Abstract
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.
Supplemental Material
Available for Download
Supplemental movie, appendix, image and software files for, Many-Objective Evolutionary Algorithms
- S. F. Adra and P. J. Fleming. 2011. Diversity management in evolutionary many-objective optimization. IEEE Transactions on Evolutionary Computation 15, 2, 183--195. Google ScholarDigital Library
- H. E. Aguirre, A. Liefooghe, S. Verel, and K. Tanaka. 2013a. A study on population size and selection lapse in many-objective optimization. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13). IEEE, Los Alamitos, CA, 1507--1514.Google Scholar
- H. E. Aguirre, A. Oyama, and K. Tanaka. 2013b. Adaptive ϵ-sampling and ϵ-hood for evolutionary many-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 322--336.Google Scholar
- H. E. Aguirre and K. Tanaka. 2004. Insights on properties of multiobjective MNK-landscapes. In Proceedings of the 2004 IEEE Congress on Evolutionary Computation (CEC’04), Vol. 1. IEEE, Los Alamitos, CA, 196--203.Google Scholar
- H. E. Aguirre and K. Tanaka. 2007. Working principles, behavior, and performance of MOEAs on MNK-landscapes. European Journal of Operational Research 181, 3, 1670--1690.Google ScholarCross Ref
- H. E. Aguirre and K. Tanaka. 2009a. Many-objective optimization by space partitioning and adaptive ϵ-ranking on MNK-landscapes. In Evolutionary Multi-Criterion Optimization. Springer, 407--422. Google ScholarDigital Library
- H. E. Aguirre and K. Tanaka. 2009b. Space partitioning with adaptive ϵ-ranking and substitute distance assignments: A comparative study on many-objective MNK-landscapes. In Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 547--554. Google ScholarDigital Library
- H. E. Aguirre and K. Tanaka. 2010a. A hybrid scalarization and adaptive ϵ-ranking strategy for many-objective optimization. In Parallel Problem Solving from Nature, PPSN XI. Springer, 11--20. Google ScholarDigital Library
- H. E. Aguirre and K. Tanaka. 2010b. Space partitioning evolutionary many-objective optimization: Performance analysis on MNK-landscapes. Information and Media Technologies 5, 2, 636--649.Google Scholar
- M. Asafuddoula, T. Ray, and R. Sarker. 2013. A decomposition based evolutionary algorithm for many objective optimization with systematic sampling and adaptive epsilon control. In Evolutionary Multi-Criterion Optimization. Springer, 413--427.Google Scholar
- A. Auger, J. Bader, D. Brockhoff, and E. Zitzler. 2009. Articulating user preferences in many-objective problems by sampling the weighted hypervolume. In Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 555--562. Google ScholarDigital Library
- J. Bader and E. Zitzler. 2011. HypE: An algorithm for fast hypervolume-based many-objective optimization. Evolutionary Computation 19, 1, 45--76. Google ScholarDigital Library
- R. Balling and S. Wilson. 2001. The maxi-min fitness function for multi-objective evolutionary computation: Application to city planning. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’01). 1079--1084.Google Scholar
- L. Batista, F. Campelo, F. Guimaraes, and J. Ramírez. 2011a. A comparison of dominance criteria in many-objective optimization problems. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 2359--2366.Google Scholar
- L. Batista, F. Campelo, F. Guimarães, and J. Ramírez. 2011b. Pareto cone ϵ-dominance: Improving convergence and diversity in multiobjective evolutionary algorithms. In Evolutionary Multi-Criterion Optimization. Springer, 76--90. Google ScholarDigital Library
- R. L. Becerra, C. A. C. Coello, and G. T. Pulido. 2013. Goal-constraint: Incorporating preferences through an evolutionary ϵ-constraint based method. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13). IEEE, Los Alamitos, CA, 741--747.Google Scholar
- S. Bechikh. 2013. Incorporating Decision Makers Preference Information in Evolutionary Multi-Objective Optimization. Ph.D. Dissertation. High Institute of Management of Tunis, University of Tunis, Tunisia.Google Scholar
- P. Bentley and J. Wakefield. 1998. Finding acceptable solutions in the Pareto-optimal range using multiobjective genetic algorithms. In Soft Computing in Engineering Design and Manufacturing. Springer, 231--240.Google Scholar
- N. Beume and G. Rudolph. 2006. Faster S-metric calculation by considering dominated hypervolume as Klee’s measure problem. In Proceedings of the 2nd IASTED Conference on Computational Intelligence (CI’06). 231--236.Google Scholar
- P. A. N. Bosman. 2012. On gradients and hybrid evolutionary algorithms for real-valued multiobjective optimization. IEEE Transactions on Evolutionary Computation 16, 1, 51--69. Google ScholarDigital Library
- P. A. N. Bosman and D. Thierens. 2003. The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Transactions on Evolutionary Computation 7, 2, 174--188. Google ScholarDigital Library
- J. Branke, T. Kaußler, and H. Schmeck. 2001. Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32, 6, 499--507.Google ScholarCross Ref
- J. P. Brans and B. Mareschal. 2005. PROMETHEE methods. In Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, 163--186.Google Scholar
- K. Bringmann, T. Friedrich, F. Neumann, and M. Wagner. 2011. Approximation-guided evolutionary multi-objective optimization. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence. 1198--1203. Google ScholarDigital Library
- D. Brockhoff, D. K. Saxena, K. Deb, and E. Zitzler. 2008. On handling a large number of objectives a posteriori and during optimization. In Multiobjective Problem Solving from Nature. Springer, 377--403.Google Scholar
- D. Brockhoff, T. Wagner, and H. Trautmann. 2012. On the properties of the R2 indicator. In Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation (GECCO’12). ACM, New York, NY, 465--472. Google ScholarDigital Library
