Department of Mechanical Engineering, Faculty of Engineering and Technology, Marwadi University, Rajkot, Gujarat, India.
Ethics Infotech, Vadodara, Gujarat, India.
PLoS One. 2024 Aug 19;19(8):e0308474. doi: 10.1371/journal.pone.0308474. eCollection 2024.
This research article presents the Multi-Objective Hippopotamus Optimizer (MOHO), a unique approach that excels in tackling complex structural optimization problems. The Hippopotamus Optimizer (HO) is a novel approach in meta-heuristic methodology that draws inspiration from the natural behaviour of hippos. The HO is built upon a trinary-phase model that incorporates mathematical representations of crucial aspects of Hippo's behaviour, including their movements in aquatic environments, defense mechanisms against predators, and avoidance strategies. This conceptual framework forms the basis for developing the multi-objective (MO) variant MOHO, which was applied to optimize five well-known truss structures. Balancing safety precautions and size constraints concerning stresses on individual sections and constituent parts, these problems also involved competing objectives, such as reducing the weight of the structure and the maximum nodal displacement. The findings of six popular optimization methods were used to compare the results. Four industry-standard performance measures were used for this comparison and qualitative examination of the finest Pareto-front plots generated by each algorithm. The average values obtained by the Friedman rank test and comparison analysis unequivocally showed that MOHO outperformed other methods in resolving significant structure optimization problems quickly. In addition to finding and preserving more Pareto-optimal sets, the recommended algorithm produced excellent convergence and variance in the objective and decision fields. MOHO demonstrated its potential for navigating competing objectives through diversity analysis. Additionally, the swarm plots effectively visualize MOHO's solution distribution of MOHO across iterations, highlighting its superior convergence behaviour. Consequently, MOHO exhibits promise as a valuable method for tackling complex multi-objective structure optimization issues.
这篇研究文章提出了多目标河马优化器（MOHO），这是一种独特的方法，擅长解决复杂的结构优化问题。河马优化器（HO）是一种新颖的元启发式方法，其灵感来自河马的自然行为。HO 基于一个三进制阶段模型，该模型结合了河马行为的关键方面的数学表示，包括它们在水生环境中的运动、防御捕食者的机制和避免策略。这个概念框架构成了开发多目标（MO）变体 MOHO 的基础，该变体应用于优化五个著名的桁架结构。在平衡安全预防措施和个体部分的应力大小限制之间，这些问题还涉及竞争目标，例如减轻结构的重量和最大节点位移。使用六种流行的优化方法的结果进行了比较。使用了四个行业标准性能指标进行了比较，并对每个算法生成的最佳 Pareto 前沿图进行了定性检查。Friedman 秩检验和比较分析获得的平均值明确表明，MOHO 在快速解决重要结构优化问题方面优于其他方法。除了发现和保存更多的 Pareto 最优集外，建议的算法在目标和决策领域产生了出色的收敛性和方差。MOHO 通过多样性分析展示了其在处理竞争目标方面的潜力。此外，群体图有效地可视化了 MOHO 在迭代过程中的解决方案分布，突出了其优越的收敛行为。因此，MOHO 有望成为解决复杂多目标结构优化问题的一种有价值的方法。
