Integrating Gaussian Random Functions with Genetic Algorithms for the Optimization of Functionally Graded Lattice Structures

TL;DR

This paper introduces a novel non-gradient optimization method combining Gaussian processes with genetic algorithms to design smooth, stress-resistant lattice structures with tailored gradation profiles.

Contribution

It presents an integrated Gaussian process and genetic algorithm framework that ensures smoothness in graded lattice structures, addressing issues of abrupt changes in traditional methods.

Findings

The proposed method produces smoother lattice designs.

The designs are less prone to stress concentration.

Numerical examples validate the effectiveness of the approach.

Abstract

The properties of lattice-based structures can be enhanced by varying their geometric parameters in a graded manner, and the gradation can be tailored to extremize a particular objective. In this manuscript, we propose a non-gradient-based optimization framework to find the tailor-made graded profiles for lattice-based structures. The key challenge addressed in the work is to ensure the graded nature/smoothness of the underlying structure in a non-gradient-based optimization scheme. As we demonstrate in the manuscript, the conventional implementation of the genetic algorithm provides structures with abrupt changes, leading to issues such as stress concentration. In this work, we propose a Gaussian random function (GRF)/Gaussian process regression (GPR) integrated genetic algorithm to obtain an optimal graded lattice profile for a given objective. The integration of the GRF/GPR along with a projection operator ensures the smoothness of the designs at each stage of the optimization. We present several numerical examples to demonstrate that the proposed framework provides smoother designs that are less susceptible to stress concentration, while ensuring satisfaction of the underlying objective.