A variational geometric framework for multi-objective level set topology optimization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918406132858880 |
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| author | Oellerich, Jan Yamada, Takayuki |
| author_facet | Oellerich, Jan Yamada, Takayuki |
| contents | This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from Hamilton's principle, resulting in a damped wave equation governing the optimization process. The objective functionals are combined using a weighted sum formulation. An analysis of the underlying system structure reveals a geometric interpretation of the problem, shifting the perspective beyond conventional approaches based on purely discrete approximations of the Pareto frontier. Under suitable regularity assumptions, the set of stationary solutions forms a structured subset in objective space, in which the Pareto frontier is locally embedded and the weighting factors act as intrinsic coordinates. This perspective motivates the introduction of a dynamic evolution of the weights, leading to a coupled dynamical system for the level set function and the weighting parameters that enables adaptive exploration of the objective landscape. Numerical results demonstrate that the proposed framework provides a stable and uniform approximation of the Pareto frontier and scales to higher-dimensional objective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A variational geometric framework for multi-objective level set topology optimization Oellerich, Jan Yamada, Takayuki Optimization and Control This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from Hamilton's principle, resulting in a damped wave equation governing the optimization process. The objective functionals are combined using a weighted sum formulation. An analysis of the underlying system structure reveals a geometric interpretation of the problem, shifting the perspective beyond conventional approaches based on purely discrete approximations of the Pareto frontier. Under suitable regularity assumptions, the set of stationary solutions forms a structured subset in objective space, in which the Pareto frontier is locally embedded and the weighting factors act as intrinsic coordinates. This perspective motivates the introduction of a dynamic evolution of the weights, leading to a coupled dynamical system for the level set function and the weighting parameters that enables adaptive exploration of the objective landscape. Numerical results demonstrate that the proposed framework provides a stable and uniform approximation of the Pareto frontier and scales to higher-dimensional objective spaces. |
| title | A variational geometric framework for multi-objective level set topology optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.22739 |