In the optimum design of reinforced concrete (RC) structural members, the robustness of the employed method is important as well as solving the optimization problem. In some cases where the algorithm parameters are defined as non-effective values, local-optimum solutions may prevail over the existing global optimum results. Any metaheuristic algorithm can be effective to solve the optimization problem but must give the same results for several runs. Due to the randomization nature of these algorithms, the performance may vary with respect to time. The essential and novel work done in this study is the comparative investigation of 10 different metaheuristic algorithms and two modifications of harmony search (HS) algorithm on the optimum cost design of RC retaining walls constrained with geotechnical and structural state limits. The employed algorithms include classical ones (genetic algorithm (GA), differential evaluation (DE), and particle swarm optimization (PSO)), proved ones on structural engineering applications (harmony search, artificial bee colony, firefly algorithm), and recent algorithms (teaching-learning-based optimization (TLBO), flower pollination algorithm (FPA), grey wolf optimization, Jaya algorithm (JA)). The modifications of HS include adaptive HS (AHS) concerning the automatic change of algorithm parameters and hybridization of AHS with JA that is developed for the investigated problem. According to the numerical investigations, recent algorithms such as TLBO, FPA, and JA are generally the best at finding the optimum values with less deviation than the others. The adaptive-hybrid HS proposed in this study is also competitive with these algorithms, while it can reach the best solution by using a lower population number which can lead to timesaving in the optimization process. By the minimization of material used in construction via best optimization, sustainable structures that support multiple types of constraints are provided.