Multi-Objective Optimization for Complex Systems Considering Both Performance Optimality and Robustness

As engineering systems become increasingly complex, performance requirements rise, and tolerance for design parameter variations becomes more crucial due to increased uncertainty. Tolerance to parameter variation can be measured by the volume of the solution space. A larger solution space implies a higher tolerance to parameter changes and thus greater robustness. The box-shaped solution space, represented by intervals with respect to each design parameter, has the advantage of showing which design parameters can be decoupled. Therefore, this paper proposes a new multi-objective optimization problem to optimize both the performance and volume of the box-shaped solution space simultaneously. Often, optimal performance and maximum volume are conflicting objectives, indicating a trade-off between performance and robustness. Furthermore, the DIRECT-NSGA-II approach is proposed for solving this multi-objective optimization problem. The DIRECT algorithm evaluates the minimum value of the performance function within the box-shaped solution space, while the NSGA-II algorithm identifies Pareto-optimal solution spaces. Finally, two case studies are implemented to illustrate the effectiveness of the DIRECT-NSGA-II method. We can conclude that (I) the proposed DIRECT-NSGA-II approach is suitable for black-box performance functions, (II) any point within the obtained solution space is a good design point, and (III) the proposed optimization problem considers both performance optimality and robustness, enabling the identification of a representative set of Pareto-optimal solution spaces that balance these two factors.