- D. Brockhoff and E. Zitzler. 2006a. Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization. In Parallel Problem Solving from Nature, PPSN IX. Springer, 533--542. Google ScholarDigital Library
- D. Brockhoff and E. Zitzler. 2006b. Dimensionality reduction in multiobjective optimization with (partial) dominance structure preservation: Generalized minimum objective subset problems. TIK Report 247.Google Scholar
- D. Brockhoff and E. Zitzler. 2007. Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods. In Proceedings of the 2007 IEEE Congress on Evolutionary Computation (CEC’07). IEEE, Los Alamitos, CA, 2086--2093.Google Scholar
- D. Brockhoff and E. Zitzler. 2009. Objective reduction in evolutionary multiobjective optimization: Theory and applications. Evolutionary Computation 17, 2, 135--166. Google ScholarDigital Library
- D. Brockhoff and E. Zitzler. 2010. Automated aggregation and omission of objectives for tackling many-objective problems. In New Developments in Multiple Objective and Goal Programming. Springer, 81--102.Google Scholar
- G. W. Characklis, B. R. Kirsch, J. Ramsey, K. E. M. Dillard, and C. T. Kelley. 2006. Developing portfolios of water supply transfers. Water Resources Research 42, 5, 1--14.Google ScholarCross Ref
- D. W. Corne and J. D. Knowles. 2007. Techniques for highly multiobjective optimisation: Some nondominated points are better than others. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 773--780. Google ScholarDigital Library
- W. R. Cotton, R. A. Pielke Sr, R. L. Walko, G. E. Liston, C. J. Tremback, H. Jiang, R. L. McAnelly, J. Y. Harrington, M. E. Nicholls, G. G. Carrio, and J. P. McFadden. 2003. RAMS 2001: Current status and future directions. Meteorology and Atmospheric Physics 82, 1--4, 5--29.Google ScholarCross Ref
- M. Črepinšek, S. H. Liu, and M. Mernik. 2013. Exploration and exploitation in evolutionary algorithms: A survey. ACM Computing Surveys 45, 3, 35. Google ScholarDigital Library
- I. Das and J. E. Dennis. 1998. Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization 8, 3, 631--657. Google ScholarDigital Library
- K. Deb. 2001. Multi-objective optimization. In Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, 13--46.Google Scholar
- K. Deb and S. Chaudhuri. 2005. I-EMO: An interactive evolutionary multi-objective optimization tool. In Pattern Recognition and Machine Intelligence. Springer, 690--695. Google ScholarDigital Library
- K. Deb, S. Gupta, D. Daum, J. Branke, A. K. Mall, and D. Padmanabhan. 2009. Reliability-based optimization using evolutionary algorithms. IEEE Transactions on Evolutionary Computation 13, 5, 1054--1074. Google ScholarDigital Library
- K. Deb and H. Jain. 2012a. Handling many-objective problems using an improved NSGA-II procedure. In Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC’12). IEEE, Los Alamitos, CA, 1--8.Google Scholar
- K. Deb and H. Jain. 2012b. An Improved NSGA-II Procedure for Many-Objective Optimization, part II: Handling Constraints and Extending to an Adaptive Approach. KanGAL Report 2012010.Google Scholar
- K. Deb and H. Jain. 2014. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints. IEEE Transactions on Evolutionary Computation 18, 4, 577--601.Google ScholarCross Ref
- K. Deb and A. Kumar. 2007. Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 781--788. Google ScholarDigital Library
- K. Deb, M. Mohan, and S. Mishra. 2005. Evaluating the ϵ-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evolutionary Computation 13, 4, 501--525. Google ScholarDigital Library
- K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. 2002. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 2, 182--197. Google ScholarDigital Library
- K. Deb and D. K. Saxena. 2006. Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In Proceedings of the World Congress on Computational Intelligence (WCCI’06). 3352--3360.Google Scholar
- K. Deb, J. Sundar, N. Udaya Bhaskara Rao, and S. Chaudhuri. 2006. Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research 2, 3, 273--286.Google ScholarCross Ref
- K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. 2002. Scalable multi-objective optimization test problems. In Proceedings of the 2002 IEEE Congress on Evolutionary Computation (CEC’02). IEEE, Los Alamitos, CA, 825--830.Google Scholar
- R. Denysiuk, L. Costa, and I. Espírito Santo. 2013. Many-objective optimization using differential evolution with variable-wise mutation restriction. In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation (GECCO’13). ACM, New York, NY, 591--598. Google ScholarDigital Library
- K. W. DeRonne and G. Karypis. 2013. Pareto optimal pairwise sequence alignment. IEEE/ACM Transactions on Computational Biology and Bioinformatics 10, 2, 481--493. Google ScholarDigital Library
- N. Drechsler, R. Drechsler, and B. Becker. 2001. Multi-objective optimisation based on relation favour. In Evolutionary Multi-Criterion Optimization. Springer, 154--166. Google ScholarDigital Library
- M. Emmerich, N. Beume, and B. Naujoks. 2005. An EMO algorithm using the hypervolume measure as selection criterion. In Evolutionary Multi-Criterion Optimization. Springer, 62--76. Google ScholarDigital Library
- S. Eppe, M. López-Ibáñez, T. Stutzle, and Y. D. Smet. 2011. An experimental study of preference model integration into multi-objective optimization heuristics. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 2751--2758.Google Scholar
- G. W. Evans. 1984. An overview of techniques for solving multiobjective mathematical programs. Management Science 30, 11, 1268--1282.Google ScholarCross Ref
- M. Farina and P. Amato. 2002. On the optimal solution definition for many-criteria optimization problems. In Proceedings of the 2002 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS’02). IEEE, Los Alamitos, CA, 233--238.Google Scholar
- J. Figueira, S. Greco, and M. Ehrgott. 2005. Multiple Criteria Decision Analysis: State of the Art Surveys. Vol. 78. Springer, New York, NY.Google Scholar
