Multi-objective Robust Optimization using a Post-optimality Sensitivity Analysis Technique: Application to a Wind Turbine Design

TL;DR

This paper introduces a post-optimality sensitivity analysis technique with two robustness indices for multi-objective robust optimization, applied to wind turbine design, enabling better comparison and decision-making of Pareto solutions under variable conditions.

Contribution

It proposes a novel post-optimality sensitivity analysis method with two robustness indices for evaluating Pareto solutions in multi-objective robust optimization problems.

Findings

The robustness indices effectively measure solution stability under small and large variations.

The method allows comparison of Pareto solutions based on robustness in a multi-objective context.

Application to wind turbine design demonstrates practical utility and effectiveness.

Abstract

Toward a multi-objective optimization robust problem, the variations in design variables and design environment pa-rameters include the small variations and the large varia-tions. The former have small effect on the performance func-tions and/or the constraints, and the latter refer to the ones that have large effect on the performance functions and/or the constraints. The robustness of performance functions is discussed in this paper. A post-optimality sensitivity analysis technique for multi-objective robust optimization problems is discussed and two robustness indices are introduced. The first one considers the robustness of the performance func-tions to small variations in the design variables and the de-sign environment parameters. The second robustness index characterizes the robustness of the performance functions to large variations in the design environment parameters. It is based on the ability of a solution to maintain a good Pareto ranking for different design environment parameters due to large variations. The robustness of the solutions is treated as vectors in the robustness function space, which is defined by the two proposed robustness indices. As a result, the designer can compare the robustness of all Pareto optimal solutions and make a decision. Finally, two illustrative examples are given to highlight the contributions of this paper. The first example is about a numerical problem, whereas the second problem deals with the multi-objective robust optimization design of a floating wind turbine.