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This paper introduces a methodology for considering the uncertainties in stability analysis of gravity dams. For this purpose, a conceptual model based on the fuzzy set theory and Genetic Algorithm (GA) optimization is developed to be coupled to a gravity dam analysis model. The uncertainties are represented by the fuzzy numbers and the GA is used to estimate in what extent the input uncertainties affect the dam safety factors. An example gravity dam is analyzed using the proposed approach. The results show that the crisp safety factors might be highly affected by the input uncertainties. For instance, ±10%uncertainty in the design parameters could result in about −346 to + 146 % uncertainty in the stability safety factors and −59 to + 134 % in the stress safety factor of the example dam.

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In this paper, set theoretical variants of the artificial bee colony (ABC) and water evaporation optmization (WEO) algorithms are proposed. The set theoretical variants are designed based on a set theoretical framework in which the population of candidate solutions is divided into some number of smaller well-arranged sub-populations. The framework aims to improve the compromise between diversification and intensification of the search and makes it possible to design various variants of a P-metaheuristic. In order to verify the stability and robustness of the set theoretical framework, the proposed algorithms are applied to solve three different benchmark structural design optimization problems. The results show that the set theoretical framework improves the performance of the ABC and WEO algorithms, especially in terms of robustness and convergence characteristics.