- P. J. Fleming, R. C. Purshouse, and R. J. Lygoe. 2005. Many-objective optimization: An engineering design perspective. In Evolutionary Multi-Criterion Optimization. Springer, 14--32. Google ScholarDigital Library
- C. M. Fonseca and P. J. Fleming. 1998. Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 28, 1, 26--37. Google ScholarDigital Library
- G. Fu, Z. Kapelan, J. R. Kasprzyk, and P. M. Reed. 2012. Optimal design of water distribution systems using many-objective visual analytics. Journal of Water Resources Planning and Management 139, 6, 624--633.Google ScholarCross Ref
- M. Garza-Fabre, G. T. Pulido, and C. A. C. Coello. 2009. Ranking methods for many-objective optimization. In MICAI 2009: Advances in Artificial Intelligence. Springer, 633--645. Google ScholarDigital Library
- M. Garza-Fabre, G. T. Pulido, and C. A. C. Coello. 2010a. Alternative fitness assignment methods for many-objective optimization problems. In Artificial Evolution. Springer, 146--157. Google ScholarDigital Library
- M. Garza-Fabre, G. T. Pulido, and C. A. C. Coello. 2010b. Two novel approaches for many-objective optimization. In Proceedings of the 2010 IEEE Congress on Evolutionary Computation (CEC’10). IEEE, Los Alamitos, CA, 1--8.Google ScholarCross Ref
- M. Garza-Fabre, G. T. Pulido, C. A. C. Coello, and E. Rodriguez-Tello. 2011. Effective ranking + speciation = many-objective optimization. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 2115--2122.Google Scholar
- I. Giagkiozis, R. C. Purshouse, and P. J. Fleming. 2013. Generalized decomposition. In Evolutionary Multi-Criterion Optimization. Springer, 428--442.Google Scholar
- R. H. Gómez and C. A. C. Coello. 2013. MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13). IEEE, Los Alamitos, CA, 2488--2495.Google ScholarCross Ref
- D. Gong, J. Sun, and X. Ji. 2013a. Evolutionary algorithms with preference polyhedron for interval multi-objective optimization problems. Information Sciences 233, 141--161. Google ScholarDigital Library
- D. Gong, G. Wang, and X. Sun. 2013b. Set-based genetic algorithms for solving many-objective optimization problems. In Proceedings of the 2013 13th UK Workshop on Computational Intelligence (UKCI’13). IEEE, Los Alamitos, CA, 96--103.Google Scholar
- F. Güneş and F. Tokan. 2010. Pattern search optimization with applications on synthesis of linear antenna arrays. Expert Systems with Applications 37, 6, 4698--4705. Google ScholarDigital Library
- X. Guo, X. Wang, M. Wang, and Y. Wang. 2012. A new objective reduction algorithm for many-objective problems: Employing mutual information and clustering algorithm. In Proceedings of the 2012 8th International Conference on Computational Intelligence and Security (CIS’12). IEEE, Los Alamitos, CA, 11--16. Google ScholarDigital Library
- X. Guo, Y. Wang, and X. Wang. 2013. Using objective clustering for solving many-objective optimization problems. Mathematical Problems in Engineering 2013, Article No. 584909.Google Scholar
- D. Hadka and P. M. Reed. 2012. Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization. Evolutionary Computation 20, 3, 423--452. Google ScholarDigital Library
- D. Hadka, P. M. Reed, and T. W. Simpson. 2012. Diagnostic assessment of the Borg MOEA for many-objective product family design problems. In Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC’12). IEEE, Los Alamitos, CA, 1--10.Google Scholar
- N. Hamada, Y. Nagata, S. Kobayashi, and I. Ono. 2011a. Adaptive weighted aggregation 2: More scalable AWA for multiobjective function optimization. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 2375--2382.Google Scholar
- N. Hamada, Y. Nagata, S. Kobayashi, and I. Ono. 2011b. On scalability of adaptive weighted aggregation for multiobjective function optimization. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 669--678.Google Scholar
- M. P. Hansen and A. Jaszkiewicz. 1998. Evaluating the Quality of Approximations to the Non-Dominated Set. IMM, Department of Mathematical Modelling, Technical University of Denmark.Google Scholar
- J. G. Herrero, A. Berlanga, and J. M. M. López. 2009. Effective evolutionary algorithms for many-specifications attainment: Application to air traffic control tracking filters. IEEE Transactions on Evolutionary Computation 13, 1, 151--168. Google ScholarDigital Library
- H. Hirano and T. Yoshikawa. 2012. A study on two-step search using global-best in PSO for multi-objective optimization problems. In Proceedings of the 2012 Joint 6th International Conference on Soft Computing and Intelligent Systems (SCIS) and the 13th International Symposium on Advanced Intelligent Systems (ISIS). IEEE, Los Alamitos, CA, 1894--1897.Google Scholar
- S. Huband, P. Hingston, L. Barone, and L. While. 2006. A review of multiobjective test problems and a scalable test problem toolkit. IEEE Transactions on Evolutionary Computation 10, 5, 477--506. Google ScholarDigital Library
- E. J. Hughes. 2003. Multiple single objective Pareto sampling. In Proceedings of the 2003 IEEE Congress on Evolutionary Computation (CEC’13), Vol. 4. IEEE, Los Alamitos, CA, 2678--2684.Google ScholarCross Ref
- E. J. Hughes. 2007a. MSOPS-II: A general-purpose many-objective optimiser. In Proceedings of the 2007 IEEE Congress on Evolutionary Computation (CEC’07). 3944--3951.Google ScholarCross Ref
- E. J. Hughes. 2007b. Radar waveform optimisation as a many-objective application benchmark. In Evolutionary Multi-Criterion Optimization. Springer, 700--714. Google ScholarDigital Library
- E. J. Hughes. 2008. Fitness assignment methods for many-objective problems. In Multiobjective Problem Solving from Nature. Springer, 307--329.Google Scholar
- E. J. Hughes. 2011. Many-objective directed evolutionary line search. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 761--768. Google ScholarDigital Library
