Scalarizing Functions in Decomposition-Based Multiobjective Evolutionary Algorithms

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm.

[1]  Qingfu Zhang,et al.  Adaptive Replacement Strategies for MOEA/D , 2016, IEEE Transactions on Cybernetics.

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

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

[4]  Heike Trautmann,et al.  Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results , 2016, Comput. Optim. Appl..

[5]  Shengxiang Yang,et al.  A Steady-State and Generational Evolutionary Algorithm for Dynamic Multiobjective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

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

[7]  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.

[8]  Hisao Ishibuchi,et al.  Adaptation of Scalarizing Functions in MOEA/D: An Adaptive Scalarizing Function-Based Multiobjective Evolutionary Algorithm , 2009, EMO.

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

[10]  Qingfu Zhang,et al.  Biased Multiobjective Optimization and Decomposition Algorithm , 2017, IEEE Transactions on Cybernetics.

[11]  Qingfu Zhang,et al.  Stable Matching-Based Selection in Evolutionary Multiobjective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

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

[13]  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.

[14]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[15]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

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

[17]  Qingfu Zhang,et al.  Constrained Subproblems in a Decomposition-Based Multiobjective Evolutionary Algorithm , 2016, IEEE Transactions on Evolutionary Computation.

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

[19]  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.

[20]  Hisao Ishibuchi,et al.  Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes , 2017, IEEE Transactions on Evolutionary Computation.

[21]  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..

[22]  Hisao Ishibuchi,et al.  Relation between Neighborhood Size and MOEA/D Performance on Many-Objective Problems , 2013, EMO.

[23]  Hai-Lin,et al.  The multiobjective evolutionary algorithm based on determined weight and sub-regional search , 2009, 2009 IEEE Congress on Evolutionary Computation.

[24]  Anna Klick.  Introduction to the Gamma Function , 2019 .

[25]  Hiroyuki Sato,et al.  Analysis of inverted PBI and comparison with other scalarizing functions in decomposition based MOEAs , 2015, J. Heuristics.

[26]  Peter J. Fleming,et al.  Generalized decomposition and cross entropy methods for many-objective optimization , 2014, Inf. Sci..

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

[28]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[29]  Mitsuo Gen,et al.  Specification of Genetic Search Directions in Cellular Multi-objective Genetic Algorithms , 2001, EMO.

[30]  Hiroyuki Sato,et al.  Chain-reaction solution update in MOEA/D and its effects on multi- and many-objective optimization , 2016, Soft Comput..

[31]  Qingfu Zhang,et al.  An External Archive Guided Multiobjective Evolutionary Algorithm Based on Decomposition for Combinatorial Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[32]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[33]  H. Abdi.  The Bonferonni and Šidák Corrections for Multiple Comparisons , 2006 .

[34]  Qingfu Zhang,et al.  Adaptive Operator Selection With Bandits for a Multiobjective Evolutionary Algorithm Based on Decomposition , 2014, IEEE Transactions on Evolutionary Computation.

[35]  Rubén Saborido,et al.  Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front , 2017, Evolutionary Computation.

[36]  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.

[37]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[38]  Qingfu Zhang,et al.  Are All the Subproblems Equally Important? Resource Allocation in Decomposition-Based Multiobjective Evolutionary Algorithms , 2016, IEEE Transactions on Evolutionary Computation.

[39]  Shengxiang Yang,et al.  An Improved Multiobjective Optimization Evolutionary Algorithm Based on Decomposition for Complex Pareto Fronts , 2016, IEEE Transactions on Cybernetics.

[40]  Hisao Ishibuchi,et al.  Use of Piecewise Linear and Nonlinear Scalarizing Functions in MOEA/D , 2016, PPSN.

[41]  Bo Zhang,et al.  Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers , 2016, IEEE Transactions on Evolutionary Computation.

[42]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

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

[44]  Sébastien Vérel,et al.  On the Impact of Multiobjective Scalarizing Functions , 2014, PPSN.

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

[46]  Shengxiang Yang,et al.  Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes , 2017, Soft Comput..

[47]  Shengxiang Yang,et al.  A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[48]  Xavier Gourdon,et al.  Introduction to the Gamma Function , 2002 .

[49]  Qingfu Zhang,et al.  Interrelationship-Based Selection for Decomposition Multiobjective Optimization , 2015, IEEE Transactions on Cybernetics.

[50]  E. Hughes.  Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[51]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

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

[53]  Qingfu Zhang,et al.  Decomposition-Based Algorithms Using Pareto Adaptive Scalarizing Methods , 2016, IEEE Transactions on Evolutionary Computation.