A multi-objective evolutionary hyper-heuristic based on multiple indicator-based density estimators

In recent years, Indicator-based Multi-Objective Evolutionary Algorithms (IB-MOEAs) have become a relatively popular alternative for solving multi-objective optimization problems. IB-MOEAs are normally based on the use of a single performance indicator. However, the effect of the combination of multiple performance indicators for selecting solutions is a topic that has rarely been explored. In this paper, we propose a hyper-heuristic which combines the strengths and compensates for the weaknesses of four density estimators based on R2, IGD+, ϵ+ and Δp. The selection of the indicator to be used at a particular moment during the search is done using online learning and a Markov chain. Additionally, we propose a novel framework that aims to reduce the computational cost involved in the calculation of the indicator contributions. Our experimental results indicate that our proposed approach can outperform state-of-the-art MOEAs based on decomposition (MOEA/D) reference points (NSGA-III) and the R2 indicator (R2-EMOA) for problems with both few and many objectives.

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

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

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

[4]  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.

[5]  Bilel Derbel,et al.  A Correlation Analysis of Set Quality Indicator Values in Multiobjective Optimization , 2016, GECCO.

[6]  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.

[7]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[8]  Michel Gendreau,et al.  Hyper-heuristics: a survey of the state of the art , 2013, J. Oper. Res. Soc..

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

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

[11]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[12]  Kent McClymont,et al.  Markov chain hyper-heuristic (MCHH): an online selective hyper-heuristic for multi-objective continuous problems , 2011, GECCO '11.

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

[14]  Isao Hayashi,et al.  Leveraging indicator-based ensemble selection in evolutionary multiobjective optimization algorithms , 2012, GECCO '12.

[15]  David W. Corne,et al.  Properties of an adaptive archiving algorithm for storing nondominated vectors , 2003, IEEE Trans. Evol. Comput..

[16]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[17]  Gary B. Lamont,et al.  Evolutionary algorithms for solving multi-objective problems, Second Edition , 2007, Genetic and evolutionary computation series.

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

[19]  Hisao Ishibuchi,et al.  Modified Distance Calculation in Generational Distance and Inverted Generational Distance , 2015, EMO.

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

[21]  Heike Trautmann,et al.  2 Indicator-Based Multiobjective Search , 2015, Evolutionary Computation.

[22]  Jie Zhang,et al.  Consistencies and Contradictions of Performance Metrics in Multiobjective Optimization , 2014, IEEE Transactions on Cybernetics.

[23]  Junichi Suzuki,et al.  Boosting Indicator-Based Selection Operators for Evolutionary Multiobjective Optimization Algorithms , 2011, 2011 IEEE 23rd International Conference on Tools with Artificial Intelligence.

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

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

[26]  Yaochu Jin,et al.  A Critical Survey of Performance Indices for Multi-Objective Optimisation , 2003 .

[27]  Carlos A. Coello Coello,et al.  A hyper-heuristic of scalarizing functions , 2017, GECCO.

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

[29]  Xin Yao,et al.  Stochastic Ranking Algorithm for Many-Objective Optimization Based on Multiple Indicators , 2016, IEEE Transactions on Evolutionary Computation.

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

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

[32]  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).