An efficient methodology for various structural design problems is needed to optimize the total cost for structures. Although some methods seem to be efficient for applications, due to using special algorithm parameters, computational cost, and some other reasons, there is still much to be done in order to develop an effective method for general design applications. This paper describes the influence of the selected procedure on the design of cost-optimized, post-tensioned axially symmetric cylindrical reinforced concrete walls. In this study, the optimum design of axially symmetric cylindrical walls using several metaheuristic algorithms is investigated. The new generation algorithms used in the study are flower pollination algorithm, teaching-learning-based optimization, and Jaya algorithm (JA). These algorithms are also compared with one of the previously developed algorithm called harmony search. The numerical examples were done for walls with 4-to 10-m height and for 1, 5, 10, 15, 20, and 25 post-tensioned load cases, respectively. Several independent runs are conducted, and in some of these runs, JA may trap to a local solution. To overcome this situation, hybrid algorithms such as JA using Lévy flights, JA using Lévy flights with probabilistic student phase (JALS), JA using Lévy Flights with consequent student phase (JALS2), and JA with probabilistic student phase are developed. It is seen that in many respects, the JALS2 and JALS are the most effective within the proposed hybrid approaches. KEYWORDS cost optimization cylindrical walls, flower pollination algorithm, hybrid algorithm analyses of cylindrical walls, Jaya algorithm, teaching-learning-based optimization 1 | INTRODUCTION Engineering designs are based on two main objectives. These two objectives, defined as safety and cost, are two opposing concepts, when one is increasing, the other one is decreasing. If all parameters belonging to these two purposes are formulated, it may be possible to obtain a solution that simultaneously provides these two goals with mathematical operations. This may not be always possible or easy task in some cases such as design of structural systems, in which many parameters affect each other. For four decades, metaheuristic algorithms have been widely used to perform this task. The most important reason why algorithms are used so widely is that not only the ability of solving problems that are difficult or impossible to express mathematically but also easily applying of these algorithms to the problems without using complex mathematical functions.From the first day to the present, a considerable number of metaheuristic algorithm has been proposed. Looking at the number of algorithms, it brings out questions such as what the reason is, why so many algorithms are proposed, are the algorithms insufficient to achieve the optimization task, if so, why more algorithms are suggested, and if algorithms are successful what is the measure of success. These questions can be further diversified. The answer to these questions can be ...