A survey on multi-objective evolutionary algorithms for many-objective problems

Multi-objective evolutionary algorithms (MOEAs) are well-suited for solving several complex multi-objective problems with two or three objectives. However, as the number of conflicting objectives increases, the performance of most MOEAs is severely deteriorated. How to improve MOEAs’ performance when solving many-objective problems, i.e. problems with four or more conflicting objectives, is an important issue since a large number of this type of problems exists in science and engineering; thus, several researchers have proposed different alternatives. This paper presents a review of the use of MOEAs in many-objective problems describing the evolution of the field, the methods that were developed, as well as the main findings and open questions that need to be answered in order to continue shaping the field.

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

[2]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

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

[4]  Peter J. Bentley,et al.  Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms , 1998 .

[5]  José Carlos Príncipe,et al.  Nonlinear Component Analysis Based on Correntropy , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

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

[7]  Kiyoshi Tanaka,et al.  Adaptive Objective Space Partitioning Using Conflict Information for Many-Objective Optimization , 2011, EMO.

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

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

[10]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

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

[12]  Eckart Zitzler,et al.  Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization , 2006, PPSN.

[13]  Jinhua Zheng,et al.  A grid-based fitness strategy for evolutionary many-objective optimization , 2010, GECCO '10.

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

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

[16]  Kalyanmoy Deb,et al.  Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions , 2003, EMO.

[17]  Mario Köppen,et al.  Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization , 2005, EMO.

[18]  Kalyanmoy Deb,et al.  Non-linear Dimensionality Reduction Procedures for Certain Large-Dimensional Multi-objective Optimization Problems: Employing Correntropy and a Novel Maximum Variance Unfolding , 2007, EMO.

[19]  Shuangzhe Liu,et al.  Global Sensitivity Analysis: The Primer by Andrea Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana, Stefano Tarantola , 2008 .

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

[21]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[22]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[23]  Daisuke Sasaki,et al.  Visualization and Data Mining of Pareto Solutions Using Self-Organizing Map , 2003, EMO.

[24]  Maarten Keijzer,et al.  Scientific discovery using genetic programming , 2001 .

[25]  Peter J. Fleming,et al.  Many-Objective Optimization: An Engineering Design Perspective , 2005, EMO.

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

[27]  Tadahiko Murata,et al.  Many-Objective Optimization for Knapsack Problems Using Correlation-Based Weighted Sum Approach , 2009, EMO.

[28]  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.

[29]  Patrick M. Reed,et al.  Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization , 2012, Evolutionary Computation.

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

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

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

[33]  Hisao Ishibuchi,et al.  Effects of the Existence of Highly Correlated Objectives on the Behavior of MOEA/D , 2011, EMO.

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

[35]  Carlos A. Coello Coello,et al.  Online Objective Reduction to Deal with Many-Objective Problems , 2009, EMO.

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

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

[38]  Hisao Ishibuchi,et al.  Scalability of multiobjective genetic local search to many-objective problems: Knapsack problem case studies , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[39]  C. A. Murthy,et al.  Unsupervised Feature Selection Using Feature Similarity , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

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

[41]  Olivier Teytaud,et al.  On the Hardness of Offline Multi-objective Optimization , 2007, Evolutionary Computation.

[42]  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.

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

[44]  Rolf Drechsler,et al.  Multi-objected Optimization in Evolutionary Algorithms Using Satisfiability Classes , 1999, Fuzzy Days.

[45]  Qingfu Zhang,et al.  Framework for Many-Objective Test Problems with Both Simple and Complicated Pareto-Set Shapes , 2011, EMO.

[46]  Nicola Beume,et al.  Multi-objective optimisation using S-metric selection: application to three-dimensional solution spaces , 2005, 2005 IEEE Congress on Evolutionary Computation.

[47]  Thomas Bäck,et al.  Evolutionary algorithms for automated drug design towards target molecule properties , 2008, GECCO '08.

[48]  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.

[49]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[50]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

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

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

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

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

[55]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

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

[57]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored , 2009, Frontiers of Computer Science in China.

[58]  Jonathan E. Fieldsend,et al.  Visualising many-objective populations , 2012, GECCO '12.

[59]  Peter J. Fleming,et al.  Preference-Driven Co-evolutionary Algorithms Show Promise for Many-Objective Optimisation , 2011, EMO.

[60]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[61]  Nicola Beume,et al.  An EMO Algorithm Using the Hypervolume Measure as Selection Criterion , 2005, EMO.

[62]  Kaisa Miettinen Graphical Illustration of Pareto Optimal Solutions , 2003 .

[63]  Kiyoshi Tanaka,et al.  Robust Optimization by epsilon-Ranking on High Dimensional Objective Spaces , 2008, SEAL.

[64]  Rolf Drechsler,et al.  Robust Multi-Objective Optimization in High Dimensional Spaces , 2007, EMO.

