Reliability-based multiobjective optimization using the satisficing trade-off method

Abstract

This study proposes a reliability-based multiobjective optimization (RBMO) approach using the satisficing trade-off method (STOM). STOM is a multiobjective optimization method that obtains a highly accurate single Pareto solution, regardless of the shape of the Pareto set. By introducing an aspiration level, STOM transforms the multiobjective optimization problem into the equivalent single objective problem. When the given Pareto solution is not satisfactory, the search process is repeated with a different aspiration level, which is selected using the automatic trade-off method, for example. RBMO considers multiobjective optimization under reliability constraints that consider uncertainties in the design parameters. In this study, the reliability is evaluated by the first-order reliability method. Therefore, the optimization problem is formulated as a conventional double-loop approach. However, the validity of the proposed method can be illustrated without a decoupled reliability-based design approach. Through numerical examples, the proposed method is shown to obtain an accurate Pareto solution for the RBMO problem. In addition, compared to multiobjective particle swarm optimization, parametrically changing the aspiration level produces a more accurate, uniformly distributed, and diverse Pareto set. The tracking ability of Pareto solutions with the same aspiration level is investigated in terms of the target reliability, which clarifies that the shift in the dominant failure mode influences the kink in the tracking trajectory. Finally, an analysis of the automatic trade-off method demonstrates that the desired Pareto solution can be obtained by updating the aspiration level, even when the Pareto surface is nonlinear.

Keywords

• reliability-based multiobjective optimization
• satisficing trade-off method
• pareto set
• automatic trade-off analysis
• first-order reliability method