- K. Ikeda, H. Kita, and S. Kobayashi. 2001. Failure of Pareto-based MOEAs: Does non-dominated really mean near to optimal? In Proceedings of the 2001 Congress on Evolutionary Computation, Vol. 2. 957--962.Google Scholar
- H. Ishibuchi, N. Akedo, and Y. Nojima. 2011. A many-objective test problem for visually examining diversity maintenance behavior in a decision space. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation (GECCO’11). 649--656. Google ScholarDigital Library
- H. Ishibuchi, N. Akedo, and Y. Nojima. 2013. Relation between neighborhood size and MOEA/D performance on many-objective problems. In Evolutionary Multi-Criterion Optimization. Springer, 459--474.Google Scholar
- H. Ishibuchi, N. Akedo, and Y. Nojima. 2015. Behavior of multiobjective evolutionary algorithms on many-objective knapsack problems. IEEE Transactions on Evolutionary Computation 19, 2, 264--283.Google ScholarCross Ref
- H. Ishibuchi, N. Akedo, H. Ohyanagi, and Y. Nojima. 2011. Behavior of EMO algorithms on many-objective optimization problems with correlated objectives. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 1465--1472.Google Scholar
- H. Ishibuchi, Y. Hitotsuyanagi, N. Tsukamoto, and Y. Nojima. 2010. Many-objective test problems to visually examine the behavior of multiobjective evolution in a decision space. In Parallel Problem Solving from Nature, PPSN XI. Springer, 91--100. Google ScholarDigital Library
- H. Ishibuchi, N. Tsukamoto, and Y. Nojima. 2008. Evolutionary many-objective optimization: A short review. In Proceedings of the IEEE World Congress on Evolutionary Computation (CEC’08). IEEE, Los Alamitos, CA, 2419--2426.Google Scholar
- A. L. Jaimes and C. A. C. Coello. 2009. Study of preference relations in many-objective optimization. In Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 611--618. Google ScholarDigital Library
- A. L. Jaimes, C. A. C. Coello, H. E. Aguirre, and K. Tanaka. 2011a. Adaptive objective space partitioning using conflict information for many-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 151--165. Google ScholarDigital Library
- A. L. Jaimes, C. A. C. Coello, and J. E. U. Barrientos. 2009. Online objective reduction to deal with many-objective problems. In Evolutionary Multi-Criterion Optimization. Springer, 423--437. Google ScholarDigital Library
- A. L. Jaimes, C. A. C. Coello, and D. Chakraborty. 2008. Objective reduction using a feature selection technique. In Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 673--680. Google ScholarDigital Library
- A. L. Jaimes, C. A. C. Coello, A. Oyama, and K. Fujii. 2013. An alternative preference relation to deal with many-objective optimization problems. In Evolutionary Multi-Criterion Optimization. Springer, 291--306.Google Scholar
- A. L. Jaimes, A. A. Montano, and C. A. C. Coello. 2011b. Preference incorporation to solve many-objective airfoil design problems. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 1605--1612.Google ScholarCross Ref
- H. Jain and K. Deb. 2013. An improved adaptive approach for elitist nondominated sorting genetic algorithm for many-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 307--321.Google Scholar
- H. Jain and K. Deb. 2014. An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach. IEEE Transactions on Evolutionary Computation 18, 4, 602--622.Google ScholarCross Ref
- A. Jaszkiewicz. 2002. On the performance of multiple-objective genetic local search on the 0/1 knapsack problem-A comparative experiment. IEEE Transactions on Evolutionary Computation 6, 4, 402--412. Google ScholarDigital Library
- Yaochu Jin and B. Sendhoff. 2003. Connectedness, regularity and the success of local search in evolutionary multi-objective optimization. In Proceedings of the 2003 Congress on Evolutionary Computation (CEC’03). Vol. 3. 1910--1917. DOI:http://dx.doi.org/10.1109/CEC.2003.1299907Google Scholar
- D. S. Johnson, L. McGeogh, F. Glover, and C. Rego. 2000. 8th DIMACS Implementation Challenge: The Traveling Salesman Problem. Retrieved July 27, 2015, from http://dimacs.rutgers.edu/Challenges/TSP/.Google Scholar
- S. Kalboussi, S. Bechikh, M. Kessentini, and L. B. Said. 2013. Preference-based many-objective evolutionary testing generates harder test cases for autonomous Agents. In Search Based Software Engineering. Springer, 245--250.Google Scholar
- J. R. Kasprzyk, P. M. Reed, G. W. Characklis, and B. R. Kirsch. 2012. Many-objective de Novo water supply portfolio planning under deep uncertainty. Environmental Modelling and Software 34, 87--104. Google ScholarDigital Library
- L. Kaufman and P. Rousseeuw. 2009. Finding Groups in Data: An Introduction to Cluster Analysis. Vol. 344. John Wiley and Sons.Google Scholar
- J. H. Kim, J. H. Han, Y. H. Kim, S. H. Choi, and E. S. Kim. 2012. Preference-based solution selection algorithm for evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation 16, 1, 20--34. Google ScholarDigital Library
- J. D. Knowles and D. W. Corne. 2003a. Instance generators and test suites for the multiobjective quadratic assignment problem. In Evolutionary Multi-Criterion Optimization. Springer, 295--310. Google ScholarDigital Library
- J. D. Knowles and D. W. Corne. 2003b. Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation 7, 2, 100--116. Google ScholarDigital Library
- J. D. Knowles and D. W. Corne. 2007. Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 757--771. Google ScholarDigital Library
- J. B. Kollat and P. M. Reed. 2006. Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design. Advances in Water Resources 29, 6, 792--807.Google ScholarCross Ref
- M. Köppen, R. Vicente-Garcia, and B. Nickolay. 2005. Fuzzy-Pareto-dominance and its application in evolutionary multi-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 399--412. Google ScholarDigital Library
- M. Köppen and K. Yoshida. 2007. Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In Evolutionary Multi-Criterion Optimization. Springer, 727--741. Google ScholarDigital Library
