Set theoretical variants of the teaching-learning-based optimization algorithm for optimal design of truss structures with multiple frequency constraints

In this paper, a set theoretical framework is proposed for the population-based metaheuristic algorithms. Using the proposed framework, two new set theoretical variants of the teaching-learning-based optimization (TLBO) algorithm are developed. These algorithms are named as OST-TLBO and STMP-TLBO, which are acronyms for the "ordered set theoretical teaching-learning-based optimization" and "set theoretical multi-phase teaching-learning-based optimization", respectively. The present framework can be applied to other population-based metaheuristic algorithms. In order to verify the stability and robustness of the presented algorithms, some optimization problems are examined. These problems include four truss optimization problems with multiple natural frequency constraints. Comparing the results obtained from the proposed algorithms with those of the standard version of the TLBO algorithm shows that the proposed set theoretical framework improves the performance of the standard TLBO in terms of robustness and convergence characteristics.