[65]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[66]  Francesco di Pierro,et al.  Many-objective evolutionary algorithms and applications to water resources engineering , 2006 .

[67]  Sanaz Mostaghim,et al.  Heatmap Visualization of Population Based Multi Objective Algorithms , 2007, EMO.

[68]  Patrick M. Reed,et al.  Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design , 2005 .

[69]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[70]  Kiyoshi Tanaka,et al.  Insights on properties of multiobjective MNK-landscapes , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

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

[72]  Alfred Inselberg,et al.  Parallel coordinates for visualizing multi-dimensional geometry , 1987 .

[73]  E. D. Weinberger,et al.  The NK model of rugged fitness landscapes and its application to maturation of the immune response. , 1989, Journal of theoretical biology.

[74]  Thomas Bäck,et al.  Combining Aggregation with Pareto Optimization: A Case Study in Evolutionary Molecular Design , 2009, EMO.

[75]  Kiyoshi Tanaka,et al.  Many-Objective Optimization by Space Partitioning and Adaptive epsilon-Ranking on MNK-Landscapes , 2009, EMO.

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

[77]  Kalyanmoy Deb,et al.  Faster Hypervolume-Based Search Using Monte Carlo Sampling , 2008, MCDM.

[78]  Frank Neumann,et al.  Do additional objectives make a problem harder? , 2007, GECCO '07.

[79]  Patrick M. Reed,et al.  Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework , 2013, Evolutionary Computation.

[80]  Peter J. Fleming,et al.  A Diversity Management Operator for Evolutionary Many-Objective Optimisation , 2009, EMO.

[81]  Gary L. Haith,et al.  Comparing a coevolutionary genetic algorithm for multiobjective optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[82]  Eckart Zitzler,et al.  A Preliminary Study on Handling Uncertainty in Indicator-Based Multiobjective Optimization , 2006, EvoWorkshops.

[83]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

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

[85]  Kiyoshi Tanaka,et al.  Effects of elitism and population climbing on multiobjective MNK-landscapes , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[86]  Eckart Zitzler,et al.  Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods , 2007, 2007 IEEE Congress on Evolutionary Computation.

[87]  Kalyanmoy Deb,et al.  On Handling a Large Number of Objectives A Posteriori and During Optimization , 2008, Multiobjective Problem Solving from Nature.

[88]  H. T. Kung,et al.  On the Average Number of Maxima in a Set of Vectors and Applications , 1978, JACM.

[89]  Kiyoshi Tanaka,et al.  Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems , 2012, Annals of Mathematics and Artificial Intelligence.

[90]  Peter J. Fleming,et al.  Conflict, Harmony, and Independence: Relationships in Evolutionary Multi-criterion Optimisation , 2003, EMO.

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

[92]  Rolf Drechsler,et al.  Multi-objective Optimisation Based on Relation Favour , 2001, EMO.

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

[94]  Kiyoshi Tanaka,et al.  Pareto partial dominance MOEA and hybrid archiving strategy included CDAS in many-objective optimization , 2010, IEEE Congress on Evolutionary Computation.

[95]  Masahiro Tanaka,et al.  GA-based decision support system for multicriteria optimization , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[96]  Andrzej Jaszkiewicz,et al.  On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment , 2002, IEEE Trans. Evol. Comput..

[97]  Evan J. Hughes,et al.  MSOPS-II: A general-purpose Many-Objective optimiser , 2007, 2007 IEEE Congress on Evolutionary Computation.

[98]  Hisao Ishibuchi,et al.  Optimization of Scalarizing Functions Through Evolutionary Multiobjective Optimization , 2007, EMO.

[99]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[100]  Kilian Q. Weinberger,et al.  Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

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

[102]  Carlos A. Coello Coello,et al.  Study of preference relations in many-objective optimization , 2009, GECCO.

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

[104]  Carlos A. Coello Coello,et al.  Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and epsilon-Dominance , 2005, EMO.

[105]  Jürgen Branke,et al.  Multi-objective particle swarm optimization on computer grids , 2007, GECCO '07.

[106]  Evan J. Hughes Multi-Objective Equivalent Random Search , 2006, PPSN.

[107]  Lishan Kang,et al.  A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[108]  Mario Köppen,et al.  Visualization of Pareto-Sets in Evolutionary Multi-Objective Optimization , 2007, 7th International Conference on Hybrid Intelligent Systems (HIS 2007).

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

[110]  Kiyoshi Tanaka,et al.  Improved Random One-Bit Climbers with Adaptive ε-Ranking and Tabu Moves for Many-Objective Optimization , 2011, EMO.

[111]  Gary G. Yen,et al.  A new fitness evaluation method based on fuzzy logic in multiobjective evolutionary algorithms , 2012, 2012 IEEE Congress on Evolutionary Computation.

[112]  David W. Corne,et al.  Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization , 2007, EMO.