A new efficient hybrid approach for reliability-based design optimization problems
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ORIGINAL ARTICLE
A new efficient hybrid approach for reliability‑based design optimization problems Ferhat Hamza1 · Djeddou Ferhat1 · Hammoudi Abderazek1 · Mohammed Dahane2 Received: 27 March 2020 / Accepted: 28 September 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract 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. Keywords Reliability-based design optimization · Reliable design space · Adaptive mixed deferential evolution · Nelder– Mead · Mixed design variable
1 Introduction Nowadays, decreasing cost and increasing safety of structures are of the most primary concerns in product and process design. This task requires developing and using powerful tools that provide the best balance between both considerations. Deterministic optimization approaches are usually limited and produce a high failure probability on the design constraint satisfaction. This is due to the uncertainties impact which can be related to various conditions like manufacturing process, material properties, and operating environments [1]. To assess the influence of variability factors * Hammoudi Abderazek a_hammoudi@univ‑setif.dz 1
Applied Precision Mechanics Laboratory, Institute of Optics and Precision Mechanics, Setif-1-University, 19000 Setif, Algeria
Universite de Lorraine, LGIPM, 57000 Metz, France
2
in optimization process, reliability-based design optimization methodology is introduced as an efficient procedure for engineering design. Wherein the uncertainties are con
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