A novel elitist multiobjective optimization algorithm: Multiobjective extremal optimization

Abstract Recently, a general-purpose local-search heuristic method called extremal optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems. This paper presents an investigation on EO with its application in numerical multiobjective optimization and proposes a new novel elitist (1 +  λ ) multiobjective algorithm, called multiobjective extremal optimization (MOEO). In order to extend EO to solve the multiobjective optimization problems, the Pareto dominance strategy is introduced to the fitness assignment of the proposed approach. We also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm. The proposed approach is validated using five popular benchmark functions. The simulation results indicate that the proposed approach is highly competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOEO can be considered a good alternative to solve numerical multiobjective optimization problems.

[1]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[2]  Seth Stovack Kessler.  Piezoelectric-based in-situ damage detection of composite materials for structural health monitoring systems , 2002 .

[3]  S. Boettcher.  Extremal optimization for Sherrington-Kirkpatrick spin glasses , 2004, cond-mat/0407130.

[4]  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).

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

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

[7]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[8]  Yu-Wang Chen,et al.  Hybrid evolutionary algorithm with marriage of genetic algorithm and extremal optimization for production scheduling , 2008 .

[9]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[10]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Comput. Intell. Mag..

[11]  Tim Hendtlass,et al.  Solving Problems with Hidden Dynamics – Comparison of Extremal Optimisation and Ant Colony System , 2006, 2006 IEEE International Conference on Evolutionary Computation.

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

[13]  Mohamed El Bachir Menai,et al.  Efficient Initial Solution to Extremal Optimization Algorithm for Weighted MAXSAT Problem , 2003, IEA/AIE.

[14]  Roberto L. Galski,et al.  Spacecraft thermal design with the Generalized Extremal Optimization Algorithm , 2007 .

[15]  Min-Rong Chen,et al.  Studies on Extremal Optimization and Its Applications in Solving RealWorld Optimization Problems , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

[16]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[17]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

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

[19]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[20]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[21]  Thomas Hanne,et al.  A multiobjective evolutionary algorithm for approximating the efficient set , 2007, Eur. J. Oper. Res..

[22]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[23]  Stefan Boettcher,et al.  Extremal Optimization for the Sherrington-Kirkpatrick Spin Glass , 2004 .

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

[25]  Ko-Hsin Liang,et al.  A new multiobjective evolutionary algorithm , 2002, Eur. J. Oper. Res..

[26]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[27]  Min-Rong Chen,et al.  Population-Based Extremal Optimization with Adaptive Lévy Mutation for Constrained Optimization , 2006, 2006 International Conference on Computational Intelligence and Security.

[28]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[29]  Fabiano Luis de Sousa,et al.  Generalized extremal optimization: An application in heat pipe design , 2004 .

[30]  Ricardo P. Beausoleil,et al.  "MOSS" multiobjective scatter search applied to non-linear multiple criteria optimization , 2006, Eur. J. Oper. Res..

[31]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[32]  Stefan Boettcher,et al.  Extremal optimization at the phase transition of the three-coloring problem. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Alex A. Freitas,et al.  Evolutionary Computation , 2002 .

[34]  Taïcir Loukil,et al.  The Pareto fitness genetic algorithm: Test function study , 2007, Eur. J. Oper. Res..

[35]  C. A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Computational Intelligence Magazine.

[36]  E. Ahmed,et al.  On Multiobjective Evolution Model , 2004, nlin/0410052.

[37]  E. Polak,et al.  On Multicriteria Optimization , 1976 .

[38]  A. Percus,et al.  Nature's Way of Optimizing , 1999, Artif. Intell..

[39]  Mohamed Fathey Elettreby.  Multiobjective Optimization Of An Extremal Evolution Model , 2005 .

[40]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[41]  Tomoyuki Hiroyasu,et al.  SPEA2+: Improving the Performance of the Strength Pareto Evolutionary Algorithm 2 , 2004, PPSN.