[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
article

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

Published: 01 July 2014 Publication History

Abstract

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.

References

[1]
Adra, S.F., Fleming, P.J.: A diversity management operator for evolutionary many-objective optimisation. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 81---94. Springer, Berlin (2009)
[2]
Aguirre, H., Tanaka, K.: Effects of elitism and population climbing on multiobjective MNK-landscapes. In: 2004 IEEE Congress on Evolutionary Computation (2004).
[3]
Aguirre, H., Tanaka, K.: Insights on properties of multiobjective MNK-landscapes. In: 2004 IEEE Congress on Evolutionary Computation (2004).
[4]
Aguirre, H., Tanaka, K.: Robust optimization by $$\epsilon $$∈-ranking on high dimensional objective spaces. In: Simulated Evolution and Learning. Springer, New York (2008).
[5]
Aguirre, H., Tanaka, K.: Many-objective optimization by space partitioning and adaptive $$\epsilon $$∈-ranking on MNK-landscapes. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 407---422. Springer, Berlin (2009)
[6]
Bader, J., Zitzler, E.: Hype: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. (2011).
[7]
Bader, J., Deb, K., Zitzler, E.: Faster hypervolume-based search using Monte Carlo sampling. In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pp. 313---326 (2010)
[8]
Basseur, M., Zitzler, E.: A preliminary study on handling uncertainty in indicator-based multiobjective optimization. In: Applications of Evolutionary Computing. Lecture Notes in Computer Science, vol. 3907, pp. 727---739. Springer, New York (2006).
[9]
Bentley, P.J., Wakefield, J.P.: Finding acceptable solutions in the Pareto-optimal range using multiobjective genetic algorithms. In: Soft Computing in Engineering Design and Manufacturing. Part 5, pp. 231---240. Springer, London (1997)
[10]
Bentley, J., Kung, H., Schkolnick, M., Thompson, C.: On the average number of maxima in a set of vectors and applications. J. ACM 25(4), 536---543 (1978)
[11]
Branke, J., Kaußler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Adv. Eng. Softw. 32, 499---507 (2001)
[12]
Brockhoff, D., Zitzler, E.: Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization. In: Parallel Problem Solving from Nature (PPSN IX). Lecture Notes in Computer Science, vol. 4193, pp. 533---542. Springer, Berlin (2006)
[13]
Brockhoff, D., Zitzler, E.: Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods. In: 2007 IEEE Congress on Evolutionary Computation (2007).
[14]
Brockhoff, D., Friedrich, T., Hebbinghaus, N., Klein, C., Neumann, F., Zitzler, E.: Do additional objectives make a problem harder? In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO '07), pp. 765---772. ACM Press, New York (2007)
[15]
Brockhoff, D., Saxena, K., Deb, K., Zitzler, E.: On handling a large number of objectives a posteriori and during optimization. In: Knowles, J., Corne, D., Deb, K. (eds.) Multi-Objective Problem Solving from Nature: From Concepts to Applications, pp. 377---403. Springer, Berlin (2008)
[16]
Coello Coello, C.: Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored. Frontiers Comput. Sci. China 3(1), 18---30 (2009)
[17]
Coello Coello, C., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007)
[18]
Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. The MIT Press, Cambridge (1990)
[19]
Corne, D.W., Knowles, J.D.: Techniques for highly multiobjective optimisation: some nondominated points are better than others. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO '07), pp. 773---780. ACM Press, New York (2007)
[20]
Corne, D.W., Knowles, J.D., Oates, M.J.: The Pareto envelope-based selection algorithm for multiobjective optimization. In: Parallel Problem Solving from Nature (PPSN VI). Lecture Notes in Computer Science, vol. 1917, pp. 839---848. Springer, Berlin (2000)
[21]
Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: Region-based selection in evolutionary multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO'2001), pp. 283---290. Morgan Kaufmann Publishers, San Francisco (2001)
[22]
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001)
[23]
Deb, K., Saxena, D.: On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. Kangal report 2005011, Indian Institute of Technology (2005)
[24]
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. (2002).
[25]
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation (2002).
[26]
Deb, K., Mohan, M., Mishra, S.: Towards a quick computation of well-spread Pareto-optimal solutions. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003). Lecture Notes in Computer Science, vol. 2632, pp. 222---236. Springer, Berlin (2003)
[27]
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Jain, L., Wu, X., Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization, Advanced Information and Knowledge Processing, pp. 105---145. Springer, Berlin (2005).
[28]
di Pierro, F.: Many-objective evolutionary algorithms and applications to water resources engineering. Ph.D. thesis, School of Engineering, Computer Science and Mathematics, UK (2006)
[29]
di Pierro, F., Khu, S.T., Savić, D.A.: An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans. Evol. Comput. (2007).