- A. Kostin, G. Guillén-Gosálbez, F. D. Mele, and L. Jiménez. 2012. Identifying key life cycle assessment metrics in the multiobjective design of bioethanol supply chains using a rigorous mixed-integer linear programming approach. Industrial and Engineering Chemistry Research 51, 14, 5282--5291.Google ScholarCross Ref
- N. Kowatari, A. Oyama, H. E. Aguirre, and K. Tanaka. 2012. Analysis on population size and neighborhood recombination on many-objective optimization. In Parallel Problem Solving from Nature, PPSN XII. Springer, 22--31. Google ScholarDigital Library
- R. Kudikala, A. R. Mills, P. J. Fleming, G. F. Tanner, and J. E. Holt. 2013. Aero engine health management system architecture design using multi-criteria optimization. In Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation (GECCO’13 Companion). ACM, New York, NY, 185--186. Google ScholarDigital Library
- S. Kukkonen and J. Lampinen. 2007. Ranking-dominance and many-objective optimization. In Proceedings of the 2007 IEEE Congress on Evolutionary Computation (CEC’07). IEEE, Los Alamitos, CA, 3983--3990.Google Scholar
- N. Kusuno, H. E. Aguirre, K. Tanaka, and M. Koishi. 2013. Evolutionary multi-objective optimization to attain practically desirable solutions. In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 639--646. Google ScholarDigital Library
- M. Laumanns, L. Thiele, K. Deb, and E. Zitzler. 2002. Combining convergence and diversity in evolutionary multiobjective optimization. Evolutionary Computation 10, 3, 263--282. Google ScholarDigital Library
- M. Laumanns and R. Zenklusen. 2011. Stochastic convergence of random search methods to fixed size Pareto front approximations. European Journal of Operational Research 213, 2, 414--421.Google ScholarCross Ref
- K. Le, D. L. Silva, and H. Li. 2009. An improved version of volume dominance for multi-objective optimisation. In Evolutionary Multi-Criterion Optimization. Springer, 231--245. Google ScholarDigital Library
- K. B. Lee and J. H. Kim. 2011. Multi-objective particle swarm optimization with preference-based sorting. In Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC’11). IEEE, Los Alamitos, CA, 2506--2513.Google Scholar
- M. Li, S. Yang, and X. Liu. 2013. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Transactions on Evolutionary Computation PP, 99, 1.Google Scholar
- M. Li, S. Yang, and X. Liu. 2014. Diversity comparison of Pareto front approximations in many-objective optimization. IEEE Transactions on Cybernetics 44, 12, 2568--2584. DOI:http://dx.doi.org/10.1109/TCYB.2014.2310651Google ScholarCross Ref
- M. Li, J. Zheng, K. Li, Q. Yuan, and R. Shen. 2010. Enhancing diversity for average ranking method in evolutionary many-objective optimization. In Parallel Problem Solving from Nature, PPSN XI. Springer, 647--656. Google ScholarDigital Library
- Z. Li and H. Liu. 2012. Preference-based evolutionary multi-objective optimization. In Proceedings of the 2012 8th International Conference on Computational Intelligence and Security (CIS’12). IEEE, Los Alamitos, CA, 71--76. Google ScholarDigital Library
- P. Lindroth, M. Patriksson, and A. B. Strömberg. 2010. Approximating the Pareto optimal set using a reduced set of objective functions. European Journal of Operational Research 207, 3, 1519--1534.Google ScholarCross Ref
- E. Løken. 2007. Use of multicriteria decision analysis methods for energy planning problems. Renewable and Sustainable Energy Reviews 11, 7, 1584--1595.Google ScholarCross Ref
- R. J. Lygoe, M. Cary, and P. J. Fleming. 2013. A real-world application of a many-objective optimisation complexity reduction process. In Evolutionary Multi-Criterion Optimization. Springer, 641--655.Google Scholar
- A. D. Manriquez, G. T. Pulido, C. A. C. Coello, and R. L. Becerra. 2013. A ranking method based on the R2 indicator for many-objective optimization. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13). IEEE, Los Alamitos, CA, 1523--1530.Google Scholar
- A. M. Mendez and C. A. C. Coello. 2012. Solving multi-objective optimization problems using differential evolution and a maximin selection criterion. In Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC’12). IEEE, Los Alamitos, CA, 1--8.Google ScholarCross Ref
- A. M. Mendez and C. A. C. Coello. 2013. Selection operators based on maximin fitness function for multi-objective evolutionary algorithms. In Evolutionary Multi-Criterion Optimization. Springer, 215--229.Google Scholar
- K. Miettinen. 1999. Nonlinear Multiobjective Optimization. Vol. 12. Springer.Google Scholar
- K. Miettinen. 2003. Graphical illustration of Pareto optimal solutions. In Multi-Objective Programming and Goal Programming. Advances in Soft Computing, Vol. 21. Springer, 197--202.Google Scholar
- L. L. Minku and X. Yao. 2013. Software effort estimation as a multiobjective learning problem. ACM Transactions on Software Engineering and Methodology 22, 4, 35:1--35:32. Google ScholarDigital Library
- P. Mitra, C. A. Murthy, and S. K. Pal. 2002. Unsupervised feature selection using feature similarity. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 3, 301--312. Google ScholarDigital Library
- H. J. F. Moen, N. B. Hansen, H. Hovland, and J. Tørresen. 2013. Many-objective optimization using taxi-cab surface evolutionary algorithm. In Evolutionary Multi-Criterion Optimization. Springer, 128--142.Google Scholar
- A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, and C. A. C. Coello. 2014a. A survey of multiobjective evolutionary algorithms for data mining: Part I. IEEE Transactions on Evolutionary Computation 18, 1, 4--19.Google ScholarCross Ref
- A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, and C. A. C. Coello. 2014b. Survey of multiobjective evolutionary algorithms for data mining: Part II. IEEE Transactions on Evolutionary Computation 18, 1, 20--35.Google ScholarCross Ref
