An efficient two-stage water cycle algorithm for complex reliability-based design optimization problems

The reliability-based design optimization (RBDO) problem considers the necessary uncertainty of measurements within the scope of planning to minimize the design objective while satisfying probabilistic constraints. Metaheuristic algorithms offer effective tools to address challenges that scientists and practitioners face in RBDO problems, including the use of multimodal objective functions, mixed design variables, and nondifference mathematical models. However, metaheuristic reliability-based design optimization (MRBDO) algorithms require reliability analysis to obtain accurate solutions, which leads to different convergence behaviors than those observed for gradient RBDO algorithms. One of the main drawbacks of such schemes is the high computational cost. In this work, we derive an error propagation rule from the inner reliability analysis to the outer optimization. Then, based on a two-stage water cycle algorithm (TSWCA), an improved MRBDO algorithm called TSWCA-MRBDO is developed to ensure universality and performance. In the proposed algorithm, the water cycle algorithm, with a global capacity, is used to find the best solution. A single-loop strategy is first adopted, in which the MRBDO problem is converted into the deterministic optimization problem to remarkably reduce the computational time of global search. Then, a two-stage algorithm is utilized to perform the local search. Numerical examples demonstrate that the proposed two-stage MRBDO algorithm can converge more quickly and efficiently in the global and local domains than other MRBDO algorithms.