Behavior of Multiobjective Evolutionary Algorithms on Many-Objective Knapsack Problems

We examine the behavior of three classes of evolutionary multiobjective optimization (EMO) algorithms on many-objective knapsack problems. They are Pareto dominance-based, scalarizing function-based, and hypervolume-based algorithms. NSGA-II, MOEA/D, SMS-EMOA, and HypE are examined using knapsack problems with 2-10 objectives. Our test problems are generated by randomly specifying coefficients (i.e., profits) in objectives. We also generate other test problems by combining two objectives to create a dependent or correlated objective. Experimental results on randomly generated many-objective knapsack problems are consistent with well-known performance deterioration of Pareto dominance-based algorithms. That is, NSGA-II is outperformed by the other algorithms. However, it is also shown that NSGA-II outperforms the other algorithms when objectives are highly correlated. MOEA/D shows totally different search behavior depending on the choice of a scalarizing function and its parameter value. Some MOEA/D variants work very well only on two-objective problems while others work well on many-objective problems with 4-10 objectives. We also obtain other interesting observations such as the performance improvement by similar parent recombination and the necessity of diversity improvement for many-objective knapsack problems.

[1]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

[2]  Eun-Soo Kim,et al.  Preference-Based Solution Selection Algorithm for Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[3]  Carlos A. Coello Coello,et al.  Some comments on GD and IGD and relations to the Hausdorff distance , 2010, GECCO '10.

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

[5]  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.

[6]  Jun Zhang,et al.  Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms , 2014, IEEE Transactions on Evolutionary Computation.

[7]  Carlos A. Coello Coello,et al.  On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem , 2011, IEEE Transactions on Evolutionary Computation.

[8]  Luís M. S. Russo,et al.  Quick Hypervolume , 2012, IEEE Transactions on Evolutionary Computation.

[9]  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.

[10]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[11]  Peter J. Fleming,et al.  Generalized Decomposition , 2013, EMO.

[12]  Murat Köksalan,et al.  A Territory Defining Multiobjective Evolutionary Algorithms and Preference Incorporation , 2010, IEEE Transactions on Evolutionary Computation.

[13]  Hisao Ishibuchi,et al.  An empirical study on similarity-based mating for evolutionary multiobjective combinatorial optimization , 2008, Eur. J. Oper. Res..

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

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

[16]  Boris Naujoks,et al.  Do Hypervolume Regressions Hinder EMOA Performance? Surprise and Relief , 2013, EMO.

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

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

[19]  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.

[20]  Qingfu Zhang,et al.  Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems , 2014, IEEE Transactions on Evolutionary Computation.

[21]  Shengxiang Yang,et al.  A Grid-Based Evolutionary Algorithm for Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[22]  Heike Trautmann,et al.  Integration of Preferences in Hypervolume-Based Multiobjective Evolutionary Algorithms by Means of Desirability Functions , 2010, IEEE Transactions on Evolutionary Computation.

[23]  Hisao Ishibuchi,et al.  Recombination of Similar Parents in SMS-EMOA on Many-Objective 0/1 Knapsack Problems , 2012, PPSN.

[24]  Hisao Ishibuchi,et al.  A many-objective test problem for visually examining diversity maintenance behavior in a decision space , 2011, GECCO '11.

[25]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.

[26]  Jouni Lampinen,et al.  Ranking-Dominance and Many-Objective Optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[27]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

[28]  Kiyoshi Tanaka,et al.  Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs , 2007, EMO.

[29]  Peter J. Fleming,et al.  Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

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

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

[32]  Jonathan E. Fieldsend,et al.  Visualizing Mutually Nondominating Solution Sets in Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[33]  Lucas Bradstreet,et al.  A Fast Way of Calculating Exact Hypervolumes , 2012, IEEE Transactions on Evolutionary Computation.

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

[35]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

[36]  Tapabrata Ray,et al.  A Study on the Performance of Substitute Distance Based Approaches for Evolutionary Many Objective Optimization , 2008, SEAL.

[37]  Xianpeng Wang,et al.  A Hybrid Multiobjective Evolutionary Algorithm for Multiobjective Optimization Problems , 2013, IEEE Transactions on Evolutionary Computation.

[38]  Kalyanmoy Deb,et al.  A Hybrid Framework for Evolutionary Multi-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[39]  Hisao Ishibuchi,et al.  Recombination of Similar Parents in EMO Algorithms , 2005, EMO.

[40]  Hisao Ishibuchi,et al.  Diversity Improvement by Non-Geometric Binary Crossover in Evolutionary Multiobjective Optimization , 2010, IEEE Transactions on Evolutionary Computation.

[41]  Kiyoshi Tanaka,et al.  Genetic Diversity and Effective Crossover in Evolutionary Many-objective Optimization , 2011, LION.

[42]  Hisao Ishibuchi,et al.  Behavior of EMO algorithms on many-objective optimization problems with correlated objectives , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

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

[45]  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.

[46]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[47]  David W. Corne,et al.  Techniques for highly multiobjective optimisation: some nondominated points are better than others , 2007, GECCO '07.

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

[49]  Hisao Ishibuchi,et al.  Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling , 2003, IEEE Trans. Evol. Comput..

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

[51]  Riccardo Poli,et al.  Topological Interpretation of Crossover , 2004, GECCO.

[52]  Mario Köppen,et al.  Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems , 2007, EMO.

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

[54]  Hisao Ishibuchi,et al.  Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems , 2008, GECCO '08.

[55]  Tong Heng Lee,et al.  Multiobjective Evolutionary Algorithms and Applications , 2005, Advanced Information and Knowledge Processing.

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

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

[58]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

[59]  Jiang Siwei,et al.  Multiobjective optimization by decomposition with Pareto-adaptive weight vectors , 2011, 2011 Seventh International Conference on Natural Computation.

[60]  Kay Chen Tan,et al.  A multiobjective evolutionary algorithm using dynamic weight design method , 2012 .