A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement

Metamodel-assisted evolutionary algorithms are low-cost optimization methods for CPU-demanding problems. Memetic algorithms combine global and local search methods, aiming at improving the quality of promising solutions. This article proposes a metamodel-assisted memetic algorithm which combines and extends the capabilities of the aforementioned techniques. Herein, metamodels undertake a dual role: they perform a low-cost pre-evaluation of population members during the global search and the gradient-based refinement of promising solutions. This reduces significantly the number of calls to the evaluation tool and overcomes the need for computing the objective function gradients. In multi-objective problems, the selection of individuals for refinement is based on domination and distance criteria. During refinement, a scalar strength function is maximized and this proves to be beneficial in constrained optimization. The proposed metamodel-assisted memetic algorithm employs principles of Lamarckian learning and is demonstrated on mathematical and engineering applications.

[1]  R. Lewontin.  ‘The Selfish Gene’ , 1977, Nature.

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

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

[4]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[5]  Kevin Kok Wai Wong,et al.  Classification of adaptive memetic algorithms: a comparative study , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Andreas Zell,et al.  Evolution strategies with controlled model assistance , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

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

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

[9]  Hisao Ishibuchi,et al.  Multi-objective genetic local search algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[10]  G. Gary Wang,et al.  An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions , 2005 .

[11]  Bernhard Sendhoff,et al.  On Evolutionary Optimization with Approximate Fitness Functions , 2000, GECCO.

[12]  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).

[13]  Natalio Krasnogor,et al.  Toward truly "memetic" memetic algorithms: discussion and proof of concepts , 2002 .

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

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

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

[17]  Bernhard Sendhoff,et al.  Generalizing Surrogate-Assisted Evolutionary Computation , 2010, IEEE Transactions on Evolutionary Computation.

[18]  Petros Koumoutsakos,et al.  Accelerating evolutionary algorithms with Gaussian process fitness function models , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[19]  Jing J. Liang,et al.  Problem Definitions for Performance Assessment of Multi-objective Optimization Algorithms , 2007 .

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

[21]  Andy J. Keane,et al.  Computational Approaches for Aerospace Design: The Pursuit of Excellence , 2005 .

[22]  Andy J. Keane,et al.  Meta-Lamarckian learning in memetic algorithms , 2004, IEEE Transactions on Evolutionary Computation.

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

[24]  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).

[25]  Andreas Zell,et al.  Model-Assisted Steady-State Evolution Strategies , 2003, GECCO.

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

[27]  Peter A. N. Bosman,et al.  Exploiting gradient information in numerical multi--objective evolutionary optimization , 2005, GECCO '05.

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

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

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

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

[32]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

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

[34]  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).

[35]  Raphael T. Haftka,et al.  Response Surface Techniques for Diffuser Shape Optimization , 2000 .

[36]  Marios K. Karakasis,et al.  Low-cost genetic optimization based on inexact pre-evaluations and the sensitivity analysis of design parameters , 2001 .

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

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

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