- K. Musselman and J. Talavage. 1980. A tradeoff cut approach to multiple objective optimization. Operations Research 28, 6, 1424--1435.Google ScholarDigital Library
- K. Narukawa. 2013. Effect of dominance balance in many-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 276--290.Google Scholar
- K. Narukawa and T. Rodemann. 2012. Examining the performance of evolutionary many-objective optimization algorithms on a real-world application. In Proceedings of the 2012 6th International Conference on Genetic and Evolutionary Computing (ICGEC’12). IEEE, Los Alamitos, CA, 316--319. Google ScholarDigital Library
- P. R. Palmer, A. M. Cristóbal, and G. T. Parks. 2011. Coherent design methodology using modelling, simulation and optimisation. In Proceedings of the 2011 Grand Challenges on Modeling and Simulation Conference. 65--75. Google ScholarDigital Library
- J. Pasia, H. E. Aguirre, and K. Tanaka. 2011. Improved random one-bit climbers with adaptive ϵ-ranking and tabu moves for many-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 182--196. Google ScholarDigital Library
- K. Praditwong, M. Harman, and X. Yao. 2011. Software module clustering as a multi-objective search problem. IEEE Transactions on Software Engineering 37, 2, 264--282. Google ScholarDigital Library
- K. Praditwong and X. Yao. 2006. A new multi-objective evolutionary optimisation algorithm: The two-archive algorithm. In Proceedings of the 2006 International Conference on Computational Intelligence and Security. Vol. 1. IEEE, Los Alamitos, CA, 286--291.Google Scholar
- R. C. Purshouse, K. Deb, M. M. Mansor, S. Mostaghim, and R. Wang. 2014. A review of hybrid evolutionary multiple criteria decision making methods. In Proceedings of the 2014 IEEE Congress on Evolutionary Computation (CEC’14). 1147--1154.Google Scholar
- R. C. Purshouse and P. J. Fleming. 2007. On the evolutionary optimization of many conflicting objectives. IEEE Transactions on Evolutionary Computation 11, 6, 770--784. Google ScholarDigital Library
- R. C. Purshouse, C. Jalbă, and P. J. Fleming. 2011. Preference-driven co-evolutionary algorithms show promise for many-objective optimisation. In Evolutionary Multi-Criterion Optimization. Springer, 136--150. Google ScholarDigital Library
- F. Qiu, Y. Wu, L. Wang, and B. Jiang. 2012. Bipolar preferences dominance based evolutionary algorithm for many-objective optimization. In Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC’12). IEEE, Los Alamitos, CA, 1--8.Google Scholar
- L. Rachmawati and D. Srinivasan. 2006. Preference incorporation in multi-objective evolutionary algorithms: A survey. In Proceedings of the 2006 IEEE Congress on Evolutionary Computation (CEC’06). IEEE, Los Alamitos, CA, 962--968.Google Scholar
- T. Ray, M. Asafuddoula, and A. Isaacs. 2013. A steady state decomposition based quantum genetic algorithm for many objective optimization. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13). IEEE, Los Alamitos, CA, 2817--2824.Google Scholar
- T. Ray, K. Tai, and K. C. Seow. 2001. Multiobjective design optimization by an evolutionary algorithm. Engineering Optimization 33, 3, 399--424.Google ScholarCross Ref
- P. M. Reed and J. B. Kollat. 2012. Save now, pay later? Multi-period many-objective groundwater monitoring design given systematic model errors and uncertainty. Advances in Water Resources 35, 55--68.Google ScholarCross Ref
- P. M. Reed and J. B. Kollat. 2013. Visual analytics clarify the scalability and effectiveness of massively parallel many-objective optimization: A groundwater monitoring design example. Advances in Water Resources 56, 1--13.Google ScholarCross Ref
- C. Reeves. 1995. A genetic algorithm for flowshop sequencing. Computers and Operations Research 22, 1, 5--13. Google ScholarDigital Library
- S. J. Ryu, K. B. Lee, and J. H. Kim. 2012. Improved version of a multiobjective quantum-inspired evolutionary algorithm with preference-based selection. In Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC’12). IEEE, Los Alamitos, CA, 1--7.Google Scholar
- A. Santiago, H. J. F. Huacuja, B. Dorronsoro, J. E. Pecero, C. G. Santillan, J. J. G. Barbosa, and J. C. S. Monterrubio. 2014. A survey of decomposition methods for multi-objective optimization. In Recent Advances on Hybrid Approaches for Designing Intelligent Systems. Springer, 453--465.Google Scholar
- H. Sato, H. E. Aguirre, and K. Tanaka. 2007. Controlling dominance area of solutions and its impact on the performance of MOEAs. In Evolutionary Multi-Criterion Optimization. Springer, 5--20. Google ScholarDigital Library
- H. Sato, H. E. Aguirre, and K. Tanaka. 2010a. Pareto partial dominance MOEA and hybrid archiving strategy included CDAS in many-objective optimization. In Proceedings of the 2010 IEEE Congress on Evolutionary Computation (CEC’10). IEEE, Los Alamitos, CA, 1--8.Google Scholar
- H. Sato, H. E. Aguirre, and K. Tanaka. 2010b. Self-controlling dominance area of solutions in evolutionary many-objective optimization. In Simulated Evolution and Learning. Springer, 455--465. Google ScholarDigital Library
- H. Sato, H. E. Aguirre, and K. Tanaka. 2011a. Genetic diversity and effective crossover in evolutionary many-objective optimization. In Learning and Intelligent Optimization. Springer, 91--105. Google ScholarDigital Library
- H. Sato, H. E. Aguirre, and K. Tanaka. 2011b. Improved S-CDAs using crossover controlling the number of crossed genes for many-objective optimization. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 753--760. Google ScholarDigital Library
- H. Sato, C. A. C. Coello, H. E. Aguirre, and K. Tanaka. 2012. Adaptive control of the number of crossed genes in many-objective evolutionary optimization. In Learning and Intelligent Optimization. Springer, 478--484. Google ScholarDigital Library
- D. K. Saxena and K. Deb. 2007. Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding. In Evolutionary Multi-Criterion Optimization. Springer, 772--787. Google ScholarDigital Library
