arXiv subjects

Tom De Weer

Publications and source records attributed to Tom De Weer.

3 recordsLinked to original sources

arXiv2026

Mapping locally nondominated curves in multiobjective topology optimization of compliance and volume

This paper studies the nondominated set for topology optimization of compliance and volume. In the multiobjective topology optimization literature, scalarization is a popular method to approximate this set, which is better known as the Pareto frontier. However, previous work indicates that the pointwise approximation obtained by scalarization obfuscates its underlying mathematical structure: under an imposed length scale, it consists of locally nondominated curve segments. To investigate this structure, the paper uses a simple methodology to (i) generate local optima with a tightly controlled topology and (ii) use continuation to extend these points to locally nondominated curves. The paper then performs two rounds of numerical experiments. The first round applies the methodology to several cantilever examples. This leads to novel insights regarding topological complexity and symmetry and confirms prior conclusions regarding continuity, smoothness and convexity. The second round investigates two numerical instabilities: (i) a lack of uniqueness and (ii) discontinuities of the locally nondominated curves. The former is linked to an observed flatness of the optimization landscape, whereas the latter is attributed to branch splitting and linked to bifurcation theory. Namely, we classify these discontinuities as higher-dimensional analogues of the subcritical, symmetry-breaking pitchfork bifurcation. The paper concludes with suggestions for future research to address these features of the multiobjective optimization landscape.

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arXiv2026

Novel insights into Pareto fronts in multiobjective topology optimization and a comparative study of scalarization strategies

Topology optimization seeks structures that minimize an objective function subject to constraints. While extensive research has focused on single-objective formulations, design is usually a trade-off between conflicting criteria. This naturally leads topology optimization to the multiobjective optimization field. Unfortunately, despite their long coexistence, interaction between these fields has remained limited. This work aims to bridge this gap. First, we provide a theoretical comparison of two common scalarization techniques, the weighted-sum and $\varepsilon$-constraint method, to the established Pascoletti-Serafini scalarization. Then, we perform extensive bi-objective numerical experiments, including minimization of volume, compliance, maximum stress and dynamic compliance. For each experiment, the four scalarization methods are aggregated, often alongside design space sampling and continuation, to better resolve the Pareto front. The major contribution of this work is the observation that the Pareto front consists of segments belonging to local fronts. Contrary to the smooth, convex fronts often reported in the literature, we show that this property can lead to discontinuous and nonconvex fronts. Finally, we numerically compare the approximation quality of the scalarization methods. The numerical examples demonstrate the robustness of the Pascoletti-Serafini scalarization against fronts with pronounced discontinuities, nonconvexities and high-curvature regions. In contrast, the weighted-sum and $\varepsilon$-constraint methods can produce clustering and gaps, depending on the shape of the front.

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arXiv2026

Continuation strategies to mitigate convergence to low-performing local optima in topology optimization of sound transmission loss

Dynamic topology optimization problems often suffer from convergence to low-performing local optima. This typically results in stiff designs that do not exploit dynamical phenomena such as antiresonance and decoupling. To obtain better designs, researchers often repeat their optimizations with different initial guesses. However, such reruns are computationally expensive and the required number is unknown. To quantify this problem, random initial guesses are sampled and tested for different frequencies on two case studies: (1) dynamic compliance minimization of a reinforced cantilever, which exhibits poor optima for driving frequencies below the first natural frequency, and (2) sound transmission loss maximization of a sandwich panel, which additionally sees a strong tendency toward low-performing optima at high frequencies. To address this issue, the study first divides techniques to reduce the needed number of reruns into four categories: global optimization, exclusion, relaxation, and frequency shift methods. For the latter three, continuation strategies are proposed, illustrated, evaluated and compared on the sound transmission loss case, using Monte Carlo sampling to estimate success rates. All strategies show measurable benefits and trade-offs. To support broader applicability, the study concludes with practical guidelines for dealing with convergence to poor local optima in dynamic topology optimization.

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