[30]
Drechsler, N., Drechsler, R., Becker, B.: Multi-objected optimization in evolutionary algorithms using satisfyability classes. In: Reusch, B. (ed.) International Conference on Computational Intelligence, Theory and Applications, 6th Fuzzy Days. Lecture Notes in Computer Science, vol. 1625, pp. 108---117. Springer, Dortmund (1999)
[31]
Drechsler, N., Drechsler, R., Becker, B.: Multi-objective optimisation based on relation favour. In: First International Conference on Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, vol. 1993, pp. 154---166. Springer, Berlin (2001)
[32]
Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005). Lecture Notes in Computer Science, vol. 3410, pp. 62---76. Springer, Berlin (2005).
[33]
Farina, M., Amato, P.: On the optimal solution definition for many-criteria optimization problems. In: Proceedings of the NAFIPS-FLINT International Conference 2002 (2002).
[34]
Fleming, P., Purshouse, R.C., Lygoe, R.J.: Many-objective optimization: an engineering design perspective. In: Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005). Lecture Notes in Computer Science, vol. 3410, pp. 14---32. Springer, Berlin (2005)
[35]
Fonseca, C.M., Fleming, P.J.: An overview of evolutionary algorithms in multiobjective optimization. Evol. Comput. (1995).
[36]
Hadka, D., Reed, P.: Borg: an auto-adaptive many-objective evolutionary computing framework. Evol. Comput. (2012).
[37]
Hadka, D., Reed, P.: Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization. Evol. Comput. (2012).
[38]
He, Z., Yen, G.G.: A new fitness evaluation method based on fuzzy logic in multiobjective evolutionary algorithms. In: 2012 IEEE Congress on Evolutionary Computation (2012).
[39]
Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans. Evol. Comput. (2006).
[40]
Hughes, E.J.: Multiple single objective Pareto sampling. In: 2003 IEEE Congress on Evolutionary Computation (2003).
[41]
Hughes, E.J.: Evolutionary many-objective optimisation: many once or one many? In: 2005 IEEE Congress on Evolutionary Computation (2005).
[42]
Hughes, E.J.: Multi-objective equivalent random search. In: Parallel Problem Solving from Nature (PPSN IX), vol. 4193, pp. 463---472 (2006)
[43]
Hughes, E.J.: MSOPS-II: a general-purpose many-objective optimiser. In: 2007 IEEE Congress on Evolutionary Computation (2007).
[44]
Inselberg, A., Dimsdale, B.: Parallel coordinates: a tool for visualizing multi-dimensional geometry. In: Proceedings of the First Conference on Visualization '90 (VIS '90), pp. 361---378. IEEE Press, Los Alamitos (1990)
[45]
Ishibuchi, H., Murata, T.: A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. Syst. Man Cybern. C 28(3), 392---403 (1998).
[46]
Ishibuchi, H., Nojima, Y.: Optimization of scalarizing functions through evolutionary multiobjective optimization. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 51---65. Springer, Berlin (2007)
[47]
Ishibuchi, H., Hitotsuyanagi, Y., Nojima, Y.: Scalability of multiobjective genetic local search to many-objective problems: knapsack problem case studies. In: 2008 IEEE Congress on Evolutionary Computation (2008).
[48]
Ishibuchi, H., Tsukamoto, N., Hitotsuyanagi, Y., Nojima, Y.: Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO '08), pp. 649---656. ACM Press, New York (2008)
[49]
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: a short review. In: 2008 IEEE Congress on Evolutionary Computation (2008).
[50]
Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Adaptation of scalarizing functions in MOEA/D: an adaptive scalarizing function-based multiobjective evolutionary algorithm. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 438---452. Springer, Berlin (2009)
[51]
Ishibuchi, H., Hitotsuyanagi, Y., Ohyanagi, H., Nojima, Y.: Effects of the existence of highly correlated objectives on the behavior of MOEA/D. In: Proceedings of the 6th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2011). Lecture Notes in Computer Science, vol. 6576, pp. 166---181. Springer, Berlin (2011)
[52]
Jaimes, López: A., Coello Coello, C., Urías Barrientos, J.E.: Online objective reduction to deal with many-objective problems. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 423---437. Springer, Berlin (2009)
[53]
Jaimes, López: A., Coello Coello, C., Aguirre, H., Tanaka, K.: Adaptive objective space partitioning using conflict information for many-objective optimization. In: Proceedings of the 6th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2011). Lecture Notes in Computer Science, vol. 6576, pp. 151---165. Springer, Berlin (2011)
[54]
Jaszkiewicz, A.: On the performance of multiple-objective genetic local search on the 0/1 knapsack problem--a comparative experiment. IEEE Trans. Evol. Comput. (2002).
[55]
Kauffman, S., Weinberger, E.: The NK model of rugged fitness landscapes and its application to maturation of the immune response. J. Theor. Biol. 141(2), 211---245 (1989)
[56]
Keijzer, M.: Scientific discovery using genetic programming. Ph.D. thesis, Technical University of Denmark, Denmark (2001)
[57]
Khare, V., Yao, X., Deb, K.: Performance scaling of multi-objective evolutionary algorithms. In: Proceedings of the 2nd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003). Lecture Notes in Computer Science, vol. 2632, pp. 376---390. Springer, Berlin (2003)
