Research Papers: Design Automation

Multi-Objective Optimization With Multiple Spatially Distributed Surrogates

[+] Author and Article Information
Kalyan Shankar Bhattacharjee

School of Engineering and IT,
The University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: k.bhattacharjee@student.adfa.edu.au

Hemant Kumar Singh

School of Engineering and IT,
The University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: h.singh@adfa.edu.au

Tapabrata Ray

School of Engineering and IT,
The University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: t.ray@adfa.edu.au

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 12, 2015; final manuscript received June 25, 2016; published online July 18, 2016. Assoc. Editor: Gary Wang.

J. Mech. Des 138(9), 091401 (Jul 18, 2016) (10 pages) Paper No: MD-15-1821; doi: 10.1115/1.4034035 History: Received December 12, 2015; Revised June 25, 2016

In engineering design optimization, evaluation of a single solution (design) often requires running one or more computationally expensive simulations. Surrogate assisted optimization (SAO) approaches have long been used for solving such problems, in which approximations/surrogates are used in lieu of computationally expensive simulations during the course of search. Existing SAO approaches often use the same type of approximation model to represent all objectives and constraints in all regions of the search space. The selection of a type of surrogate model over another is nontrivial and an a priori choice limits flexibility in representation. In this paper, we introduce a multi-objective evolutionary algorithm (EA) with multiple adaptive spatially distributed surrogates. Instead of a single global surrogate, local surrogates of multiple types are constructed in the neighborhood of each offspring solution and a multi-objective search is conducted using the best surrogate for each objective and constraint function. The proposed approach offers flexibility of representation by capitalizing on the benefits offered by various types of surrogates in different regions of the search space. The approach is also immune to illvalidation since approximated and truly evaluated solutions are not ranked together. The performance of the proposed surrogate assisted multi-objective algorithm (SAMO) is compared with baseline nondominated sorting genetic algorithm II (NSGA-II) and NSGA-II embedded with global and local surrogates of various types. The performance of the proposed approach is quantitatively assessed using several engineering design optimization problems. The numerical experiments demonstrate competence and consistency of SAMO.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Wang, G. G. , and Shan, S. , 2007, “ Review of Metamodeling Techniques in Support of Engineering Design Optimization,” ASME J. Mech. Des., 129(4), pp. 370–380. [CrossRef]
Jin, Y. , 2005, “ A Comprehensive Survey of Fitness Approximation in Evolutionary Computation,” Soft Comput. Fusion Found. Methodol. Appl., 9(1), pp. 3–12.
Wilson, B. , Cappelleri, D. , Simpson, T. W. , and Frecker, M. , 2001, “ Efficient Pareto Frontier Exploration Using Surrogate Approximations,” Optim. Eng., 2(1), pp. 31–50. [CrossRef]
Goel, T. , Haftka, R. T. , Shyy, W. , and Queipo, N. V. , 2007, “ Ensemble of Surrogates,” Struct. Multidiscip. Optim., 33(3), pp. 199–216. [CrossRef]
