Comparison of evolutionary-based optimization algorithms for structural design optimization

Abstract

In this paper, a comparison of evolutionary-based optimization techniques for structural design optimization problems is presented. Furthermore, a hybrid optimization technique based on differential evolution algorithm is introduced for structural design optimization problems. In order to evaluate the proposed optimization approach a welded beam design problem taken from the literature is solved. The proposed approach is applied to a welded beam design problem and the optimal design of a vehicle component to illustrate how the present approach can be applied for solving structural design optimization problems. A comparative study of six population-based optimization algorithms for optimal design of the structures is presented. The volume reduction of the vehicle component is 28.4% using the proposed hybrid approach. The results show that the proposed approach gives better solutions compared to genetic algorithm, particle swarm, immune algorithm, artificial bee colony algorithm and differential evolution algorithm that are representative of the state-of-the-art in the evolutionary optimization literature.

Introduction

Structural design optimization has been a very important and challenging topic in the field of engineering design for obtaining more efficient and lighter structures. The aim of the design optimization is to determine the optimal shape of a structure to maximize or minimize a given criterion, such as minimize the weight, maximize the stiffness, subjected to the stress or displacement constraint conditions.

The evolutionary algorithms have emerged as a powerful tool for finding optimum solutions of complex optimization problems. In the past few decades, a number of evolutionary algorithms such as genetic algorithm, cuckoo search algorithm, particle swarm optimization algorithm, artificial bee colony algorithm, harmony search algorithm and artificial immune algorithm have been used extensively to obtain optimal designs and overcome the computational drawbacks of traditional mathematical optimization methods (Yildiz and Durgun, 2012a, Yildiz (2012b), Yildiz and Saitou, 2011, Perez and Behdinan, 2007, Ferhat et al., 2011, Omkar et al., 2008, Karaboga and Basturk, (2003), Woon et al., 2001).

Recently, Yildiz and Saitou (2011) developed a novel topology optimization approach for continuum structures using the genetic algorithms. The developed approach is applied to multi-component topology optimization of a vehicle floor frame.

The differential evolution (DE) algorithm introduced by Storn and Price (1995) is an efficient population-based optimization method. The DE has received considerable attention and has been successfully used in various areas. The use of the DE in the optimum solution of problems resulted in better solutions compared to classical methods (Wu and Tseng, 2010, Hull et al., 2006, J´armai et al., 2003, Thangaraj et al., 2010, Dragoi et al., 2011, Khoei et al., 2002).

Although the DE algorithm is very effective at finding relatively good neighborhoods of solutions in a complex search space, they may have a premature convergence to a local minimum (Wang et al., 2011, Isaacs et al., 2007).

Some researchers have used the robustness issues to solve optimization problems (Chen et al., 2002, Lee et al., 2003). Robinson et al. (2004) presents a review paper which focuses largely on the work done since 1992 and a historical perspective of parameter design is also given. Kunjur and Krishnamurty (1997) presented a robust optimization approach that integrates optimization concepts with statistical robust design techniques.

Hybrid optimization algorithms have received significant interest for fast convergence speed and robustness in finding the global minimum at the same time (Yildiz, 2009a, Yildiz, 2009b, Yildiz, 2009c, Yildiz and Solanki, 2011). Tsai et al. (2004) proposed a hybrid algorithm in which the Taguchi's method is inserted between crossover and mutation operations of a genetic algorithm. The Taguchi method is incorporated in the crossover operations to select the better genes to achieve crossover, and consequently, enhance the performance of genetic algorithm. Yildiz (2012b) developed a novel hybrid robust optimization method (HRABC) based on the Taguchi's method and the artificial bee colony algorithm. The HRABC was applied to structural design optimization problem of an automobile component from industry and a milling optimization problem. Yildiz (2009b) hybridized immune algorithm with hill climbing local search algorithm and applied to multi-objective disc brake and manufacturing optimization problems from literature. Yildiz (2009c) developed a new hybrid particle swarm optimization approach to solve optimization problems in design and manufacturing area.

In this paper, a comparative study of six evolutionary-based optimization algorithms for the structural design optimization is presented. Furthermore, a hybrid technique (HTDEA) based on differential evolution algorithm is introduced. The HTDEA is applied to a welded beam design problem and the optimal design of a vehicle component to illustrate how the present approach can be applied for solving structural design optimization problems. The results show the effectiveness of the proposed approach.