Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

Abstract

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

A Brief Review of Firefly Algorithm: Application in Structural Optimization Problem

“…First, embedding the random weight in classical firefly algorithm, that helps to enhance global exploration in the initial stage of the search process. Second, using improved attractiveness to enhance the local exploration that helps to provide the ability to escape from poor local optima in an accurate and fast way, and also helps to avoid excessive pace for location updating and lead to repeated oscillation in the last stage of the search process where the algorithm depends mainly on the local search [25,29].…”

“…FA is used by many researchers to solve the various type of problems such as routing problem [22], image processing [20], classification/clustering problems [26], optimization problems [3,25,29,33,5,23,32,21,13,1]. FA is also used to solve various structural engineering problems.…”

“…FA is also used to solve various structural engineering problems. It has successfully tested in the various field of structural engineering, such as, earthquake engineering [14], Beam section design [10,7] and design and optimization of steel structures [8], Shape, size and topology optimization of truss structures [3,25,29], Structural damage detection [12] etc.…”

“…They depend on objective functions selected, variables used, constraint types and the degree of complexity. Structural optimization problems are classified as; continuous [3], discrete [25,29], combinatorial, constrained [17,8], unconstrained [19], mixed variable [16], multi-objective [34], multi-modal [24], Multiple load case [3], dynamic [28,2] and noisy [9].…”

Shape Generation of Grid Structures by Inverse Hanging Method Coupled with Multiobjective Optimization

“…The parameter Tol is set to 0.1 m because the error in this order of magnitude is acceptable in the shape generation of realistic structures. The parameters β 0 , γ, and α are usually set to 1, 1, and 0.2 in most studies of firefly algorithm (Wu et al, ; Ferreira et al., ). Many trial numerical examples show that they are also optimal values for the shape‐generation problem.…”