Zhou, Z. , Ong, Y. S. , Nair, P. B. , Keane, A. J. , and Lum, K. Y. , 2007, “ Combining Global and Local Surrogate Models to Accelerate Evolutionary Optimization,” IEEE Trans. Syst. Man Cybern. Part C, 37(1), pp. 66–76. [CrossRef]
Wang, G. G. , and Simpson, T. W. , 2004, “ Fuzzy Clustering Based Hierarchical Metamodeling for Space Reduction and Design Optimization,” J. Eng. Optim., 36(3), pp. 313–335. [CrossRef]
Breiman, L. , 1996, “ Bagging Predictors,” Mach. Learn., 24(2), pp. 123–140.
Abney, S. , Schapire, R. E. , and Singer, Y. , 1999, “ Boosting Applied to Tagging and pp Attachment,” Joint SIGDAT Conference on Empirical Methods in Natural Language Processing and Very Large Corpora, University of Maryland, College Park, MD.
Acar, E. , 2010, “ Various Approaches for Constructing an Ensemble of Metamodels Using Local Measures,” Struct. Multidiscip. Optim., 42(6), pp. 879–896. [CrossRef]
Zhao, Y. , Gao, J. , and Yang, X. , 2005, “ A Survey of Neural Network Ensembles,” International Conference on Neural Networks and Brain, Beijing, China, Vol. 1, pp. 438–442.
Zerpa, L. E. , Queipo, N. V. , Pintos, S. , and Salager, J. L. , 2005, “ An Optimization Methodology of Alkaline-Surfactant-Polymer Flooding Processes Using Field Scale Numerical Simulation and Multiple Surrogates,” J. Pet. Sci. Eng., 47(3–4), pp. 197–208. [CrossRef]
Hamza, K. , and Saitou, K. , 2012, “ A Co-evolutionary Approach for Design Optimization Via Ensembles of Surrogates with Application to Vehicle Crashworthiness,” ASME J. Mech. Des., 134(1), p. 011001. [CrossRef]
Glaz, B. , Goel, T. , Liu, L. , Friedmann, P. P. , and Haftka, R. T. , 2009, “ Multiple-Surrogate Approach to Helicopter Rotor Blade Vibration Reduction,” AIAA J., 47(1), pp. 271–282. [CrossRef]
Mack, Y. , Goel, T. , Shyy, W. , Haftka, R. T. , and Queipo, N. V. , 2005, “ Multiple Surrogates for the Shape Optimization of Bluff Body-Facilitated Mixing,” AIAA Paper No. 2005-333.
Goel, T. , Haftka, R. T. , Queipo, N. V. , and Shyy, W. , 2006, “ Performance Estimate and Simultaneous Application of Multiple Surrogates,” AIAA Paper No. 2006-7047.
Zhou, Z. , Ong, Y. S. , Lim, M. H. , and Lee, B. S. , 2007, “ Memetic Algorithm Using Multi-Surrogates for Computationally Expensive Optimization Problems,” Soft Comput. Fusion Found. Methodol. Appl., 11(10), pp. 957–971.
Nain, P. , and Deb, K. , 2002, “ A Computationally Effective Multi-Objective Search and Optimization Techniques Using Coarse-To-Fine Grain Modeling,” Workshop on Evolutionary Multiobjective Optimization, Parallel Problem Solving From Nature, Granada, Spain.
Ray, T. , and Smith, W. , 2006, “ Surrogate Assisted Evolutionary Algorithm for Multiobjective Optimization,” International Conference on AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials, Newport, RI, pp. 1–8.
Knowles, J. , 2006, “ ParEGO: A Hybrid Algorithm With On-Line Landscape Approximation for Expensive Multiobjective Optimization Problems,” IEEE Trans. Evol. Comput., 10(1), pp. 50–66. [CrossRef]
Chafekar, D. , Shi, L. , Rasheed, K. , and Xuan, J. , 2005. “ Multiobjective GA Optimization Using Reduced Models,” IEEE Trans. Syst. Man Cybern., Part C, 35(2), pp. 261–265. [CrossRef]
Zhang, J. , Chowdhury, S. , Mehmani, A. , and Messac, A. , 2012, “ Uncertainty Quantification in Surrogate Models Based on Pattern Classification of Cross-Validation Errors,” AIAA Paper No. 2012-5437.
Deb, K. , Pratap, A. , Agarwal, S. , and Meyarivan, T. , 2002, “ A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. Evol. Comput., 6(2), pp. 182–197. [CrossRef]
