Comparison of three novel hybrid metaheuristic algorithms for structural optimization problems

Computational efficiency of metaheuristic optimization algorithms depends on appropriate balance between exploration and exploitation. An important concern in metaheuristic optimization is that there is no guarantee that new trial designs will always improve the current best record. In this regard, there not exist any metaheuristic algorithm inherently superior over all other methods. This study compares three advanced formulations of state-of-the-art metaheuristic optimization algorithms – Simulated Annealing (SA), Harmony Search (HS) and Big Bang-Big Crunch (BBBC) – including enhanced approximate line search and computationally cheap gradient evaluation strategies. The rationale behind the new formulations is to generate high quality trial designs lying on a properly chosen set of descent directions. This is done throughout the optimization process. Besides hybridizing the metaheuristic search engines of HS/BBBC/SA with gradient information and approximate line search, HS and BBBC are also hybridized with an enhanced 1-D probabilistic search derived from SA. All these enhancements allow to approach more quickly the region of design space hosting the global optimum. The new algorithms are tested in four weight minimization problems of skeletal structures and three mechanical/civil engineering design problems with up to 204 continuous/discrete variables and 20,070 nonlinear constraints. All test problems may contain multiple local minima. The optimization results and an extensive comparison with the literature clearly demonstrate the validity of the proposed approach which allows to significantly reduce the number of function evaluations/structural analyses with respect to the literature and improves robustness of metaheuristic search engines.