Impact analysis of crossovers in a multi-objective evolutionary algorithm

Multi-objective optimization has become mainstream because several real-world problems are naturally posed as a Multi-objective optimization problems (MOPs) in all fields of engineering and science. Usually MOPs consist of more than two conflicting objective functions and that demand trade-off solutions. Multi-objective evolutionary algorithms (MOEAs) are extremely useful and well-suited for solving MOPs due to population based nature. MOEAs evolve its population of solutions in a natural way and searched for compromise solutions in single simulation run unlike traditional methods. These algorithms make use of various intrinsic search operators in efficient manners. In this paper, we experimentally study the impact of different multiple crossovers in multi-objective evolutionary algorithm based on decomposition (MOEA/D) framework and evaluate its performance over test instances of 2009 IEEE congress on evolutionary computation (CEC?09) developed for MOEAs competition. Based on our carried out experiment, we observe that used variation operators are considered to main source to improve the algorithmic performance of MOEA/D for dealing with CEC?09 complicated test problems.

[1]  Tey Jing Yuen,et al.  Comparision Of Compuational Efficiency Of MOEA\D and NSGA-II For Passive Vehicle Suspension Optimization , 2010, ECMS.

[2]  Shigenobu Kobayashi,et al.  A real-coded genetic algorithm using the unimodal normal distribution crossover , 2003 .

[3]  Donald Davendra,et al.  Traveling Salesman Problem, Theory and Applications , 2010 .

[4]  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.

[5]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[6]  Shigenobu Kobayashi,et al.  A Real-Coded Genetic Algorithm for Function Optimization Using the Unimodal Normal Distribution Crossover , 1999 .

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

[8]  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.

[9]  Matthias Ehrgott,et al.  Multicriteria Optimization (2. ed.) , 2005 .

[10]  Wali Khan Mashwani.  A multimethod search approach based on adaptive generations level , 2011, 2011 Seventh International Conference on Natural Computation.

[11]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[12]  Carlos A. Coello Coello,et al.  Evolutionary multiobjective optimization , 2011, WIREs Data Mining Knowl. Discov..

[13]  A. Messac,et al.  The normalized normal constraint method for generating the Pareto frontier , 2003 .

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

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

[16]  Antonin Ponsich,et al.  A Survey on Multiobjective Evolutionary Algorithms for the Solution of the Portfolio Optimization Problem and Other Finance and Economics Applications , 2013, IEEE Transactions on Evolutionary Computation.

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

[18]  P. Siarry,et al.  Multiobjective Optimization: Principles and Case Studies , 2004 .

[19]  Enrique Alba,et al.  MOCell: A cellular genetic algorithm for multiobjective optimization , 2009, Int. J. Intell. Syst..

[20]  Ricardo Landa Becerra,et al.  Evolutionary Multiobjective Optimization in Materials Science and Engineering , 2009 .

[21]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[22]  William M. Spears,et al.  Adapting Crossover in Evolutionary Algorithms , 1995, Evolutionary Programming.

[23]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  Qingfu Zhang,et al.  MOEA/D-ACO: A Multiobjective Evolutionary Algorithm Using Decomposition and AntColony , 2013, IEEE Transactions on Cybernetics.

[25]  Wali Khan Mashwani,et al.  A decomposition-based hybrid multiobjective evolutionary algorithm with dynamic resource allocation , 2012, Appl. Soft Comput..

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

[27]  Xin Yao,et al.  A Memetic Algorithm for Periodic Capacitated Arc Routing Problem , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Dirk Thierens,et al.  An Adaptive Pursuit Strategy for Allocating Operator Probabilities , 2005, BNAIC.

[29]  Godfrey C. Onwubolu,et al.  New optimization techniques in engineering , 2004, Studies in Fuzziness and Soft Computing.

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

[31]  Wali Khan Mashwani,et al.  Multiobjective evolutionary algorithm based on multimethod with dynamic resources allocation , 2016, Appl. Soft Comput..

[32]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[33]  Qingfu Zhang,et al.  MOEA/D-DRA with two crossover operators , 2010, 2010 UK Workshop on Computational Intelligence (UKCI).