- D. K. Saxena, J. A. Duro, A. Tiwari, K. Deb, and Q. Zhang. 2013. Objective reduction in many-objective optimization: Linear and nonlinear algorithms. IEEE Transactions on Evolutionary Computation 17, 1, 77--99. Google ScholarDigital Library
- D. K. Saxena, Q. Zhang, J. A. Duro, and A. Tiwari. 2011. Framework for many-objective test problems with both simple and complicated Pareto-set shapes. In Evolutionary Multi-Criterion Optimization. Springer, 197--211. Google ScholarDigital Library
- A. S. Sayyad, T. Menzies, and H. Ammar. 2013. On the value of user preferences in search-based software engineering: A case study in software product lines. In Proceedings of the 2013 International Conference on Software Engineering. IEEE, Los Alamitos, CA, 492--501. Google ScholarDigital Library
- O. Schütze, X. Esquivel, A. Lara, and C. A. C. Coello. 2010. Measuring the Averaged Hausdorff Distance to the Pareto Front of a Multi-Objective Optimization Problem. Technical Report TR-OS-2010-02. CINVESTAV.Google Scholar
- T. W. Simpson, W. Chen, J. K. Allen, and F. Mistree. 1996. Conceptual design of a family of products through the use of the robust concept exploration method. In Proceedings of the 6th AIAA/NASA/USAF MultiDisciplinary Analysis and Optimization Symposium. 1535--1545.Google Scholar
- H. K. Singh, A. Isaacs, and T. Ray. 2011. A Pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Transactions on Evolutionary Computation 15, 4, 539--556. Google ScholarDigital Library
- A. Sinha, D. K. Saxena, K. Deb, and A. Tiwari. 2013. Using objective reduction and interactive procedure to handle many-objective optimization problems. Applied Soft Computing 13, 1, 415--427. Google ScholarDigital Library
- D. W. Stouch, E. Zeidman, M. Richards, K. D. McGraw, and W. Callahan. 2011. Coevolving collection plans for UAS constellations. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 1691--1698. Google ScholarDigital Library
- A. Sülflow, N. Drechsler, and R. Drechsler. 2007. Robust multi-objective optimization in high dimensional spaces. In Evolutionary Multi-Criterion Optimization. Springer, 715--726. Google ScholarDigital Library
- K. Tagawa and A. Imamura. 2013. Many-hard-objective optimization using differential evolution based on two-stage constraint-handling. In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 671--678. Google ScholarDigital Library
- R. Takahashi, E. Carrano, and E. Wanner. 2011. On a stochastic differential equation approach for multiobjective optimization up to Pareto-criticality. In Evolutionary Multi-Criterion Optimization. Springer, 61--75. Google ScholarDigital Library
- Y. Tan, Y. Jiao, H. Li, and X. Wang. 2013. MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives. Computers and Operations Research 40, 6, 1648--1660. Google ScholarDigital Library
- J. Tang, S. Alam, C. Lokan, and H. Abbass. 2012. A multi-objective evolutionary method for dynamic airspace re-sectorization using sectors clipping and similarities. In Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC’12). IEEE, Los Alamitos, CA, 1--8.Google Scholar
- J. Tate, B. Woolford-Lim, I. Bate, and X. Yao. 2012. Evolutionary and principled search strategies for sensornet protocol optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 42, 1, 163--180. Google ScholarDigital Library
- L. Thiele, K. Miettinen, P. Korhonen, and J. Molina. 2009. A preference-based evolutionary algorithm for multi-objective optimization. Evolutionary Computation 17, 3, 411--436. Google ScholarDigital Library
- R. Ursem. 2010. Centrifugal Pump Design: Three Benchmark Problems for Many-Objective Optimization. Technical Report 2010-01. Grundfos A/S.Google Scholar
- L. J. P. Van der Maaten, E. O. Postma, and H. J. Van Den Herik. 2009. Dimensionality reduction: A comparative review. Journal of Machine Learning Research 10, 1--41.Google Scholar
- D. A. Van Veldhuizen and G. B. Lamont. 1998. Evolutionary computation and convergence to a Pareto front. In Proceedings of the Genetic Programming Conference. 221--228.Google Scholar
- M. Velasquez and P. T. Hester. 2013. An analysis of multi-criteria decision making methods. International Journal of Operations Research 10, 56--66.Google Scholar
- N. Venkatarayalu and T. Ray. 2004. Optimum design of Yagi-Uda antennas using computational intelligence. IEEE Transactions on Antennas and Propagation 52, 7, 1811--1818.Google ScholarCross Ref
- S. Verel, A. Liefooghe, and C. Dhaenens. 2011. Set-based multiobjective fitness landscapes: A preliminary study. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. 769--776. Google ScholarDigital Library
- C. A. R. Villalobos and C. A. C. Coello. 2012. A new multi-objective evolutionary algorithm based on a performance assessment indicator. In Proceedings of the 14th International Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 505--512. Google ScholarDigital Library
- C. Von Lücken, B. Barán, and C. Brizuela. 2014. A survey on multi-objective evolutionary algorithms for many-objective problems. Computational Optimization and Applications 1, 1--50.Google Scholar
- M. Wagner and F. Neumann. 2013. A fast approximation guided evolutionary multi-objective algorithm. In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation (GECCO’13). ACM, New York, NY, 687--694. Google ScholarDigital Library
- T. Wagner, N. Beume, and B. Naujoks. 2007. Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In Evolutionary Multi-Criterion Optimization. Springer, 742--756. Google ScholarDigital Library
- D. J. Walker, R. M. Everson, and J. E. Fieldsend. 2013. Visualizing mutually nondominating solution sets in many-objective optimization. IEEE Transactions on Evolutionary Computation 17, 2, 165--184. Google ScholarDigital Library
- H. Wang, L. Jiao, and X. Yao. 2014. An improved two-archive algorithm for many-objective optimization. IEEE Transactions on Evolutionary Computation PP, 99, 1. DOI:http://dx.doi.org/10.1109/TEVC.2014.2350987Google Scholar
