Stochastic level-set method for shape optimisation

TL;DR

This paper introduces a stochastic level-set method for shape optimization that enhances the exploration of multiple local optima, improving the search for globally optimal structures in engineering design.

Contribution

It generalizes existing deterministic shape optimization algorithms by incorporating stochastic sampling based on statistical mechanics, enabling better global optimization.

Findings

The stochastic method can escape local optima in non-convex problems.

Demonstrated effectiveness on simple geometrical shape optimization problems.

Proof-of-principle shown for an engineering structure.

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.