- Volume 34 Issue 12
DOI QR Code
Development of a Multiobjective Optimization Algorithm Using Data Distribution Characteristics
데이터 분포특성을 이용한 다목적함수 최적화 알고리즘 개발
- Hwang, In-Jin (Dept. of Mechanical Engineering, Hanyang Univ.) ;
- Park, Gyung-Jin (Dept. of Mechanical Engineering, Hanyang Univ.)
- Received : 2009.12.29
- Accepted : 2010.10.14
- Published : 2010.12.01
The weighting method and goal programming require weighting factors or target values to obtain a Pareto optimal solution. However, it is difficult to define these parameters, and a Pareto solution is not guaranteed when the choice of the parameters is incorrect. Recently, the Mahalanobis Taguchi System (MTS) has been introduced to minimize the Mahalanobis distance (MD). However, the MTS method cannot obtain a Pareto optimal solution. We propose a function called the skewed Mahalanobis distance (SMD) to obtain a Pareto optimal solution while retaining the advantages of the MD. The SMD is a new distance scale that multiplies the skewed value of a design point by the MD. The weighting factors are automatically reflected when the SMD is calculated. The SMD always gives a unique Pareto optimal solution. To verify the efficiency of the SMD, we present two numerical examples and show that the SMD can obtain a unique Pareto optimal solution without any additional information.
Mahalanobis Distance;Skewed Mahalanobis Distance;Weighting Method;Goal Programming;Standard Deviation
Supported by : 한국연구재단
- Marler, R.T. and Arora, J.S., 2004, “Survey of Multi- Objective Optimization Method for Engineering,” Struct Multidisc Optim 26, pp. 369-395. https://doi.org/10.1007/s00158-003-0368-6
- Taguchi, G. and Jugulum, R., 2002, “The Mahalanobis-Taguchi Strategy : A Pattern Technology ystem,” John Wiley & Sons.
- Maesschalck, R.D., Jouan, R. and Massart, D.L., 2002, “Tutorial: The Mahalanobis distance,” Chemometrics and Intelligent Laboratory Systems 50, pp. 1-18. https://doi.org/10.1016/S0169-7439(99)00047-7
- Kim, I.Y. and de Weck, O.L., 2005, “Adaptive Weighted-Sum Method for Bi-Objective Optimization: Pareto Front Generation,” Struct Multidisc Optim 29, pp. 149-158. https://doi.org/10.1007/s00158-004-0465-1
- Athan, T.W. and Papalambros, P.Y., 1996, “A Note on Weighted Criteria Methods for Compromise Solutions in Multi-Objective Optimization,” Engineering Optimization. 27, pp. 155-176. https://doi.org/10.1080/03052159608941404
- Osyczka, A., 1989, “Multicriterion Decision Making with Min-Max Approach,” Optimization Methods in Structural Design, Edited by H.Eschenauer, N. Olhoff, Euromech-Colloquium 164, Wissenschaftsverlag.
- Nakayama, H. and Furukawa, K., 1985, “Satisficing Trade-Off Method with an Application to Multiobjective Structure Design,” Large Scale Systems, Vol. 8, pp. 47-57.
- Miettinen, K. and Makela, M.M., 2002, “On Scalarizing Functions in Multiobjective Optimization,” OR Spectrum 24, pp. 193-213. https://doi.org/10.1007/s00291-001-0092-9
- Goel, P.S. and Singh, N., 1998, “A Multi-Objective Design-Optimization Model with Total Life Cycle Consideration,” Society of Automotive Engineer, 982167.
- Yoon, K.P. and Hwang, C.L., “Multiple Attribute Decision Making,” An Introduction. London: Sage Publications.
- Saaty, T.L., 1997, “A Scaling Method for Priorities in Hierarchies, Multiple Objectives and Fuzzy Sets,” J.Math. Psych.15, pp. 234-281. https://doi.org/10.1016/0022-2496(77)90033-5
- Charnes, A. and Cooper, W.W., 1961, “Management Models and Industrial Applications of Linear Programming,” Vols. 1 and 2. John Wiley, New York.
- Charnes, A. and Cooper, W.W., 1977, “Goal Programming and Multiple Objective Optimization,” Part 1. Eur. J. Oper. Res. 1, pp. 39-54. https://doi.org/10.1016/S0377-2217(77)81007-2
- Hwang, C.L. and Md.Masud, A.S., 1979, “Multiple Objective Decision Making, Methods and Applications: A State-of-the-Art Survey,” In: Beckmann, M. and Kunzi, H.P.(Eds.) Lecture Notes in Economics and mathematical Systems, No.164.
- Hwang, I.J., Hyun, Y.J. and Park, J.H., 2007, “The Study for the Improvement of On-Center Feel with MTS Technique,” Society of Automotive Engineers, 2007-01-0090.
- Kenney, J.F. and Keeping, E.S., 1962, “Mathematics of Statistics,” Pt.1,3rd ed. Princeton, NJ: Van Nostrand.
- Kim, W.C., Kim, J.J., Park, B.W., Park, S.H., Song, M.S., Lee, S.Y., Lee, Y.C., Chon, C.W. and Cho, S.S, 1998, “Modern Statistics, 4th Edition,” Young-ji MunhaSa.
- FRAMAX Inc., 2007, “PIAnO(Process Integration, Automation and Optimization) User’s manual”, ver 2.1.