Many-Objective Evolutionary Algorithms

Multiobjective evolutionary algorithms (MOEAs) have been widely used in real-world applications. However, most MOEAs based on Pareto-dominance handle many-objective problems (MaOPs) poorly due to a high proportion of incomparable and thus mutually nondominated solutions. Recently, a number of many-objective evolutionary algorithms (MaOEAs) have been proposed to deal with this scalability issue. In this article, a survey of MaOEAs is reported. According to the key ideas used, MaOEAs are categorized into seven classes: relaxed dominance based, diversity-based, aggregation-based, indicator-based, reference set based, preference-based, and dimensionality reduction approaches. Several future research directions in this field are also discussed.

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

[2]  Qguhm -DVNLHZLF.  On the performance of multiple objective genetic local search on the 0 / 1 knapsack problem . A comparative experiment , 2000 .

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

[4]  Yoshua Bengio,et al.  Exploring Strategies for Training Deep Neural Networks , 2009, J. Mach. Learn. Res..

[5]  Ki-Baek Lee,et al.  Multi-objective particle swarm optimization with preference-based sorting , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[6]  Hisao Ishibuchi,et al.  Effects of duplicated objectives in many-objective optimization problems on the search behavior of hypervolume-based evolutionary algorithms , 2013, 2013 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM).

[7]  Markus Wagner,et al.  Approximation-Guided Evolutionary Multi-Objective Optimization , 2011, IJCAI.

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

[9]  T. Simpson,et al.  Conceptual design of a family of products through the use of the robust concept exploration method , 1996 .

[10]  Tim Menzies,et al.  On the value of user preferences in search-based software engineering: A case study in software product lines , 2013, 2013 35th International Conference on Software Engineering (ICSE).

[11]  Colin R. Reeves,et al.  A genetic algorithm for flowshop sequencing , 1995, Comput. Oper. Res..

[12]  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.

[13]  Tapabrata Ray,et al.  A Decomposition Based Evolutionary Algorithm for Many Objective Optimization with Systematic Sampling and Adaptive Epsilon Control , 2013, EMO.

[14]  Lino A. Costa,et al.  Many-objective optimization using differential evolution with variable-wise mutation restriction , 2013, GECCO '13.

[15]  Dun-Wei Gong,et al.  Evolutionary algorithms with preference polyhedron for interval multi-objective optimization problems , 2013, Inf. Sci..

[16]  Jim Tørresen,et al.  Many-Objective Optimization Using Taxi-Cab Surface Evolutionary Algorithm , 2013, EMO.

[17]  Carlos A. Brizuela,et al.  A survey on multi-objective evolutionary algorithms for many-objective problems , 2014, Comput. Optim. Appl..

[18]  E. Løken.  Use of multicriteria decision analysis methods for energy planning problems , 2007 .

[19]  Kiyoshi Tanaka,et al.  A Hybrid Scalarization and Adaptive epsilon-Ranking Strategy for Many-Objective Optimization , 2010, PPSN.

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

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

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

[23]  Ujjwal Maulik,et al.  Survey of Multiobjective Evolutionary Algorithms for Data Mining: Part II , 2014, IEEE Transactions on Evolutionary Computation.

[24]  Hisao Ishibuchi,et al.  Behavior of Multiobjective Evolutionary Algorithms on Many-Objective Knapsack Problems , 2015, IEEE Transactions on Evolutionary Computation.

[25]  Xin Yao,et al.  A New Multi-objective Evolutionary Optimisation Algorithm: The Two-Archive Algorithm , 2006, 2006 International Conference on Computational Intelligence and Security.

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

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

[28]  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).

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

[30]  Kiyoshi Tanaka,et al.  Space partitioning with adaptive ε-ranking and substitute distance assignments: a comparative study on many-objective mnk-landscapes , 2009, GECCO '09.

[31]  K. Deb,et al.  I-EMO: An Interactive Evolutionary Multi-objective Optimization Tool , 2005, PReMI.

[32]  Qingfu Zhang,et al.  Combining Model-based and Genetics-based Offspring Generation for Multi-objective Optimization Using a Convergence Criterion , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[33]  Peter J. Fleming,et al.  Preference-inspired co-evolutionary algorithm using weights for many-objective optimization , 2013, GECCO '13 Companion.