Zitzler, E. , and Thiele, L. , 1999, “ Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach,” IEEE Trans. Evol. Comput., 3(4), pp. 257–271. [CrossRef]
Zitzler, E. , Thiele, L. , Laumanns, M. , Fonseca, C. , and da Fonseca, V. , 2003, “ Performance Assessment of Multiobjective Optimizers: An Analysis and Review,” IEEE Trans. Evol. Comput., 7(2), pp. 117–132. [CrossRef]
Barbosa, H. , Bernardino, H. , and Barreto, A. , 2010, “ Using Performance Profiles to Analyze the Results of the 2006 CEC Constrained Optimization Competition,” IEEE Congress on Evolutionary Computation, Barcelona, Spain, pp. 1–8.
Dolan, E. D. , and Moré, J. J. , 2002, “ Benchmarking Optimization Software With Performance Profiles,” Math. Program., 91(2), pp. 201–213. [CrossRef]
Zitzler, E. , Deb, K. , and Thiele, L. , 2000, “ Comparison of Multiobjective Evolutionary Algorithms: Empirical Results,” Evol. Comput., 8(2), pp. 173–195. [CrossRef] [PubMed]
Deb, K. , 2000, “ An Efficient Constraint Handling Method for Genetic Algorithms,” Comput. Methods Appl. Mech. Eng., 186(2–4), pp. 311–338. [CrossRef]
Cus, F. , and Balic, J. , 2003, “ Optimization of Cutting Process by GA Approach,” Rob. Comput. Integr. Manuf., 19(1–2), pp. 113–121. [CrossRef]
Sardiñas, R. Q. , Santana, M. R. , and Brindis, E. A. , 2006, “ Genetic Algorithm-Based Multi-Objective Optimization of Cutting Parameters in Turning Processes,” Eng. Appl. Artif. Intell., 19(2), pp. 127–133. [CrossRef]
Tan, K. , Lee, T. , and Khor, E. , 2001, “ Evolutionary Algorithms With Dynamic Population Size and Local Exploration for Multiobjective Optimization,” IEEE Trans. Evol. Comput., 5(6), pp. 565–588. [CrossRef]
Deb, K. , and Datta, R. , 2012, “ Hybrid Evolutionary Multi-Objective Optimization and Analysis of Machining Operations,” Eng. Optim., 44(6), pp. 685–706. [CrossRef]
Shiau, C. S. N. , Nikhil, K. , Hendrickson, C. T. , Peterson, S. B. , Whitacre, J. F. , and Michalek, J. J. , 2010, “ Optimal Plug-In Hybrid Electric Vehicle Design and Allocation for Minimum Life Cycle Cost, Petroleum Consumption, and Greenhouse Gas Emissions,” ASME J. Mech. Des., 132(9), p. 091013. [CrossRef]
Liao, X. , Li, Q. , Yang, X. , Zhang, W. , and Li, W. , 2008, “ Multiobjective Optimization for Crash Safety Design of Vehicles Using Stepwise Regression Model,” Struct. Multidiscip. Optim., 35(6), pp. 561–569. [CrossRef]
Sen, P. , and Yang, J. B. , 1998, Multiple Criteria Decision Support in Engineering Design, Springer, London.
Augusto, O. B. , Bennis, F. , and Caro, S. , 2012, “ A New Method for Decision Making in Multi-Objective Optimization Problems,” Pesqui. Operacional, 32(2), pp. 331–369. [CrossRef]
Bhattacharjee, K. S. , Singh, H. K. , and Ray, T. , 2016, “ Surrogate Assisted Multi-Objective Optimization (SAMO) Code and Instructions,” http://www.mdolab.net/Ray/Research-Data/SAMO_JMD.zip, Multidisciplinary Optimization Group, UNSW Canberra, Australia.


Grahic Jump Location
Fig. 1

Nondominated front for the median HV run (a) ZDT1, (b) Welded Beam, (c) CNC Machining, (d) Tool Spindle Design, (e) Metal Cutting, (f) PHEV Design, (g) Crash Safety Design, (h) Bulk Carrier Design

Grahic Jump Location
Fig. 2

Mean HV convergence (a) ZDT1, (b) Welded Beam, (c) CNC Machining, (d) Tool Spindle Design, (e) Metal Cutting, (f) PHEV Design, (g) Crash Safety Design, (h) Bulk Carrier Design

Grahic Jump Location
Fig. 3

Performance profile: (a) median (inverse of) HV statistics and (b) median IGD statistics



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In