Integrating user preferences and decomposition methods for many-objective optimization

Evolutionary algorithms that rely on dominance ranking often suffer from a low selection pressure problem when dealing with many-objective problems. Decomposition and user-preference based methods can help to alleviate this problem to a great extent. In this paper, a user-preference based evolutionary multi-objective algorithm is proposed that uses decomposition methods for solving many-objective problems. Decomposition techniques that are widely used in multi-objective evolutionary optimization require a set of evenly distributed weight vectors to generate a diverse set of solutions on the Pareto-optimal front. The newly proposed algorithm, R-MEAD2, improves the scalability of its previous version, R-MEAD, which uses a simplexlattice design method for generating weight vectors. This makes the population size is dependent on the dimension size of the objective space. R-MEAD2 uses a uniform random number generator to remove the coupling between dimension and the population size. This paper shows that a uniform random number generator is simple and able to generate evenly distributed points in a high dimensional space. Our comparative study shows that R-MEAD2 outperforms the dominance-based method R-NSGA-II on many-objective problems.

[1]  Kalyanmoy Deb,et al.  Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions , 2003 .

[2]  Lothar Thiele,et al.  A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization , 2009, Evolutionary Computation.

[3]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[4]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[5]  Kalyanmoy Deb,et al.  Integrating User Preferences into Evolutionary Multi-Objective Optimization , 2005 .

[6]  J. Branke,et al.  Guidance in evolutionary multi-objective optimization , 2001 .

[7]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization by NSGA-II and MOEA/D with large populations , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[8]  Maliha S. Nash,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 2001, Technometrics.

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

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

[11]  Xiaodong Li,et al.  Reference point based multi-objective optimization through decomposition , 2012, 2012 IEEE Congress on Evolutionary Computation.

[12]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

[13]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

[14]  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.

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

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

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

[18]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[19]  Xiaodong Li,et al.  Using a distance metric to guide PSO algorithms for many-objective optimization , 2009, GECCO.

[20]  Kalyanmoy Deb,et al.  Light beam search based multi-objective optimization using evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

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

[23]  Arnold J. Stromberg,et al.  Number-theoretic Methods in Statistics , 1996 .

[24]  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..

[25]  Xiaodong Li,et al.  Integrating user preferences with particle swarms for multi-objective optimization , 2008, GECCO '08.

[26]  Hong Li,et al.  MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives , 2013, Comput. Oper. Res..

[27]  Dennis K. J. Lin,et al.  Ch. 4. Uniform experimental designs and their applications in industry , 2003 .

[28]  Peter J. Fleming,et al.  Evolutionary many-objective optimisation: an exploratory analysis , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

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