SoftFEM: The Soft Finite Element Method

Abstract

Summary While the finite element method (FEM) has now reached full maturity both in academy and industry, its use in optimization pipelines remains either computationally intensive or cumbersome. In particular, currently used optimization schemes leveraging FEM still require the choice of dedicated optimization algorithms for a specific design problem, and a “black box” approach to FEM‐based optimization remains elusive. To this end, we propose here an integrated finite element‐soft computing method, ie, the soft FEM (SoftFEM), which integrates a finite element solver within a metaheuristic search wrapper. To illustrate this general method, we focus here on solid mechanics problems. For these problems, SoftFEM is able to optimize geometry changes and mechanistic measures based on geometry constraints and material properties inputs. From the optimization perspective, the use of a fitness function based on finite element calculation imposes a series of challenges. To bypass the limitations in search capabilities of the usual optimization techniques (local search and gradient‐based methods), we propose, instead a hybrid self adaptive search technique, the multiple offspring sampling (MOS), combining two metaheuristics methods: one population‐based differential evolution method and a local search optimizer. The formulation coupling FEM to the optimization wrapper is presented in detail and its flexibility is illustrated with three representative solid mechanics problems. More particularly, we propose here the MOS as the most versatile search algorithm for SoftFEM. A new method for the identification of nonfully determined parameters is also proposed.

BIMBOT-(Artificial intelligence applied to BIM design)

“…In particular, the previously mentioned soft computing techniques, metaheuristics, which provide search methods based on stochastic and heuristic strategies. Their widespread application in other engineering fields makes them very promising (Saridakis and Dentsoras, 2008) (Roy, Furuhashi and Chawdhry, 2012) (Jun, Annan, Zhiwu and Jingping, 2013: 11) (Noilublao and Bureerat, 2013: 12) (Saka, Hasançebi and Geem, 2016) (Peña, LaTorre and Jérusalem, 2019).…”

“…The technology of this optimization engine has also been successfully applied in other AI-based design approaches, such as airframe design (Muelas,Peña,Muzhetskaya,LaTorre and Miguel,208). Recently, we have applied this optimisation approach to design processes in the design of materials with crystalline plasticity simulations performed with finite element calculation (Peña, LaTorre and Jérusalem, 2019).…”

“…En especial las técnicas de soft computing antes mencionadas, las metaheurísticas, las cuales proporcionan métodos de búsqueda basadas en estrategias estocásticas y heurísticas. Su aplicación de forma generalizada en otros campos de la ingeniería las hace muy prometedoras (Saridakis and Dentsoras, 2008) (Roy, Furuhashi and Chawdhry, 2012) (Jun, Annan, Zhiwu and Jingping, 2013: 11) (Noilublao and Bureerat, 2013: 12) (Saka, Hasançebi and Geem, 2016) (Peña, LaTorre and Jérusalem, 2019).…”

“…Asimismo, la tecnología de este motor de optimización se ha aplicado con éxito en otros enfoques de diseño basado en IA, como el diseño de fuselaje de aviones (Muelas,Peña,Muzhetskaya,LaTorre and Miguel,208). Recientemente, este enfoque de optimización aplicada a procesos de diseño lo hemos aplicado al diseño de materiales con simulaciones de plasticidad cristalina realizadas con cálculo de elementos finitos (Peña, LaTorre and Jérusalem, 2019).…”

Model calibration using a parallel differential evolution algorithm in computational neuroscience: Simulation of stretch induced nerve deficit

“…Most of the optimization approaches based on heuristic optimization have used genetic algorithms [72,73], but many other heuristic approaches have also been used, such as particle swarm optimization [74,75], ant colony optimization [76], scattersearch [77], or local search methods like simulated annealing or tabu search [78]. Recently, hybrid heuristic optimization approaches have also been used for the calibration of computational simulation models, for instance, multiple offspring sampling [79], or memetic algorithms [80].…”