[58]
Knowles, J., Corne, D.: Quantifying the effects of objective space dimension. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 757---771. Springer, Berlin (2007)
[59]
Kollat, J.B., Reed, P.M.: Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design. Adv. Water Resour. 29(6), 792---807 (2006)
[60]
Köppen, M., Yoshida, K.: Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 727---741. Springer, Berlin (2007)
[61]
Köppen, M., Yoshida, K.: Visualization of Pareto-sets in evolutionary multi-objective optimization. In: 7th International Conference on Hybrid Intelligent Systems, 2007 (HIS 2007), pp. 156---161. IEEE (2007)
[62]
Köppen, M., Vicente-Garcia, R., Nickolay, B.: Fuzzy-Pareto-dominance and its application in evolutionary multi-objective optimization. In: Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005). Lecture Notes in Computer Science, vol. 3410, pp. 399---412. Springer, Berlin (2005)
[63]
Kruisselbrink, J.W., Bäck, T., IJzerman, A.P., van der Horst, E.: Evolutionary algorithms for automated drug design towards target molecule properties. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO '08), pp. 1555---1562. ACM Press, New York (2008)
[64]
Kruisselbrink, J.W., Emmerich, M.T., Bäck, T., Bender, A.: IJzerman, A.P., van der Horst, E.: Combining aggregation with Pareto optimization: a case study in evolutionary molecular design. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 453---467. Springer, Berlin (2009)
[65]
Kukkonen, S., Lampinen, J.: GDE3: The third evolution step of generalized differential evolution. In: 2005 IEEE Congress on Evolutionary Computation (2005).
[66]
Kukkonen, S., Lampinen, J.: Ranking-dominance and many-objective optimization. In: 2007 IEEE Congress on Evolutionary Computation (2007).
[67]
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evol. Comput. (2002).
[68]
Li, M., Zheng, J., Shen, R., Li, K., Yuan, Q.: A grid-based fitness strategy for evolutionary many-objective optimization. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation (GECCO '10), pp. 463---470. ACM Press, New York (2010).
[69]
Lohn, J.D., Kraus, W.F., Haith, G.L.: Comparing a coevolutionary genetic algorithm for multiobjective optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation (2002).
[70]
López Jaimes, A., Coello Coello, C., Chakraborty, D.: Objective reduction using a feature selection technique. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO '08), pp. 673---680. ACM Press, New York (2008)
[71]
López Jaimes, A., Coello Coello, C.: Study of preference relations in many-objective optimization. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation (GECCO '09), pp. 611---618. ACM Press, New York (2009)
[72]
Miettinen, K.: Nonlinear Multiobjective Optimization. Springer, New York (1999)
[73]
Miettinen, K.: Graphical illustration of Pareto optimal solutions. In: Multi-Objective Programming and Goal Programming: Theory and Applications, pp. 197---202. Springer, Berlin (2003)
[74]
Mitra, P., Murthy, C., Pal, S.: Unsupervised feature selection using feature similarity. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 301---312 (2002)
[75]
Mostaghim, S., Branke, J., Schmeck, H.: Multi-objective particle swarm optimization on computer grids. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO '07), pp. 869---875. ACM Press, New York (2007)
[76]
Murata, T., Taki, A.: Many-objective optimization for knapsack problems using correlation-based weighted sum approach. In: Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2009). Lecture Notes in Computer Science, vol. 5467, pp. 468---480. Springer, Berlin (2009)
[77]
Murata, T., Ishibuchi, H., Gen, M.: Specification of genetic search directions in cellular multi-objective genetic algorithms. In: First International Conference on Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, vol. 1993, pp. 82---95. Springer, Berlin (2001).
[78]
Naujoks, B., Beume, N., Emmerich, M.: Multi-objective optimization using S-metric selection: application to three-dimensional solution spaces. In: 2005 IEEE Congress on Evolutionary Computation (2005).
[79]
Obayashi, S., Sasaki, D.: Visualization and data mining of Pareto solutions using self-organizing map. In: Proceedings of the 2nd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003). Lecture Notes in Computer Science, vol. 2632, pp. 796---809. Springer, Berlin (2003)
[80]
Pasia, J., Aguirre, H., Tanaka, K.: Improved random one-bit climbers with adaptive $$\epsilon $$∈-ranking and tabu moves for many-objective optimization. In: Proceedings of the 6th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2011). Lecture Notes in Computer Science, vol. 6576, pp. 182---196. Springer, Berlin (2011)
[81]
Pryke, A., Mostaghim, S., Nazemi, A.: Heatmap visualization of population based multi objective algorithms. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 361---375. Springer, Berlin (2007)
[82]
Purshouse, R., Fleming, P.J.: Conflict, harmony, and independence: relationships in evolutionary multi-criterion optimisation. In: Proceedings of the 2nd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003). Lecture Notes in Computer Science, vol. 2632, pp. 16---30. Springer, Berlin (2003)
