This study proposes a comprehensive optimization framework that integrates single- and multi-objective algorithms for solving complex problems in structural mechanics. A genetic algorithm (GA) and non-dominated sorting genetic algorithm II (NSGA-II) are developed and validated through multiple mechanical case studies, including truss structures, beam vibration and fluid-structure interactions. An isogeometric analysis (IGA) approach is incorporated to improve the accuracy of boundary representation. The numerical results demonstrate the robustness and precision of the proposed methods compared to existing literature, providing an efficient and reliable optimization strategy for practical engineering applications.
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