explores the evolution of nature-inspired algorithms, including the Hippopotamus Optimization and Wild Horse Optimizer, alongside physics-inspired and human-inspired methods that showcase significant improvements in performance through hybridization and enhancement strategies. Multi-objective optimization approaches and constraint handling techniques are analyzed for their roles in addressing real-world challenges, with notable advancements in methods like MOEDO and NSGA-II. Applications across diverse engineering domains demonstrate the practical benefits of these optimization techniques, yielding improvements in efficiency and sustainability. The review concludes with an acknowledgment of ongoing challenges and future research directions, emphasizing the need for refined performance metrics and structured frameworks for algorithm selection. As optimization techniques continue to evolve, their synergy with artificial intelligence and machine learning is poised to drive further innovations in engineering solutions.