Finite element methods (FEMs) are more advantageous for analyzing complex geometry and structures than analytical methods. Local search optimization techniques are suitable for the unimodal problem because final result depends on the starting point. On the other hand, to optimize the parameters of multi-minima/maxima problems, global optimization-based FEM is used. Unfortunately, global optimization solvers are not present in, COMSOL Multiphysics, a versatile tool for solving varieties of problems using FEM. Teaching–learning-based optimization (TLBO) is a global optimization technique and does not require any algorithm-specific parameter. In this paper, FEM is coupled with TLBO algorithms in COMSOL Multiphysics for solving the global optimization problem. The TLBO algorithm is implemented in COMSOL Multiphysics using the JAVA application programming interface and tested with the standard benchmark functions. The solutions of the standard benchmark problem in COMSOL Multiphysics are in close agreement with the results presented in literature. Furthermore, the optimization procedure thus established is used for the optimization of actuator voltage for piezoelectric bimorphs to achieve the desired shapes. The FEM-based TLBO method is compared with two optimization methods present in COMSOL Multiphysics for a shape control problem; (i) method of moving asymptotes (MMA) and (ii) Bound Optimization BY Quadratic Approximation (BOBYQA). The root mean square error shows that the FEM-based TLBO algorithm converges to a global minimum and gives the same result (19.3 nm) at multiple runs, whereas MMA and BOBYQA trapped in local minimum and gave different results for different starting points.

有限元方法 (FEM) 比分析方法更适合分析复杂的几何形状和结构。局部搜索优化技术适用于单峰问题，因为最终结果取决于起点。另一方面，为了优化多极小值/极大值问题的参数，使用了基于全局优化的 FEM。遗憾的是，COMSOL Multiphysics 中没有全局优化求解器，这是一种使用 FEM 解决各种问题的通用工具。基于教学的优化 (TLBO) 是一种全局优化技术，不需要任何特定于算法的参数。在本文中，FEM 结合 COMSOL Multiphysics 中的 TLBO 算法来解决全局优化问题。TLBO 算法使用 JAVA 应用程序编程接口在 COMSOL Multiphysics 中实现，并使用标准基准函数进行测试。COMSOL Multiphysics 中标准基准问题的解与文献中的结果非常一致。此外，由此建立的优化程序用于优化压电双压电晶片的致动器电压以实现所需形状。针对形状控制问题，将基于 FEM 的 TLBO 方法与 COMSOL Multiphysics 中的两种优化方法进行了比较；(i) 移动渐近线 (MMA) 方法和 (ii) 二次逼近边界优化 (BOBYQA)。均方根误差表明基于 FEM 的 TLBO 算法收敛到全局最小值并在多次运行时给出相同的结果 (19.3 nm)，