[34]  Carlos A. Coello Coello,et al.  Two novel approaches for many-objective optimization , 2010, IEEE Congress on Evolutionary Computation.

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

[36]  Geoffrey T. Parks,et al.  Coherent design methodology using modelling, simulation and optimisation , 2011 .

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

[38]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[39]  Akira Oyama,et al.  Space trajectory design: Analysis of a real-world many-objective optimization problem , 2013, 2013 IEEE Congress on Evolutionary Computation.

[40]  R. J. Balling,et al.  The maximin fitness function for multi-objective evolutionary computation: application to city planning , 2001 .

[41]  Xin Yao,et al.  Software effort estimation as a multiobjective learning problem , 2013, TSEM.

[42]  Patrick T. Hester,et al.  An Analysis of Multi-Criteria Decision Making Methods , 2013 .

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

[44]  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..

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

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

[47]  Carlos A. Coello Coello,et al.  Alternative Fitness Assignment Methods for Many-Objective Optimization Problems , 2009, Artificial Evolution.

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

[49]  Joseph R. Kasprzyk,et al.  Optimal Design of Water Distribution Systems Using Many-Objective Visual Analytics , 2013 .

[50]  Carlos A. Coello Coello,et al.  Preference incorporation to solve many-objective airfoil design problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

[52]  Peter J. Fleming,et al.  Aero engine health management system architecture design using multi-criteria optimization , 2013, GECCO '13 Companion.

[53]  Carl Tim Kelley,et al.  Developing portfolios of water supply transfers , 2005 .

[54]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[55]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

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

[57]  Kiyoshi Tanaka,et al.  Analysis on Population Size and Neighborhood Recombination on Many-Objective Optimization , 2012, PPSN.

[58]  Patrick M. Reed,et al.  Save now, pay later? Multi-period many-objective groundwater monitoring design given systematic model errors and uncertainty , 2011 .

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

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

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

[62]  Hisao Ishibuchi,et al.  A Study on the Specification of a Scalarizing Function in MOEA/D for Many-Objective Knapsack Problems , 2013, LION.

[63]  Tao Zhang,et al.  An enhanced MOEA/D using uniform directions and a pre-organization procedure , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[65]  Marjan Mernik,et al.  Exploration and exploitation in evolutionary algorithms: A survey , 2013, CSUR.

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

[67]  Joseph R. Kasprzyk,et al.  Many-objective de Novo water supply portfolio planning under deep uncertainty , 2012, Environ. Model. Softw..

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

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

[70]  Gonzalo Guillén-Gosálbez,et al.  Identifying key life cycle assessment metrics in the multiobjective design of bioethanol supply chains using a rigorous mixed-integer linear programming approach , 2012 .

[71]  Peter A. N. Bosman,et al.  On Gradients and Hybrid Evolutionary Algorithms for Real-Valued Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[72]  Kiyoharu Tagawa,et al.  Many-hard-objective optimization using differential evolution based on two-stage constraint-handling , 2013, GECCO '13.

[73]  Kalyanmoy Deb,et al.  Reliability-Based Optimization Using Evolutionary Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

[74]  Mehrdad Tamiz.  Multi-Objective Programming and Goal Programming , 1996 .

[75]  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.

[76]  Marouane Kessentini,et al.  Preference-Based Many-Objective Evolutionary Testing Generates Harder Test Cases for Autonomous Agents , 2013, SSBSE.

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

[78]  Lily Rachmawati,et al.  Preference Incorporation in Multi-objective Evolutionary Algorithms: A Survey , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[79]  P. Yu.  Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[80]  Elizabeth F. Wanner,et al.  On a Stochastic Differential Equation Approach for Multiobjective Optimization up to Pareto-Criticality , 2011, EMO.

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

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

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

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

[85]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

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

[87]  Tapabrata Ray,et al.  A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems , 2011, IEEE Transactions on Evolutionary Computation.

[88]  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.

[89]  Naoki Hamada,et al.  Adaptive Weighted Aggregation 2: More scalable AWA for multiobjective function optimization , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

[91]  Xiaoyan Sun,et al.  Set-based genetic algorithms for solving many-objective optimization problems , 2013, 2013 13th UK Workshop on Computational Intelligence (UKCI).

