Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization

In recent years, performance indicators were introduced as a selection mechanism in multi-objective evolutionary algorithms (MOEAs). A very attractive option is the R2 indicator due to its low computational cost and weak-Pareto compatibility. This indicator requires a set of utility functions, which map each objective to a single value. However, not all the utility functions available in the literature scale properly for more than four objectives and the diversity of the approximation sets is sensitive to the choice of the reference points during normalization. In this paper, we present an improved version of a MOEA based on the $R2$ indicator, which takes into account these two key aspects, using the achievement scalarizing function and statistical information about the population's proximity to the true Pareto optimal front. Moreover, we present a comparative study with respect to some other emerging approaches, such as NSGA-III (based on Pareto dominance), Δp-DDE (based on the Δp indicator) and some other MOEAs based on the R2 indicator, using the DTLZ and WFG test problems. Experimental results indicate that our approach outperforms the original algorithm as well as the other MOEAs in the majority of the test instances, making it a suitable alternative for solving many-objective optimization problems.

[1]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[2]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[3]  Heike Trautmann,et al.  On the properties of the R2 indicator , 2012, GECCO '12.

[4]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[5]  Thorsten Dickhaus,et al.  Simultaneous Statistical Inference , 2014, Springer Berlin Heidelberg.

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

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

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

[9]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

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

[11]  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).

[12]  Junichi Suzuki,et al.  R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[14]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[15]  Carlos A. Coello Coello,et al.  A new multi-objective evolutionary algorithm based on a performance assessment indicator , 2012, GECCO.

[16]  Carlos A. Coello Coello,et al.  MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[18]  Simon Wessing,et al.  Sequential parameter optimization for multi-objective problems , 2010, IEEE Congress on Evolutionary Computation.

[19]  M. Agha,et al.  Experiments with Mixtures , 1992 .

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

[21]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

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

[23]  Carlos A. Coello Coello,et al.  A ranking method based on the R2 indicator for many-objective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.