Stochastic level-set method for shape optimisation

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 buil...

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Bibliographic Details
Published inJournal of computational physics Vol. 348; pp. 82 - 107
Main Authors Hedges, Lester O., Kim, H. Alicia, Jack, Robert L.
Format Journal Article
LanguageEnglish
Published Cambridge Elsevier Inc 01.11.2017
Elsevier Science Ltd
Subjects
Algorithms
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational physics
DETERMINISTIC ESTIMATION
Level-set method
Mathematical programming
OPTIMIZATION
Optimization algorithms
STATISTICAL MECHANICS
Statistical methods
Stochastic models
Stochastic motion of shape boundaries
STOCHASTIC PROCESSES
Studies
Topology optimisation
Topology optimisation
Level-set method
Stochastic motion of shape boundaries
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.07.010