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

[93]  Zhenhua Li,et al.  Preference-Based Evolutionary Multi-objective Optimization , 2012, 2012 Eighth International Conference on Computational Intelligence and Security.

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

[95]  Xiaofang Guo,et al.  Using Objective Clustering for Solving Many-Objective Optimization Problems , 2013 .

[96]  Marco Laumanns,et al.  Stochastic convergence of random search methods to fixed size Pareto front approximations , 2011, Eur. J. Oper. Res..

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

[98]  Frederico G. Guimarães,et al.  Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms , 2011, EMO.

[99]  Evan J. Hughes,et al.  Radar Waveform Optimisation as a Many-Objective Application Benchmark , 2007, EMO.

[100]  Evan J. Hughes,et al.  Many-objective directed evolutionary line search , 2011, GECCO '11.

[101]  Peter J. Fleming,et al.  Local preference-inspired co-evolutionary algorithms , 2012, GECCO '12.

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

[103]  Kiyoshi Tanaka,et al.  Space Partitioning Evolutionary Many-Objective Optimization: Performance Analysis on MNK-Landscapes , 2010 .

[104]  Kalyanmoy Deb,et al.  A review of hybrid evolutionary multiple criteria decision making methods , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[105]  Fumito Ito,et al.  Current Status and Future Directions , 2013 .

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

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

[108]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[109]  Xin Yao,et al.  Corner Sort for Pareto-Based Many-Objective Optimization , 2014, IEEE Transactions on Cybernetics.

[110]  Hui Li,et al.  An Improved Version of Volume Dominance for Multi-Objective Optimisation , 2009, EMO.

[111]  Peter J. Rousseeuw,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1991 .

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

[113]  Xin Yao,et al.  Multi-Objective Approaches to Optimal Testing Resource Allocation in Modular Software Systems , 2010, IEEE Transactions on Reliability.

[114]  Bernabé Dorronsoro,et al.  A Survey of Decomposition Methods for Multi-objective Optimization , 2014, Recent Advances on Hybrid Approaches for Designing Intelligent Systems.

[115]  共立出版株式会社.  コンピュータ・サイエンス : ACM computing surveys , 1978 .

[116]  Frederico G. Guimarães,et al.  A comparison of dominance criteria in many-objective optimization problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

[118]  Xin Yao,et al.  Software Module Clustering as a Multi-Objective Search Problem , 2011, IEEE Transactions on Software Engineering.

[119]  Kiyoshi Tanaka,et al.  Adaptive ε-Sampling and ε-Hood for Evolutionary Many-Objective Optimization , 2013, EMO.

[120]  Qiu Fei-yue,et al.  Bipolar preferences dominance based evolutionary algorithm for many-objective optimization , 2012, 2012 IEEE Congress on Evolutionary Computation.

[121]  Kaname Narukawa,et al.  Examining the Performance of Evolutionary Many-Objective Optimization Algorithms on a Real-World Application , 2012, 2012 Sixth International Conference on Genetic and Evolutionary Computing.

[122]  Thomas Stützle,et al.  An experimental study of preference model integration into multi-objective optimization heuristics , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[123]  Adriana Menchaca-Mendez,et al.  Solving multi-objective optimization problems using differential evolution and a maximin selection criterion , 2012, 2012 IEEE Congress on Evolutionary Computation.

[124]  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.

[125]  Shengxiang Yang,et al.  Diversity Comparison of Pareto Front Approximations in Many-Objective Optimization , 2014, IEEE Transactions on Cybernetics.

[126]  K. C. Seow,et al.  MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM , 2001 .

[127]  Xiaodong Li,et al.  Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm , 2010, IEEE Congress on Evolutionary Computation.

[128]  Ki-Baek Lee,et al.  Improved version of a multiobjective quantum-inspired evolutionary algorithm with preference-based selection , 2012, 2012 IEEE Congress on Evolutionary Computation.

[129]  Peter Dueholm Justesen,et al.  Many-objective Distinct Candidates Optimization using Differential Evolution on centrifugal pump design problems , 2010, IEEE Congress on Evolutionary Computation.

