Local Search with Quadratic Approximations into Memetic Algorithms for Optimization with Multiple Criteria

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.

[1]  Frederico G. Guimarães,et al.  A Differential Mutation operator for the archive population of multi-objective evolutionary algorithms , 2009, 2009 IEEE Congress on Evolutionary Computation.

[2]  Joshua D. Knowles,et al.  Memetic Algorithms for Multiobjective Optimization: Issues, Methods and Prospects , 2004 .

[3]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[4]  Konstantinos G. Margaritis,et al.  Performance comparison of memetic algorithms , 2004, Appl. Math. Comput..

[5]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[6]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[7]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[8]  James Smith,et al.  A tutorial for competent memetic algorithms: model, taxonomy, and design issues , 2005, IEEE Transactions on Evolutionary Computation.

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

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

[11]  Frederico G. Guimarães,et al.  Quadratic Approximation-Based Coordinate Change in Genetic Algorithms , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[12]  Jaime A. Ramírez,et al.  Hybrid optimization in electromagnetics using sensitivity information from a neuro-fuzzy model , 2000 .

[13]  Francisco Herrera,et al.  Real-Coded Memetic Algorithms with Crossover Hill-Climbing , 2004, Evolutionary Computation.

[14]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[15]  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).

[16]  Bin Li,et al.  Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization , 2010, Memetic Comput..

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

[18]  Elizabeth F. Wanner,et al.  A new performance metric for multiobjective optimization: the integrated sphere counting , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[20]  P. Khargonekar,et al.  Mixed H/sub 2//H/sub infinity / control: a convex optimization approach , 1991 .

[21]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[22]  Yacov Y. Haimes,et al.  Approach to performance and sensitivity multiobjective optimization: The goal attainment method , 1975 .

[23]  Fan Jiancong,et al.  An Evolutionary Mining Model in Incremental Data Mining , 2009, 2009 Fifth International Conference on Natural Computation.

[24]  Xiaolin Hu,et al.  Hybridization of the multi-objective evolutionary algorithms and the gradient-based algorithms , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[25]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[26]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[27]  Mikkel T. Jensen,et al.  Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms , 2003, IEEE Trans. Evol. Comput..

[28]  Joshua D. Knowles.  Local-search and hybrid evolutionary algorithms for Pareto optimization , 2002 .

[29]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored , 2009, Frontiers of Computer Science in China.

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

[31]  J. D. Schaffer,et al.  Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition) , 1984 .

[32]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[33]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[34]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[35]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[36]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[37]  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).

[38]  Frederico G. Guimarães,et al.  New operators for multi‐objective clonal selection algorithms , 2009 .

[39]  M. Dwass.  Modified Randomization Tests for Nonparametric Hypotheses , 1957 .

[40]  Daniel,et al.  Estimation of Pareto sets in the mixed H 2 = H 1 control problem , 2004 .

[41]  Carlos M. Fonseca,et al.  Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function , 2001, EMO.

[42]  Paulo Ferreira,et al.  Multiobjective H/sub 2//H/sub /spl infin// guaranteed cost PID design , 1997 .

[43]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[44]  Kees Roos,et al.  On convex quadratic approximation , 2000 .

[45]  Frederico G. Guimarães,et al.  A Quadratic Approximation-Based Local Search Procedure for Multiobjective Genetic Algorithms , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[46]  Bernd Freisleben,et al.  Fitness landscapes and memetic algorithm design , 1999 .

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

[48]  Anikó Ekárt,et al.  Genetic algorithms in computer aided design , 2003, Comput. Aided Des..

[49]  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).

[50]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[51]  Bernhard Sendhoff,et al.  A critical survey of performance indices for multi-objective optimisation , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

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

[53]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[54]  K. Rasheed,et al.  An incremental-approximate-clustering approach for developing dynamic reduced models for design optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[55]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[56]  Carlos A. Coello Coello,et al.  Solving Multiobjective Optimization Problems Using an Artificial Immune System , 2005, Genetic Programming and Evolvable Machines.

[57]  Frederico G. Guimarães,et al.  Constraint quadratic approximation operator for treating equality constraints with genetic algorithms , 2005, 2005 IEEE Congress on Evolutionary Computation.

[58]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).