[34]  Kalyanmoy Deb,et al.  A population-based, steady-state procedure for real-parameter optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[35]  Qingfu Zhang,et al.  Expensive Multiobjective Optimization by MOEA/D With Gaussian Process Model , 2010, IEEE Transactions on Evolutionary Computation.

[36]  Shigeyoshi Tsutsui,et al.  A study on the effect of multi-parent recombination in real coded genetic algorithms , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[37]  Hrvoje Gold,et al.  Vehicle Routing Problem , 2008, Encyclopedia of GIS.

[38]  Byung Ro Moon,et al.  An empirical study on the synergy of multiple crossover operators , 2002, IEEE Trans. Evol. Comput..

[39]  Qingfu Zhang,et al.  Decomposition-Based Multiobjective Evolutionary Algorithm With an Ensemble of Neighborhood Sizes , 2012, IEEE Transactions on Evolutionary Computation.

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

[41]  Ajith Abraham,et al.  A New PSO Algorithm with Crossover Operator for Global Optimization Problems , 2008, Innovations in Hybrid Intelligent Systems.

[42]  Wali Khan Mashwani,et al.  Multiobjective memetic algorithm based on decomposition , 2014, Appl. Soft Comput..

[43]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

[44]  Wali Khan Mashwani.  MOEA/D with DE and PSO: MOEA/D-DE+PSO , 2011, SGAI Conf..

[45]  Peter Ross,et al.  Adapting Operator Settings in Genetic Algorithms , 1998, Evolutionary Computation.

[46]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[47]  M. Raghuwanshi,et al.  Simulated Binary Crossover with Lognormal Distribution , 2005 .

[48]  Qing Li,et al.  Multiobjective optimization for crash safety design of vehicles using stepwise regression model , 2008 .

[49]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[50]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[51]  M. Yamamura,et al.  Multi-parent recombination with simplex crossover in real coded genetic algorithms , 1999 .

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

[53]  Kun-Mao Chao,et al.  Spanning trees and optimization problems , 2004, Discrete mathematics and its applications.

[54]  Shigeyoshi Tsutsui,et al.  Multi-parent Recombination in Genetic Algorithms with Search Space Boundary Extension by Mirroring , 1998, PPSN.

[55]  Qingfu Zhang,et al.  The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances , 2009, 2009 IEEE Congress on Evolutionary Computation.

[56]  Wali Khan Mashwani,et al.  Comprehensive Survey of the Hybrid Evolutionary Algorithms , 2013, Int. J. Appl. Evol. Comput..

[57]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[58]  A. Sorsa,et al.  Real-coded genetic algorithms and nonlinear parameter identification , 2008, 2008 4th International IEEE Conference Intelligent Systems.

[59]  Andrzej Jaszkiewicz,et al.  On the computational efficiency of multiple objective metaheuristics. The knapsack problem case study , 2004, Eur. J. Oper. Res..

[60]  Optimization Zitzler,et al.  28 Evolutionary Multiobjective , 2012 .

[61]  D. Popescu,et al.  Multi‐Criteria Optimization , 2014 .

[62]  Wali Khan Mashwani.  Enhanced versions of differential evolution: state-of-the-art survey , 2014, Int. J. Comput. Sci. Math..

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

[64]  Qingfu Zhang,et al.  MOEA/D with NBI-style Tchebycheff approach for portfolio management , 2010, IEEE Congress on Evolutionary Computation.

[65]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[66]  Hisao Ishibuchi,et al.  Simultaneous use of different scalarizing functions in MOEA/D , 2010, GECCO '10.

[67]  Tonci Caric and Hrvoje Gold.  Vehicle Routing Problem , 2008 .

[68]  Carlos A. Coello Coello,et al.  Applications of multi-objective evolutionary algorithms in economics and finance: A survey , 2007, 2007 IEEE Congress on Evolutionary Computation.

[69]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[70]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[71]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[72]  Carlos A. Brizuela,et al.  A survey on multi-objective evolutionary algorithms for many-objective problems , 2014, Computational Optimization and Applications.

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

[74]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[75]  Michiel Steyaert,et al.  Massively multi-topology sizing of analog integrated circuits , 2009, 2009 Design, Automation & Test in Europe Conference & Exhibition.

[76]  Isao Ono,et al.  A Real Coded Genetic Algorithm for Function Optimization Using Unimodal Normal Distributed Crossover , 1997, ICGA.