Integrated multiobjective framework for reliability-based design optimization with discrete design variables

• SVR (Support Vector Regression), MOPSO (Multiobjective Particle Swarm Optimization) and SS (Subset Simulation) are integrated into MO-PS2 to solve the MO-RBDO (Multiobjective Reliability-Based Design Optimization) problem.
• A retraining mechanism contributes to high estimation accuracy and good solution quality.
• MO-PS2 addresses practical concerns without restrictive assumptions.
• Non-dominated solutions produced by MO-PS2 can facilitate decision making.
• MO-PS2 outperforms the conventional single-loop and double-loop approaches.

A Multiobjective Reliability-based Design Optimization (MO-RBDO) problem is of great interest as it can reveal the tradeoff between cost and reliability in the design of structures. The MO-RBDO problem, however, is computationally demanding and difficult to solve in practical situations. The present study proposes a new framework to solve the MO-RBDO problem by simultaneously minimizing the cost and associated failure probability. The proposed framework, dubbed as MO-PS2, extends and combines three methods: Multiobjective Particle Swarm Optimization (MOPSO), Support vector regression (SVR), and Subset simulation (SS). A unique retraining mechanism is developed not only to increase the accuracy of reliability estimation, but also to improve overall optimization performance. MO-PS2 relaxes restrictive assumptions required by existing methods to address practical concerns, such as discrete design variables, nonlinear and non-differentiable performance functions, and disjoint failure domains. A tower space truss example is used to illustrate the application of MO-PS2, whose performance is further validated by comparisons with conventional double-loop and single-loop approaches. The comparison results verify that MO-PS2 outperforms the conventional approaches, in terms of various criteria: solution quality, computational efficiency, performance consistency, and the accuracy of reliability estimation.