[83]
Purshouse, R.C., Fleming, P.J.: Evolutionary multi-objective optimisation: an exploratory analysis. In: 2003 IEEE Congress on Evolutionary Computation (2003).
[84]
Purshouse, R.C., Fleming, P.J.: On the evolutionary optimization of many conflicting objectives. IEEE Trans. Evol. Comput. (2007).
[85]
Purshouse, R., Jalba, C., Fleming, P.: Preference-driven co-evolutionary algorithms show promise for many-objective optimisation. In: Proceedings of the 6th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2011). Lecture Notes in Computer Science, vol. 6576, pp. 136---150. Springer, Berlin (2011)
[86]
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis: The Primer. Wiley-Interscience, Hoboken (2008)
[87]
Sato, H., Aguirre, H.E., Tanaka, K.: Controlling dominance area of solutions and its impact on the performance of MOEAs. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 5---20. Springer, Berlin (2007)
[88]
Sato, H., Aguirre, H.E., Tanaka, K.: Pareto partial dominance MOEA and hybrid archiving strategy included CDAS in many-objective optimization. In: 2010 IEEE Congress on Evolutionary Computation (2010).
[89]
Sato, H., Aguirre, H., Tanaka, K.: Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems. Ann. Math. Artif. Intell. 1---28 (2012).
[90]
Saxena, D.K., Deb, K.: Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: employing correntropy and a novel maximum variance unfolding. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 772---787. Springer, Berlin (2007)
[91]
Saxena, D., Zhang, Q., Duro, J., Tiwari, A.: Framework for many-objective test problems with both simple and complicated Pareto-set shapes. In: Proceedings of the 6th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2011). Lecture Notes in Computer Science, vol. 6576, pp. 197---211. Springer, Berlin (2011)
[92]
Saxena, D., Duro, J., Tiwari, A., Deb, K., Zhang, Q.: Objective reduction in many-objective optimization: Linear and nonlinear algorithms. IEEE Trans. Evol. Comput. (2012).
[93]
Schütze, O., Lara, A.: Coello Coello, C.: On the influence of the number of objectives on the hardness of a multiobjective optimization problem. IEEE Trans. Evol. Comput. (2011).
[94]
Sierra, M.R.: Coello Coello, C.A.: Improving PSO-based multi-objective optimization using crowding, mutation and $$\epsilon $$∈-dominance. In: Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005). Lecture Notes in Computer Science, vol. 3410, pp. 505---519. Springer, Berlin (2005)
[95]
Sülflow, A., Drechsler, N., Drechsler, R.: Robust multi-objective optimization in high dimensional spaces. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 715---726. Springer, Berlin (2007)
[96]
Tanaka, M., Watanabe, H., Furukawa, Y., Tanino, T.: GA-based decision support system for multicriteria optimization. In: Proceedings of the International Conference on Systems. Man, and Cybernetics, vol. 2, pp. 1556---1561. IEEE, Piscataway (1995)
[97]
Teytaud, O.: On the hardness of offline multi-objective optimization. Evol. Comput. (2007).
[98]
Veldhuizen, D.A.V.: Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB (1999)
[99]
Veldhuizen, D.A.V., Lamont, G.B.: Multiobjective evolutionary algorithm research: a history and analysis. Technical report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB (1998)
[100]
Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007). Lecture Notes in Computer Science, vol. 4403, pp. 742---756. Springer, Berlin (2007)
[101]
Walker, D., Fieldsend, J., Everson, R.: Visualising many-objective populations. In: Proceedings of the Fourteenth International Conference on Genetic and Evolutionary Computation Conference Companion (GECCO Companion '12) (2012).
[102]
Weinberger, K.Q., Saul, L.K.: Unsupervised learning of image manifolds by semidefinite programming. Int. J. Comput. Vis. 70(1), 77---90 (2006)
[103]
Xu, J.W., Pokharel, P., Paiva, A., Principe, J.: Nonlinear component analysis based on correntropy. In: International Joint Conference on Neural Networks, 2006 (IJCNN '06), pp. 1851---1855 (2006)
[104]
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. (2007).
[105]
Zhang, Q., Liu, W., Li, H.: The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: 2009 IEEE Congress on Evolutionary Computation (2009).
[106]
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Parallel Problem Solving from Nature (PPSN VIII). Lecture Notes in Computer Science, vol. 3242, pp. 832---842. Springer, Berlin (2004)
[107]
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms--a comparative study. In: Parallel Problem Solving from Nature (PPSN V), pp. 292---301. Springer, Amsterdam (1998)
[108]
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. (1999).
[109]
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. (2000).
[110]
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm. Technical report 103, Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology Zurich (2001)
[111]
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. (2003).
[112]
Zou, X., Chen, Y., Liu, M., Kang, L.: A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans. Syst. Man Cybern. B 38(5), 1402---1412 (2008)

