Stochastic level-set method for shape optimisation

Lester O. Hedges, H. Alicia Kim, Robert L. Jack

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical programming. The stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a Boltzmann–Gibbs distribution of structures. In non-convex optimisation problems, the deterministic algorithm can get trapped in local optima: the stochastic generalisation enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of-principle calculation is shown for a simple engineering structure.

Original languageEnglish
Pages (from-to)82-107
Number of pages26
JournalJournal of Computational Physics
Volume348
DOIs
Publication statusPublished - 1 Nov 2017

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shape optimization
Shape optimization
mathematical programming
engineering
Statistical mechanics
Mathematical programming
statistical mechanics
sampling
Sampling
optimization

Keywords

  • Level-set method
  • Stochastic motion of shape boundaries
  • Topology optimisation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

Stochastic level-set method for shape optimisation. / Hedges, Lester O.; Kim, H. Alicia; Jack, Robert L.

In: Journal of Computational Physics, Vol. 348, 01.11.2017, p. 82-107.

Research output: Contribution to journalArticle

Hedges, Lester O. ; Kim, H. Alicia ; Jack, Robert L. / Stochastic level-set method for shape optimisation. In: Journal of Computational Physics. 2017 ; Vol. 348. pp. 82-107.
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