Hybrid Taguchi-Harmony Search Algorithm for Solving Engineering Optimization Problems Ali Rıza Yıldız Uludag University, Mechanical Engineering Department, 16059, Bursa, Turkey e-mail :
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This paper describes a new optimization strategy that offers significant improvements in performance over existing methods to support multi-objective design optimization applications in industry. A new design optimization approach is based on two-stages which are (1) Taguchi’s robust design approach to find appropriate interval levels of design parameters (2) Harmony search algorithm to generate optimal multi-objective solutions using refined intervals from the previous stage. This research is the first application of harmony search algorithm to shape design optimization problems in the literature. The validity and efficiency of proposed new approach are evaluated and illustrated with multi objective twobar truss problem taken from literature. Finally, it is applied to the shape design optimization of a vehicle component to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems. Keywords: Design optimization, Harmony search algorithm, Taguchi’s method, Robust Design
1. Introduction
In order to meet today`s competition requirements and to produce higher quality products at lower cost with shorter lead times, there is a crucial need to use new optimization techniques in industry. The real world design problems are usually multi-objective, often conflicting, and they have uncontrollable variations in their design parameters with complex nature. There is a need to obtain solutions that are multi-objectively optimum and insensitive to uncontrollable parameter variations. The whole problem must be taken as multi-objective with the Pareto optimal set instead of single objective optimization. It is difficult to design the best product by classical optimization methods under all these conditions. Classical optimization methods are not only time consuming in solving complex nature problems that include multivariable and multi-objective but also they may not be used efficiently in finding global or near global optimum solutions. In addition, they can stick to the local optimum values. Although classical optimization methods were widely used to solve multi-objective optimization problems in
design and manufacturing area, the inefficiency of classical methods in complex nature problems have forced researchers to search for new approaches. There is an increasing interest to apply the new approaches and to further improve the performance of multi-objective design optimization techniques for the solution of shape optimization problems. Although some improvements regarding multi-objective design optimization issues are achieved, the complexity of design problems with conflicting objectives presents shortcomings. The main goal of present research is to further develop and strengthen the harmony search algorithm based multiobjective optimization approach to generate real world design solutions. A new hybrid approach based on robustness issues are used to help better initialize harmony search algorithm search. It has been aimed to reach optimum designs by using Taguchi’s robust parameter design approach coupled with harmony search algorithms. 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 search population of harmony search algorithm process is defined according to these interval levels. Then, optimum results of multi-objective design optimization problem are obtained using harmony search algorithm. The validity and efficiency of proposed approach are evaluated and illustrated with a test problem of the two-bar truss design taken from literature. Then, a vehicle part design problem taken from automotive industry is introduced to demonstrate the application of the present approach to real world design problems. The results of the proposed multi-objective design optimization algorithm are better and more robust compared to computational experimental solutions of design optimization test problems.
2. Global optimization using harmony search algorithm and robust parameter design
A larger population makes the algorithm more likely to locate a good making string, but also increases the time taken by the algorithm. The problem with larger population is to tend evolutionary algorithms to converge and stick around certain solutions; therefore, there is a need to define the efficient range of population intervals to achieve better Pareto optimal sets in shorter times. This shortcoming is eliminated by introducing Taguchi’s based initial population.
The algorithm of proposed hybrid approach can be outlined as follows
BEGIN Step 1: Taguchi method’
Begin 1.a Choose convenient orthogonal array from Taguchi’s standard orthogonal arrays 1.b Define levels and intervals 1.c For i:=1 to NOE (number of experiments) do begin Compute objective function values end; 1.d Choose convenient S/N ratio type (smaller the best or larger the best or nominal the best) based on minimization or maximization of objective functions 1.e For i:=1 to NOE do begin Compute S/N ratios end; 1.f Constitute Anova table for objective functions using S/N ratios 1.g Determine optimum levels and intervals using percentage contribution to performance using Anova table Use these levels and intervals for forming initial population end; ‘Generate Pareto optimal set using harmony search algorithm and computed robust initial population space’ Begin Input Use Initial population found in previous part of the program as input to harmony search algorithm Step 2: Harmony search algorithm Step 1: Initialize the problem and algorithm parameters. Step 2: Initialize the harmony memory. Step 3: Improvise a new harmony. Step 4: Update the harmony memory. Step 5: Check the stopping criterion. end; END.
