In this article, a new version of a biogeography-based optimization algorithm with Levy flight distribution (LFBBO) is introduced and used for the optimum design of reinforced concrete cantilever retaining walls under seismic loading. The cost of the wall is taken as an objective function, which is minimized under the constraints implemented by the American Concrete Institute (ACI 318-05) design code and geometric limitations. The influence of peak ground acceleration (PGA) on optimal cost is also investigated. The solution of the problem is attained by the LFBBO algorithm, which is developed by adding Levy flight distribution to the mutation part of the biogeography-based optimization (BBO) algorithm. Five design examples, of which two are used in literature studies, are optimized in the study. The results are compared to test the performance of the LFBBO and BBO algorithms, to determine the influence of the seismic load and PGA on the optimal cost of the wall.

This work evaluates the performance of the salp swarm algorithm (SSA) for truss system optimization problems and presents a novel method called the modified salp swarm algorithm (MSSA). Five truss structures, previously optimized by metaheuristics and containing discrete and continuous variables, were used for the evaluations. Size and size–shape optimization types were considered. Although the SSA performs poorly and has convergence issues in initial random solutions, it reaches comparable solutions to previously published results, particularly in continuous problems. In contrast, the MSSA achieves the best solutions for discrete problems and is relatively close to the best results in the reference literature on continuous problems. Moreover, the MSSA convergence curves exhibit a modest increase in convergence rates, especially for discrete problems. It is envisaged that the findings will contribute to improving solution performance, convergence speed and security for future real-world applications.