[130]  Kalyanmoy Deb,et al.  An Improved Adaptive Approach for Elitist Nondominated Sorting Genetic Algorithm for Many-Objective Optimization , 2013, EMO.

[131]  Sébastien Vérel,et al.  A study on population size and selection lapse in many-objective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[132]  David A. Van Veldhuizen,et al.  Evolutionary Computation and Convergence to a Pareto Front , 1998 .

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

[134]  Kiyoshi Tanaka,et al.  Working principles, behavior, and performance of MOEAs on MNK-landscapes , 2007, Eur. J. Oper. Res..

[135]  Naoki Hamada,et al.  On scalability of Adaptive Weighted Aggregation for multiobjective function optimization , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[136]  Kiyoshi Tanaka,et al.  Improved S-CDAs using crossover controlling the number of crossed genes for many-objective optimization , 2011, GECCO '11.

[137]  Hussein A. Abbass,et al.  A multi-objective evolutionary method for Dynamic Airspace Re-sectorization using sectors clipping and similarities , 2012, 2012 IEEE Congress on Evolutionary Computation.

[138]  Patrick M. Reed,et al.  Diagnostic assessment of the borg MOEA for many-objective product family design problems , 2012, 2012 IEEE Congress on Evolutionary Computation.

[139]  Eric O. Postma,et al.  Dimensionality Reduction: A Comparative Review , 2008 .

[140]  Yaochu Jin,et al.  Connectedness, regularity and the success of local search in evolutionary multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

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

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

[143]  Yuping Wang,et al.  A New Objective Reduction Algorithm for Many-Objective Problems: Employing Mutual Information and Clustering Algorithm , 2012, 2012 Eighth International Conference on Computational Intelligence and Security.

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

[145]  Kalyanmoy Deb,et al.  Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions , 2005, Evolutionary Computation.

[146]  Carlos A. Coello Coello,et al.  Effective ranking + speciation = Many-objective optimization , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[147]  Michael Patriksson,et al.  Approximating the Pareto optimal set using a reduced set of objective functions , 2010, Eur. J. Oper. Res..

[148]  Kalyanmoy Deb,et al.  Using objective reduction and interactive procedure to handle many-objective optimization problems , 2013, Appl. Soft Comput..

[149]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[150]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

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

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

[153]  Xin Yao,et al.  Two_Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[155]  Jinhua Zheng,et al.  Enhancing Diversity for Average Ranking Method in Evolutionary Many-Objective Optimization , 2010, PPSN.

[156]  Nicola Beume,et al.  S-Metric Calculation by Considering Dominated Hypervolume as Klee's Measure Problem , 2009, Evolutionary Computation.

[157]  Hisao Ishibuchi,et al.  Many-objective and many-variable test problems for visual examination of multiobjective search , 2013, 2013 IEEE Congress on Evolutionary Computation.

[158]  José M. Molina López,et al.  Effective Evolutionary Algorithms for Many-Specifications Attainment: Application to Air Traffic Control Tracking Filters , 2009, IEEE Transactions on Evolutionary Computation.

[159]  Markus Wagner,et al.  A fast approximation-guided evolutionary multi-objective algorithm , 2013, GECCO '13.

[160]  Eckart Zitzler,et al.  Automated Aggregation and Omission of Objectives for Tackling Many-Objective Problems , 2010 .

[161]  Dirk Thierens,et al.  The balance between proximity and diversity in multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[162]  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).

[163]  Kiyoshi Tanaka,et al.  Adaptive Control of the Number of Crossed Genes in Many-Objective Evolutionary Optimization , 2012, LION.

[164]  Evan J. Hughes.  Fitness Assignment Methods for Many-Objective Problems , 2008, Multiobjective Problem Solving from Nature.

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

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

[167]  Patrick M. Reed,et al.  Visual Analytics Clarify The Scalability And Effectiveness Of Massively Parallel Many-Objective Optimization: A Groundwater Monitoring Design Example , 2013 .

[168]  David W. Corne,et al.  Instance Generators and Test Suites for the Multiobjective Quadratic Assignment Problem , 2003, EMO.

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

[170]  Kirk D. McGraw,et al.  Coevolving collection plans for UAS constellations , 2011, GECCO '11.

