A new design optimization framework based on immune algorithm and Taguchi's method

Abstract

This paper describes an innovative optimization approach that offers significant improvements in performance over existing methods to solve shape optimization problems. The new approach is based on two-stages which are (1) Taguchi's robust design approach to find appropriate interval levels of design parameters (2) Immune algorithm to generate optimal solutions using refined intervals from the previous stage. A benchmark test problem is first used to illustrate the effectiveness and efficiency of the approach. Finally, it is applied to the shape design optimization of a vehicle component to illustrate how the present approach can be applied for solving shape design optimization problems. The results show that the proposed approach not only can find optimal but also can obtain both better and more robust results than the existing algorithm reported recently in the literature.

Introduction

The optimal design of structures includes sizing, shape and topology optimization. In the last 30 years, there has been extensive research focused on shape optimization due to its great contribution to cost, material and time savings in the procedures of the engineering design. The purpose of shape optimization is to determine the optimal shape of a continuum medium to maximize or minimize a given criterion (often called an objective function), such as minimize the weight of the body, maximize the stiffness of the structure or remove the stress concentrations, subjected to the stress or displacement constraint conditions.

Computer-aided optimization has been commonly used to obtain more economical designs since 1970s. Numerous algorithms have been developed to solve shape design optimization problems in the last four decades. The early works on the topic mostly use various mathematical techniques. These methods are not only time consuming in solving complex nature problems but also they may not be used efficiently in finding global or near global optimum solutions. In the past few decades, a number of innovative approaches, such as tabu search, genetic algorithm, simulated annealing, particle swarm optimization algorithm, ant colony algorithm and immune algorithm have been developed and widely applied in various fields of science [1], [2], [3], [4], [5], [6], [7], [8], [9], [10].

Fast convergence speed and robustness in finding the global minimum are not easily achieved at the same time. Fast convergence requires a minimum number of calculations, increasing the probability of missing important points; on the other hand, the evaluation of more points for finding the global minimum decreases the convergence speed. This leads to the question: ‘how to obtain both fast convergence speed and global search capability at the same time.’ There have been a number of attempts to answer this question, while hybrid algorithms have shown outstanding reliability and efficiency in application to the engineering optimization problems [11], [12], [13], [14], [15].

Therefore, the researchers are paying great attention on hybrid approaches to answer this question, particularly to avoid premature convergence towards a local minimum and to reach the global optimum results.

There is an increasing interest to apply the new approaches and to further improve the performance of optimization techniques for the solution of shape design optimization problems. Although some improvements regarding shape design optimization issues are achieved, the complexity of design problems presents shortcomings. The main goal of present research is to further develop and strengthen the immune algorithm which is a computational intelligence paradigm inspired by the biological immune system to generate real world design solutions. A new hybrid approach based on robustness issues is used to help better initialize immune algorithm search. It has been aimed to reach optimum designs by using Taguchi's robust parameter design approach coupled with immune algorithm. In this new hybrid approach, S/N values are calculated and ANOVA (analysis of variance) table for each of the objectives are formed using S/N ratios respectively. According to results of ANOVA table, appropriate interval levels of design parameters are found and then, initial antibody population of immune algorithm is defined according to these interval levels. Then, optimum results of design optimization problem are obtained using immune algorithm.

The hybrid approach is evaluated using a well-known benchmark problem and compared with other optimization methods in the literature. Finally, the developed new hybrid optimization approach is applied to a vehicle part design optimization problem taken from automotive industry to demonstrate the application of the present approach to real world design problems. The results show that the proposed optimization method converges rapidly to the global optimum solution and provides reliable and accurate solutions for even the most complicated of optimization problems.