Surrogate-Assisted Evolutionary Optimization Frameworks for High-Fidelity Engineering Design Problems

Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where high-fidelity analysis models are used, each function evaluation may require a Computational Structural Mechanics (CSM), Computational Fluid Dynamics (CFD) or Computational Electro-Magnetics (CEM) simulation costing minutes to hours of supercomputer time. Since EAs typically require thousands of function evaluations to locate a near optimal solution, the use of EAs often becomes computationally prohibitive for this class of problems. In this chapter, we present frameworks that employ surrogate models for solving computationally expensive optimization problems on a limited computational budget. In particular, the key factors responsible for the success of these frameworks are discussed. Experimental results obtained on benchmark test functions and real-world complex design problems are presented.

[1]  Marc A. Stelmack,et al.  Design of an Aircraft Brake Component Using an Interactive Multidisciplinary Design Optimization Framework , 2000 .

[2]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  James N. Siddall,et al.  Optimal Engineering Design: Principles and Applications , 1982 .

[5]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[6]  D. Quagliarella,et al.  Airfoil and wing design through hybrid optimization strategies , 1998 .

[7]  A. Tits,et al.  Nonlinear Equality Constraints in Feasible Sequential Quadratic Programming , 1996 .

[8]  Nostrand Reinhold,et al.  the utility of using the genetic algorithm approach on the problem of Davis, L. (1991), Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York. , 1991 .

[9]  Ramana V. Grandhi,et al.  Multipoint approximation development: thermal structural optimization case study , 2000 .

[10]  I. C. Parmee Adaptive Computing in Design and Manufacture , 1998 .

[11]  C. Houck,et al.  Utilizing Lamarckian Evolution and the Baldwin Effect in Hybrid Genetic Algorithms , 2007 .

[12]  Mitchell A. Potter,et al.  The design and analysis of a computational model of cooperative coevolution , 1997 .

[13]  David Levin,et al.  The approximation power of moving least-squares , 1998, Math. Comput..

[14]  Andy J. Keane,et al.  Passive Vibration Suppression of Flexible Space Structures via Optimal Geometric Redesign , 2001 .

[15]  X. Yao Evolutionary Search of Approximated N-dimensional Landscapes , 2000 .

[16]  Ian C. Parmee,et al.  Multiobjective Satisfaction within an Interactive Evolutionary Design Environment , 2000, Evolutionary Computation.

[17]  Johan Andersson,et al.  Response Surface Methods and Pareto Optimization in Crashworthiness Design , 2003, DAC 2003.

[18]  E. Sachs,et al.  Trust-region proper orthogonal decomposition for flow control , 2000 .

[19]  Markus Olhofer,et al.  A Framework for Evolutionary Optimization with ApproximateFitness Fun tionsYao , 2002 .

[20]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[21]  R. Carter On the global convergence of trust region algorithms using inexact gradient information , 1991 .

[22]  Jongsoo Lee,et al.  Genetic algorithms in multidisciplinary rotor blade design , 1995 .

[23]  Andy J. Keane,et al.  A case for multi-level optimisation in aeronautical design , 1999, The Aeronautical Journal (1968).

[24]  Andy J. Keane,et al.  Surrogate-assisted coevolutionary search , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[25]  Andy J. Keane,et al.  Metamodeling Techniques For Evolutionary Optimization of Computationally Expensive Problems: Promises and Limitations , 1999, GECCO.

[26]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[27]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[28]  Jason Weston,et al.  Transductive Inference for Estimating Values of Functions , 1999, NIPS.

[29]  Alain Ratle,et al.  Kriging as a surrogate fitness landscape in evolutionary optimization , 2001, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[30]  Andy J. Keane,et al.  Aircraft wing design using GA-based multi-level strategies , 2000 .

[31]  Kyriakos C. Giannakoglou,et al.  Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence , 2002 .

[32]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[33]  Hiroshi Furuya,et al.  Combining genetic and deterministic algorithms for locating actuators on space structures , 1995 .

[34]  Robert Canfield,et al.  Multipoint Cubic Surrogate Functions for Sequential Approximate Optimization , 2002 .

[35]  Z. K. Zhang,et al.  Global convergence of unconstrained and bound constrained surrogate-assisted evolutionary search in aerodynamic shape design , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[36]  Vassili Toropov,et al.  Multiparameter structural optimization using FEM and multipoint explicit approximations , 1993 .

[37]  A. Keane,et al.  Evolutionary Optimization of Computationally Expensive Problems via Surrogate Modeling , 2003 .

[38]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[39]  Mitchell A. Potter,et al.  EVOLVING NEURAL NETWORKS WITH COLLABORATIVE SPECIES , 2006 .

[40]  Andy J. Keane,et al.  Combining approximation concepts with genetic algorithm-based structural optimization procedures , 1998 .

[41]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[42]  N. M. Alexandrov,et al.  A trust-region framework for managing the use of approximation models in optimization , 1997 .

[43]  T. W. Layne,et al.  A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models , 1998 .

[44]  Kenneth A. De Jong,et al.  A Cooperative Coevolutionary Approach to Function Optimization , 1994, PPSN.

[45]  Bernhard Sendhoff,et al.  Optimisation of a Stator Blade Used in a Transonic Compressor Cascade with Evolution Strategies , 2000 .

[46]  John E. Dennis,et al.  A framework for managing models in nonlinear optimization of computationally expensive functions , 1999 .

[47]  Ian Foster,et al.  The Grid 2 - Blueprint for a New Computing Infrastructure, Second Edition , 1998, The Grid 2, 2nd Edition.

[48]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[49]  Zbigniew Michalewicz,et al.  Genetic Algorithms Plus Data Structures Equals Evolution Programs , 1994 .

[50]  Wentong Cai,et al.  "Gridifying" Aerodynamic Design Problem Using GridRPC , 2003, GCC.

[51]  J. Friedman Multivariate adaptive regression splines , 1990 .

[52]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[53]  P. Toint Global Convergence of a a of Trust-Region Methods for Nonconvex Minimization in Hilbert Space , 1988 .

[54]  Pablo Moscato,et al.  On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms , 1989 .

[55]  Carl E. Rasmussen,et al.  In Advances in Neural Information Processing Systems , 2011 .

[56]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[57]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[58]  Reinhard Männer,et al.  Parallel Problem Solving from Nature — PPSN III , 1994, Lecture Notes in Computer Science.

[59]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[60]  Jerome H. Friedman Multivariate adaptive regression splines (with discussion) , 1991 .

[61]  Layne T. Watson,et al.  Improved Genetic Algorithm for the Design of Stiffened Composite Panels , 1994 .

[62]  Ami Marowka,et al.  The GRID: Blueprint for a New Computing Infrastructure , 2000, Parallel Distributed Comput. Pract..