Abstract:Topology optimization produces optimized structures by minimizing an objective function under a set of constraints. While considerable research has focused on improving and extending such single-objective formulations, design is usually a trade-off between conflicting criteria. This brings topology optimization into the realm of multiobjective optimization. Unfortunately, cross-fertilization has been limited despite the long coexistence of these two fields. This work aims to bridge this gap through three contributions. The first is a theoretical comparison of two common scalarization techniques, the weighted-sum and $\varepsilon$-constraint method, to the more advanced Pascoletti-Serafini scalarization. The second contribution is a novel insight: the Pareto frontier in topology optimization contexts consists of pieces belonging to local fronts. This can cause disconnected and nonconvex fronts, in contrast to what is often seen in the literature. Finally, the third contribution is a numerical comparison of the scalarization methods, highlighting more uniform approximations obtained with the Pascoletti-Serafini scalarization and clustering observed for the weighted-sum scalarization. The paper contains a large number of bi-objective examples, including minimization of volume, compliance, maximum stress and dynamic compliance.
From: Tom De Weer [view email]
[v1]
Mon, 15 Jun 2026 14:36:26 UTC (19,304 KB)
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