Cited By

View all
  • (2024)Handling Varied Objectives by Online Decision MakingProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671812(2130-2140)Online publication date: 25-Aug-2024
  • (2024)Distributed genetic algorithm for application placement in the compute continuum leveraging infrastructure nodes for optimizationFuture Generation Computer Systems10.1016/j.future.2024.05.044160:C(154-170)Online publication date: 1-Nov-2024
  • (2024)A many-objective evolutionary algorithm under diversity-first selection based frameworkExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123949250:COnline publication date: 18-Jul-2024
  • Show More Cited By
  1. A survey on multi-objective evolutionary algorithms for many-objective problems

      Recommendations

      Comments

      Please enable JavaScript to view thecomments powered by Disqus.

      Information & Contributors

      Information

      Published In

      cover image Computational Optimization and Applications
      Computational Optimization and Applications  Volume 58, Issue 3
      July 2014
      278 pages

      Publisher

      Kluwer Academic Publishers

      United States

      Publication History

      Published: 01 July 2014

      Author Tags

      1. Many-objective optimization
      2. Multi-objective evolutionary algorithms
      3. Multi-objective optimization problems

      Qualifiers

      • Article

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)0
      • Downloads (Last 6 weeks)0
      Reflects downloads up to 01 Jan 2025

      Other Metrics

      Citations

      Cited By

      View all
      • (2024)Handling Varied Objectives by Online Decision MakingProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671812(2130-2140)Online publication date: 25-Aug-2024
      • (2024)Distributed genetic algorithm for application placement in the compute continuum leveraging infrastructure nodes for optimizationFuture Generation Computer Systems10.1016/j.future.2024.05.044160:C(154-170)Online publication date: 1-Nov-2024
      • (2024)A many-objective evolutionary algorithm under diversity-first selection based frameworkExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123949250:COnline publication date: 18-Jul-2024
      • (2024)A dual distance dominance based evolutionary algorithm with selection-replacement operator for many-objective optimizationExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.121244237:PAOnline publication date: 27-Feb-2024
      • (2022)Optimal planning of a quantum key distribution systemProceedings of the 2022 Latin America Networking Conference10.1145/3545250.3560850(26-33)Online publication date: 19-Oct-2022
      • (2022)Pursuing Optimal Trade-Off Solutions in Multi-Objective Recommender SystemsProceedings of the 16th ACM Conference on Recommender Systems10.1145/3523227.3547425(727-729)Online publication date: 12-Sep-2022
      • (2022)A survey of recommender systems with multi-objective optimizationNeurocomputing10.1016/j.neucom.2021.11.041474:C(141-153)Online publication date: 14-Feb-2022
      • (2022)Collaborative granular sievingInformation Sciences: an International Journal10.1016/j.ins.2022.09.007613:C(288-308)Online publication date: 1-Oct-2022
      • (2022)Dynamic computation offloading for ground and flying robotsComputer Science Review10.1016/j.cosrev.2022.10048845:COnline publication date: 1-Aug-2022
      • (2022)A review of Pareto pruning methods for multi-objective optimizationComputers and Industrial Engineering10.1016/j.cie.2022.108022167:COnline publication date: 1-May-2022
      • Show More Cited By

      View Options

      View options

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media