Interactive particle swarm optimization for the architectural design of truss structures

Abstract

This paper presents an interactive framework for the design of truss structures with aesthetic criteria. The truss chords are described using NURBS, a tool widely used in computer aided design (CAD) programs to describe free-form geometry. This allows for a convenient interface between the optimization scheme, a particle swarm optimizer, and the user. Driven from the fact that aesthetic design goals are not easily quantifiable, key elements are introduced and implemented herein towards an interactive framework for algorithmic design of truss structures. Within this framework, the user can visually assess interesting solutions, save them for later assessment, actively drive the optimization towards individual aims, re-initialize the optimization with a set of available solutions, or restart the design process. A criterion is introduced as a means of quantifying subjective goals, expressing the similarity of the shape of candidate solutions with respect to reference designs. The framework is tested on a benchmark case and then applied to the design of a truss tower. The effectiveness of the similarity criteria, as well as the ability of the user to drive the process towards specific design goals is demonstrated.

Interactive truss design using Particle Swarm Optimization and NURBS curves

“…For structural analysis purposes a finite element package, such as ANSYS, could be coupled to MATLAB serving as the numerical analysis tool as the authors have demonstrated before [49]. The idea behind selecting such a tool, which comes with a strong finite element (FE) solver, is to later expand this semi-automated design framework on surface and 3D structures.…”

“…In previous works, the efficacy of the PSO was validated on a finite element implementation for the well-known 10-bar truss benchmark problem [3,49]. This section presents the design of a 2D horizontal truss without user interaction, i.e., for purely structural optimization, in order to demonstrate the advantages of the NURBS parametrization.…”

“…However, any other meta-heuristic optimizer, e.g., the firefly or the bat algorithm [48], could be employed when appropriately calibrated. This paper builds on previous work of the authors [49]. The present paper includes the mathematical description of NURBS, and a discussion on and quantification of the advantages of NURBS.…”

“…Further, the present manuscript includes a set of more realistic and architecturally more relevant examples, as well as an extension to 3D problems. Finally, in [49] the choice of the user is included in the objective function through an artificial weight reduction, whereas in this work, it is more formally incorporated via an updated similarity constraint.…”

Advantages of surrogate models for architectural design optimization

“…Grasshopper ® , a free parametric design plugin for the popular three-dimensional modeling application Rhinoceros ® , includes an easy-to-use evolutionary solver named Galapagos (Rutten, 2013). Simulated annealing (also implemented in Galapagos) and particle swarm optimization are other metaheuristics that are sometimes used in the architectural field (e.g., Luebkeman & Shea, 2005; Felkner et al, 2013). According to Yang (2010), metaheuristics are also widespread in engineering design.…”