- H. Wang and X. Yao. 2014. Corner sort for Pareto-based many-objective optimization. IEEE Transactions on Cybernetics 44, 1, 92--102.Google ScholarCross Ref
- R. Wang, R. C. Purshouse, and P. J. Fleming. 2012. Local preference-inspired co-evolutionary algorithms. In Proceedings of the 14th International Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 513--520. Google ScholarDigital Library
- R. Wang, R. C. Purshouse, and P. J. Fleming. 2013a. On finding well-spread Pareto optimal solutions by preference-inspired co-evolutionary algorithm. In Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation. ACM, New York, NY, 695--702. Google ScholarDigital Library
- R. Wang, R. C. Purshouse, and P. J. Fleming. 2013b. Preference-inspired co-evolutionary algorithm using weights for many-objective optimization. In Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation. ACM, New York, NY, 101--102. Google ScholarDigital Library
- R. Wang, R. C. Purshouse, and P. J. Fleming. 2013c. Preference-inspired coevolutionary algorithms for many-objective optimization. IEEE Transactions on Evolutionary Computation 17, 4, 474--494. Google ScholarDigital Library
- R. Wang, T. Zhang, and B. Guo. 2013. An enhanced MOEA/D using uniform directions and a pre-organization procedure. In Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC’13). IEEE, Los Alamitos, CA, 2390--2397.Google Scholar
- Z. Wang, K. Tang, and X. Yao. 2010. Multi-objective approaches to optimal testing resource allocation in modular software systems. IEEE Transactiona on Reliability 59, 3, 563--575.Google ScholarCross Ref
- L. While, L. Bradstreet, and L. Barone. 2012. A fast way of calculating exact hypervolumes. IEEE Transactions on Evolutionary Computation 16, 1, 86--95. Google ScholarDigital Library
- L. While, P. Hingston, L. Barone, and S. Huband. 2006. A faster algorithm for calculating hypervolume. IEEE Transactions on Evolutionary Computation 10, 1, 29--38. Google ScholarDigital Library
- U. Wickramasinghe, R. Carrese, and X. Li. 2010. Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm. In Proceedings of the 2010 IEEE Congress on Evolutionary Computation (CEC’10). IEEE, Los Alamitos, CA, 1--8.Google Scholar
- S. Yang, M. Li, X. Liu, and J. Zheng. 2013. A grid-based evolutionary algorithm for many-objective optimization. IEEE Transactions on Evolutionary Computation 17, 5, 721--736. Google ScholarDigital Library
- P. L. Yu. 1974. Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. Journal of Optimization Theory and Applications 14, 3, 319--377.Google ScholarCross Ref
- Q. Zhang and H. Li. 2007. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation 11, 6, 712--731. Google ScholarDigital Library
- Q. Zhang, W. Liu, and H. Li. 2009. The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In Proceedings of the 2009 IEEE Congress on Evolutionary Computation (CEC’09). IEEE, Los Alamitos, CA, 203--208. Google ScholarDigital Library
- Q. Zhang, A. Zhou, S. Zhao, P. N. Suganthan, W. Liu, and S. Tiwari. 2008. Multiobjective Optimization Test Instances for the CEC 2009 Special Session and Competition. Technical Report. University of Essex, Colchester, UK.Google Scholar
- A. Zhou, Y. Jin, Q. Zhang, B. Sendhoff, and E. Tsang. 2006. Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In Proceedings of the 2006 IEEE Congress on Evolutionary Computation (CEC’06). IEEE, Los Alamitos, CA, 892--899.Google Scholar
- A. Zhou, B. Qu, H. Li, S. Zhao, P. N. Suganthan, and Q. Zhang. 2011. Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation 1, 1, 32--49.Google ScholarCross Ref
- E. Zitzler and S. Künzli. 2004. Indicator-based selection in multiobjective search. In Parallel Problem Solving from Nature, PPSN VIII. Springer, 832--842.Google Scholar
- E. Zitzler, M. Laumanns, and L. Thiele. 2001. SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report 103. Eidgenössische Technische Hochschule Zürich (ETH).Google Scholar
- E. Zitzler and L. Thiele. 1998. Multiobjective optimization using evolutionary algorithms: A comparative case study. In Parallel Problem Solving from Nature, PPSN V. Springer, 292--301. Google ScholarDigital Library
- E. Zitzler and L. Thiele. 1999. Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation 3, 4, 257--271. Google ScholarDigital Library
- E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G Da Fonseca. 2003. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7, 2, 117--132. Google ScholarDigital Library
- X. Zou, Y. Chen, M. Liu, and L. Kang. 2008. A new evolutionary algorithm for solving many-objective optimization problems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38, 5, 1402--1412. Google ScholarDigital Library
Index Terms
- Many-Objective Evolutionary Algorithms: A Survey
Recommendations
Approximate non-dominated sorting for evolutionary many-objective optimization
Non-dominated sorting has widely been adopted and shown to be very effective in dominance based evolutionary multi-objective optimization where the number of objectives is two or three. In dealing with many-objective optimization problems, where the ...
An improved NSGA-III procedure for evolutionary many-objective optimization
GECCO '14: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary ComputationMany-objective (four or more objectives) optimization problems pose a great challenge to the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs), such as NSGA-II and SPEA2. This is mainly due to the fact that the selection ...
Achievement scalarizing function sorting for strength Pareto evolutionary algorithm in many-objective optimization
AbstractMulti-objective evolutionary algorithms (MOEAs) have proven their effectiveness in solving two or three objective problems. However, recent research shows that Pareto-based MOEAs encounter selection difficulties facing many similar non-dominated ...
Comments