A new efficient hybrid approach for reliability-based design optimization problems

The reliability-based design optimization (RBDO) is performed for mechanical design to compromise effectively between economy and safety requirements. In real mechanical applications, such RBDO problems are a highly complex task by involving computational difficulties and its resolution requires the use of appropriate optimization techniques. In this paper, a new RBDO solution approach is introduced for mechanical engineering problems. It is a combination of the reliable design space (RDS) technique with an efficient hybrid algorithm (AMDE-NM) based on the adaptive mixed differential evolution (AMDE) and Nelder-Mead local search (NM). First, the RDS strategy is used to turn the RBDO problem into a simple deterministic optimization (SDO) one, through converting the probabilistic constraints to approximate deterministic constraints, while the resolution is then carried out with the AMDE-NM algorithm. The new proposed integrated approach (RDS-AMDE-NM) is able to handle the mixed design variables with continuous, discrete, and integer types. Six mechanical problems with different features are studied to analyze the applicability and the efficiency of RDS-AMDE-NM. The obtained simulation results show the performance of the proposed approach, while new optimal solutions for two RBDO problems are presented. Furthermore, an industry case on a cylindrical spur gear is studied to investigate the reliability of the proposed method in solving real challenging mechanical RBDO problems. The obtained results reveal really that RDS-AMDE-NM is a promising RBDO approach with extensive applicability.