Compliant mechanisms are promising candidates in precision engineering, soft robotics, space, and bioengineering due to their advantages of free friction, free lubricant, no backlash, monolithic structure, and minimal assembly. However, designing and analyzing of compliant mechanisms are facing the high complexity due to a coupling of kinematic and mechanical behavior in comparison to rigid-body mechanisms. Especially, considering a multi-objective optimization design for compliant mechanisms, the problem is more complicated. Thus, this paper presents a new efficient hybrid methodology for solving the multi-objective optimization design. A hybridization is developed through a combination of finite element method, statistical technique, desirability function approach, fuzzy logic system, adaptive neuro-fuzzy inference system (ANFIS), and Lightning attachment procedure optimization (LAPO). A bistable compliant mechanism is investigated as an application example of the proposed method. First, design variables of the mechanism are determined, and then central composite design is employed to construct a numerically experimental matrix. Though using analysis of variance and Taguchi approach, the design variables are refined to make new populations. Subsequently, desirability values of two performances of the mechanism are computed, and the results are transferred into the fuzzy logic system. The output of fuzzy logic system is considered as single combined objective function. By developing the ANFIS model, the relation between the refined design variables and the output of fuzzy logic system is established. Finally, LAPO algorithm is adopted for solving the multi-objective optimization problem for the mechanism. Three numerical examples are investigated to validate the performance efficiency of the proposed method. The results demonstrate that the proposed method is more efficient than Taguchi-based fuzzy logic. Besides, through Wilcoxon signed rank test and Friedman test, it reveals that the performances of proposed approach are superior to those of the Jaya algorithm and TLBO algorithm. The results of this article can be extended for other complex compliant mechanisms as well as optimization problems with multiple objective functions and more complex constraints.

顺应性机制具有自由摩擦，自由润滑剂，无反冲，整体结构和最小化组装的优势，因此在精密工程，软机器人，空间和生物工程领域有望成为有前途的候选者。但是，与刚性机构相比，由于运动学和机械性能的耦合，柔性机构的设计和分析面临着很高的复杂性。特别是，考虑到针对顺应性机制的多目标优化设计，该问题更加复杂。因此，本文提出了一种新的有效的混合方法来解决多目标优化设计问题。通过将有限元方法，统计技术，合意函数方法，模糊逻辑系统，自适应神经模糊推理系统（ANFIS），和闪电附加程序优化（LAPO）。研究了双稳态顺应性机制作为该方法的一个应用实例。首先，确定机构的设计变量，然后采用中央复合设计来构建数值实验矩阵。尽管使用了方差分析和田口方法，但设计变量仍得到了完善，以产生新的总体。随后，计算该机构的两种性能的期望值，并将结果转移到模糊逻辑系统中。模糊逻辑系统的输出被视为单个组合目标函数。通过开发ANFIS模型，建立了改进的设计变量与模糊逻辑系统输出之间的关系。最后，采用LAPO算法解决了该机构的多目标优化问题。研究了三个数值示例，以验证所提出方法的性能效率。结果表明，所提出的方法比基于Taguchi的模糊逻辑更有效。此外，通过Wilcoxon符号秩检验和Friedman检验，表明该方法的性能优于Jaya算法和TLBO算法。本文的结果可以扩展到其他复杂的兼容机制以及具有多个目标函数和更复杂约束的优化问题。结果表明，所提出的方法比基于Taguchi的模糊逻辑更有效。此外，通过Wilcoxon符号秩检验和Friedman检验，表明该方法的性能优于Jaya算法和TLBO算法。本文的结果可以扩展到其他复杂的兼容机制以及具有多个目标函数和更复杂约束的优化问题。结果表明，所提出的方法比基于Taguchi的模糊逻辑更有效。此外，通过Wilcoxon符号秩检验和Friedman检验，表明该方法的性能优于Jaya算法和TLBO算法。本文的结果可以扩展到其他复杂的兼容机制以及具有多个目标函数和更复杂约束的优化问题。