Dimensional optimization of truss structures using differential evolution coupled with the FEM

Abstract

This study aims to develop, implement, and validate a computational methodology for the continuous dimensional optimization of planar trusses by integrating the Differential Evolution method with linear structural analysis based on the Finite Element Method within the Scilab environment. The formulation assumes linear elastic behavior, infinitesimal deformations, and stress and displacement constraints, while the cross-sectional areas of the members are defined as continuous design variables. To evaluate the influence of the stochastic nature of the algorithm, ten independent runs were performed for each problem, and statistical indicators were determined, including the mean and standard deviation of the optimal masses, the average number of generations required for convergence, and the average processing time, in addition to the convergence histories of the structural mass and the population diversity. The methodology was validated using three classical truss optimization problems containing 10, 15, and 17 members. The results showed good agreement with reference solutions available in the literature, repeatability among the independent runs, and compliance with the structural constraints. It is concluded that the developed algorithm constitutes a potential computational tool for the dimensional optimization of trusses subjected to linear analysis, contributing to the reduction of structural mass, material consumption, and CO₂ emissions.