Multiobjective Metamodel–Assisted Memetic Algorithms

The hybridization of global metaheuristics, such as evolutionary algorithms (EAs), and gradient-based methods for local search, in the framework of the so-called memetic algorithms (MAs) can be used to solve multi-objective optimization problems, either in the Lamarckian or Baldwinian spirit. Reducing the CPU cost of MAs is necessary for problems with computationally demanding evaluations. For the same purpose, in EAs, metamodels are in widespread use, giving rise to various kinds of metamodelassisted EAs (MAEAs). Metamodels are surrogate evaluation models of various types: multilayer perceptrons, radial basis function networks, polynomial regressions models, kriging, etc. A good practice is to use local metamodels, trained on the fly for each new individual, using selected entries from a database where all the previously evaluated offspring are recorded. The selection of suitable training patterns is important in order to minimize the prediction error of the metamodel. The MAEA developed by the authors in the past uses the inexact pre-evaluation (IPE) technique which starts after running a conventional EA for just a few generations on the exact evaluation model. The exactly evaluated offspring are all stored in the database. For the subsequent generations, local metamodels are trained for each new offspring to get an approximation to the objective functions so that, based on it, a few top individuals (in the Pareto front sense) are selected for exact re-evaluation.

[1]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[2]  Natalio Krasnogor,et al.  Studies on the theory and design space of memetic algorithms , 2002 .

[3]  R. Belew,et al.  Evolutionary algorithms with local search for combinatorial optimization , 1998 .

[4]  Yaochu Jin,et al.  A comprehensive survey of fitness approximation in evolutionary computation , 2005, Soft Comput..

[5]  Pablo Moscato,et al.  Memetic algorithms: a short introduction , 1999 .

[6]  D. E. Goldberg,et al.  Genetic Algorithms in Search, Optimization & Machine Learning , 1989 .

[7]  Raphael T. Haftka,et al.  Assessment of neural net and polynomial-based techniques for aerodynamic applications , 1999 .

[8]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[9]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[10]  X. Yao,et al.  Combining landscape approximation and local search in global optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[12]  M. Giles,et al.  Viscous-inviscid analysis of transonic and low Reynolds number airfoils , 1986 .

[13]  Kyriakos C. Giannakoglou.  Designing Turbomachinery Blades Using Evolutionary Methods , 1999 .

[14]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[15]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[16]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[17]  D. Grierson,et al.  Optimal sizing, geometrical and topological design using a genetic algorithm , 1993 .

[18]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

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

[20]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[21]  Chris Bishop,et al.  Improving the Generalization Properties of Radial Basis Function Neural Networks , 1991, Neural Computation.

[22]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[23]  Alain Ratle,et al.  Accelerating the Convergence of Evolutionary Algorithms by Fitness Landscape Approximation , 1998, PPSN.

[24]  Christine A. Shoemaker,et al.  Local function approximation in evolutionary algorithms for the optimization of costly functions , 2004, IEEE Transactions on Evolutionary Computation.

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

[26]  Man-Wai Mak,et al.  Exploring the effects of Lamarckian and Baldwinian learning in evolving recurrent neural networks , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[27]  Marios K. Karakasis,et al.  On the use of metamodel-assisted, multi-objective evolutionary algorithms , 2006 .

[28]  Diego Federici,et al.  Combining genes and memes to speed up evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[29]  Bernhard Sendhoff,et al.  A framework for evolutionary optimization with approximate fitness functions , 2002, IEEE Trans. Evol. Comput..

[30]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

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

[32]  M. Giles,et al.  Two-Dimensional Transonic Aerodynamic Design Method , 1987 .

[33]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[34]  Marios K. Karakasis,et al.  Hierarchical distributed metamodel‐assisted evolutionary algorithms in shape optimization , 2007 .

[35]  Hisao Ishibuchi,et al.  Selection of initial solutions for local search in multiobjective genetic local search , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[36]  Michel Verleysen,et al.  Width optimization of the Gaussian kernels in Radial Basis Function Networks , 2002, ESANN.

[37]  A. Ratle.  Optimal sampling strategies for learning a fitness model , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[38]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .

[39]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[40]  Joshua D. Knowles,et al.  M-PAES: a memetic algorithm for multiobjective optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[41]  W. Hart.  Adaptive global optimization with local search , 1994 .

[42]  Andy J. Keane,et al.  Combining Global and Local Surrogate Models to Accelerate Evolutionary Optimization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[43]  Bu-Sung Lee,et al.  Memetic algorithm using multi-surrogates for computationally expensive optimization problems , 2007, Soft Comput..

[44]  Michael T. M. Emmerich,et al.  Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels , 2006, IEEE Transactions on Evolutionary Computation.

[45]  Kemper Lewis,et al.  EFFICIENT GLOBAL OPTIMIZATION USING HYBRID GENETIC ALGORITHMS , 2002 .

[46]  Bernd Fritzke,et al.  Fast learning with incremental RBF networks , 1994, Neural Processing Letters.

[47]  David Corne,et al.  A Comparative Assessment of Memetic, Evolutionary, and Constructive Algorithms on Multiobjective $d$-MST Problems , 2001 .

[48]  Marios K. Karakasis,et al.  Inexact information aided, low‐cost, distributed genetic algorithms for aerodynamic shape optimization , 2003 .

[49]  David Corne,et al.  A comparison of diverse approaches to memetic multiobjective combinatorial optimization , 2000 .

[50]  Andrzej Jaszkiewicz,et al.  Genetic local search for multi-objective combinatorial optimization , 2022 .

[51]  Hisao Ishibuchi,et al.  Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling , 2003, IEEE Trans. Evol. Comput..