A firefly algorithm based hybrid method for structural topology optimization

Hailu Shimels Gebremedhen,Dereje Engida Woldemichael,Fakhruldin Mohd Hashim

doi:10.1186/s40323-020-00183-0

Abstract

In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5 to 15% compared to the OC method.

Highlights

Continuum structural topology optimization as a generalized shape optimization problem that has received extensive attention and considerable progress over the past few years
Result and discussion The proposed method was used to solve benchmark problems under different discretization size and the results are compared with solutions using an optimality criteria (OC) method
Supported The other benchmark problem used for validation of the proposed method was a supported beam under the loading and boundary condition defined in Fig. and generated topologies are shown in Fig. under different discretization sizes

Summary

Introduction

Continuum structural topology optimization as a generalized shape optimization problem that has received extensive attention and considerable progress over the past few years. Objective function Generate an initial population on fireflies Light intensity at is determined by Define the light absorption coefficient While For For j=1: n (all n fireflies, inner loop) If. Move firefly towards End if Vary attractiveness with distance via Evaluate the new solution and update light intensity End for End for Rank the fireflies and find the current global best ∗ End while Post-process of results and visualization. Determination input parameters Before using FA to solve stressed based topology optimization problems, input parameters must first be determined These parameters include the number of fireflies, the maximum number of iterations, the randomness parameter α and initial brightness value β. Number of iterations An optimization problem based on Eq 13 was formulated and solved using FA for the range of function evaluations for 100 test runs. From the initial topology generated from the firefly algorithm, we can Objective funtion

Objective function

Design domain

Conclusion