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 Levy flights, JA using Levy flights with probabilistic student phase (JALS), JA using Levy 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.