[171]  Carlos A. Coello Coello,et al.  Ranking Methods for Many-Objective Optimization , 2009, MICAI.

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

[173]  Joseph J. Talavage,et al.  A Tradeoff Cut Approach to Multiple Objective Optimization , 1980, Oper. Res..

[174]  Kaname Narukawa.  Effect of Dominance Balance in Many-Objective Optimization , 2013, EMO.

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

[176]  Peter J. Fleming,et al.  Diversity Management in Evolutionary Many-Objective Optimization , 2011, IEEE Transactions on Evolutionary Computation.

[177]  Iain Bate,et al.  Evolutionary and Principled Search Strategies for Sensornet Protocol Optimization , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[179]  T. Ray,et al.  Optimum design of Yagi-Uda antennas using computational intelligence , 2004, IEEE Transactions on Antennas and Propagation.

[180]  C. Coello,et al.  Measuring the Averaged Hausdorff Distance to the Pareto Front of a Multi-Objective Optimization Problem , 2010 .

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

[182]  Tomohiro Yoshikawa,et al.  A study on two-step search using global-best in PSO for Multi-Objective Optimization Problems , 2012, The 6th International Conference on Soft Computing and Intelligent Systems, and The 13th International Symposium on Advanced Intelligence Systems.

[183]  Filiz Günes,et al.  Pattern Search optimization with applications on synthesis of linear antenna arrays , 2010, Expert Syst. Appl..

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

[185]  A. Shamsai,et al.  Multi-objective Optimization , 2017, Encyclopedia of Machine Learning and Data Mining.

[186]  Kiyoshi Tanaka,et al.  Self-Controlling Dominance Area of Solutions in Evolutionary Many-Objective Optimization , 2010, SEAL.

[187]  Eckart Zitzler,et al.  Dimensionality Reduction in Multiobjective Optimization with (Partial) Dominance Structure Preservation: Generalized Minimum Objective Subset Problems , 2006 .

[188]  Kiyoshi Tanaka,et al.  Evolutionary multi-objective optimization to attain practically desirable solutions , 2013, GECCO '13.

[189]  W. Cotton,et al.  RAMS 2001: Current status and future directions , 2003 .

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

[191]  G. W. Evans,et al.  An Overview of Techniques for Solving Multiobjective Mathematical Programs , 1984 .

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

[193]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[194]  Carlos A. Coello Coello,et al.  Goal-constraint: Incorporating preferences through an evolutionary ε-constraint based method , 2013, 2013 IEEE Congress on Evolutionary Computation.

[195]  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.

[196]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

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

[198]  Tapabrata Ray,et al.  A steady state decomposition based quantum genetic algorithm for many objective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

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

[201]  Anne Auger,et al.  Articulating user preferences in many-objective problems by sampling the weighted hypervolume , 2009, GECCO.

[202]  Kalyanmoy Deb,et al.  Handling many-objective problems using an improved NSGA-II procedure , 2012, 2012 IEEE Congress on Evolutionary Computation.

[203]  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.

[204]  Ujjwal Maulik,et al.  A Survey of Multiobjective Evolutionary Algorithms for Data Mining: Part I , 2014, IEEE Transactions on Evolutionary Computation.

[205]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

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

[207]  Sébastien Vérel,et al.  Set-based multiobjective fitness landscapes: a preliminary study , 2011, GECCO '11.

[208]  George Karypis,et al.  Pareto Optimal Pairwise Sequence Alignment , 2013, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[209]  Peter J. Fleming,et al.  On finding well-spread pareto optimal solutions by preference-inspired co-evolutionary algorithm , 2013, GECCO '13.

[210]  Xin Yao,et al.  An improved Two Archive Algorithm for Many-Objective optimization , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[211]  Adriana Menchaca-Mendez,et al.  Selection Operators Based on Maximin Fitness Function for Multi-Objective Evolutionary Algorithms , 2013, EMO.

[212]  Akira Oyama,et al.  An Alternative Preference Relation to Deal with Many-Objective Optimization Problems , 2013, EMO.

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

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

[215]  Peter J. Fleming,et al.  A Real-World Application of a Many-Objective Optimisation Complexity Reduction Process , 2013, EMO.

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

[217]  Hisao Ishibuchi,et al.  Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space , 2010, PPSN.

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