Hybrid teaching–learning-based optimization for solving engineering and mathematical problems

In this work, a new and effective algorithm called hybrid teaching–learning-based optimization (TLBO) and charged system search (CSS) algorithms (HTC) are proposed to solve engineering and mathematical problems. The CSS is inspired by Coulomb and Gauss’s electrostatic laws of physics as well as the Newtonian mechanic laws of motion. The TLBO is inspired by the interaction between teacher and student in a classroom. Usually, the TLBO gets trapped in the local optimal due to the lack of a system for measuring the distance between the student and the optimal point. In order to solve this problem, the CSS algorithm, which is based on the electrical physics laws, is utilized. In the CSS algorithm, each factor is stored under the influence of the best local and global positions, and it is used in subsequent iterations as the possible optimal answers. In fact, this leads to a better balance between exploration and exploitation. In order to validate the proposed method, the CEC2021 and CEC2005 mathematical functions are optimized. Additionally, to show the applicability of the proposed algorithm and to evaluate its performance and convergence rate, several benchmark truss structures are optimized. The weight of the structural elements is taken into account as the objective function, which is optimized under displacement and stress constraints. The results of the proposed algorithm are compared with some other well-known meta-heuristic methods. The results show that the hybrid HTC algorithm improved the convergence rate and quickly obtained the optimal and desired design. The hybrid HTC algorithm can be adapted to solve other complex mathematical and optimization problems.