×

Using objective clustering for solving many-objective optimization problems. (English) Zbl 1299.90445

Summary: Many-objective optimization problems involving a large number (more than four) of objectives have attracted considerable attention from the evolutionary multiobjective optimization field recently. With the increasing number of objectives, many-objective optimization problems may lead to stagnation in search process, high computational cost, increased dimensionality of Pareto-optimal front, and difficult visualization of the objective space. In this paper, a special kind of many-objective problems which has redundant objectives and which can be degenerated to a lower dimensional Pareto-optimal front has been investigated. Different from the works in the previous literatures, a novel metric, interdependence coefficient, which represents the nonlinear relationship between pairs of objectives, is introduced in this paper. In order to remove redundant objectives, PAM clustering algorithm is employed to identify redundant objectives by merging the less conflict objectives into the same cluster, and one of the least conflict objectives is removed. Furthermore, the potential of the proposed algorithm is demonstrated by a set of benchmark test problems scaled up to 20 objectives and a practical engineering design problem.

MSC:

90C90 Applications of mathematical programming
90C29 Multi-objective and goal programming
62H30 Classification and discrimination; cluster analysis (statistical aspects)

Software:

MSOPS-II; clusfind
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] C. A. Coello Coello, G. B. Lamont, and D. A. van Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems, Springer, New York, NY, USA, 2009. · Zbl 1142.90029
[2] H. Ishibuchi, N. Tsukamoto, and Y. Nojima, “Evolutionary many-objective optimization: a short review,” in Proceedings of IEEE Congress on Evolutionary Computation (CEC ’08), pp. 2419-2426, IEEE Service Center, Hong Kong, June 2008.
[3] P. J. Bentley and J. P. Wakefield, “Finding acceptable solutions in the pareto-optimal range using mult-iobjective genetic algorithms,” in Soft Computing in Engineering Design and Manufacturing,, pp. 231-240, Springer, London, UK, 1997.
[4] N. Drechsler, R. Drechsler, and B. Becker, “Multi-objective optimisation based on relation favour,” in Evolutionary Multi-Criterion Optimization (Zurich, 2001), vol. 1993 of Lecture Notes in Computer Science, pp. 154-166, Springer, Berlin, 2001.
[5] F. di Pierro, S. T. Khu, and D. A. Savić, “An investigation on preference order ranking scheme for multiobjective evolutionary optimization,” IEEE Transactions on Evolutionary Computation, vol. 11, no. 1, pp. 17-45, 2007. · Zbl 05516189
[6] X. Zou, Y. Chen, M. Liu, and L. Kang, “A new evolutionary algorithm for solving many-objective optimization problems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 38, no. 5, pp. 1402-1412, 2008.
[7] E. J. Hughes, “Multiple single objective pareto sampling,” in Congress on Evolutionary Computation, pp. 2678-2684, IEEE Press, December 2003.
[8] E. J. Hughes, “MSOPS-II: a general-purpose many-objective optimiser,” in Proceedings of IEEE Congress on Evolutionary Computation (CEC ’07), pp. 3944-3951, Singapore, September 2007.
[9] H. J. F. Moen and S. Kristoffersen, “Spanning the pareto front of a counter radar detection problem,” in Proceedings of the 13th Annual Genetic and Evolutionary Computation Conference (GECCO ’11), pp. 1835-1842, Dublin, Ireland, 2011.
[10] K. Deb and R. Datta, “Hybrid evolutionary multi-objective optimization and analysis of machining operations,” Engineering Optimization, vol. 44, no. 6, pp. 685-706, 2012.
[11] D. Brockhoff and E. Zitzler, “Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization,” in Parallel Problem Solving from Nature, vol. 4193 of Lecture Notes in Computer Science, pp. 533-542, Springer, 2006.
[12] A. López Jaimes, C. A. Coello Coello, and J. E. Urías Barrientos, “Online objective reduction to deal with many-objective problems,” in Evolutionary Multi-Criterion Optimization, vol. 5467 of Lecture Notes in Computer Science, pp. 423-437, 2010. · Zbl 05546878
[13] A. L. Jaimes, C. A. Coello Coello, and D. Chakraborty, “Objective reduction using a feature selection technique,” in Proceedings of the 10th Annual Genetic and Evolutionary Computation Conference (GECCO ’08), pp. 673-680, July 2008.
[14] D. Brockhoff and E. Zitzler, “Improving hypervolume-based multiobjective evolutionary algorithms by using objective reduction methods,” in Proceedings of IEEE Congress on Evolutionary Computation (CEC ’07), pp. 2086-2093, September 2007.
[15] D. Brockhoff and E. Zitzler, “Objective reduction in evolutionary multiobjective optimization: theory and applications,” Evolutionary Computation, vol. 17, no. 2, pp. 135-166, 2009. · Zbl 05741867
[16] K. Deb and D. Saxena, “On finding pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems,” Kangal Technique Report, 2005.
[17] K. Deb and D. K. Saxena, “Searching for pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems,” in Congress on Evolutionary Computation (CEC ’06), pp. 3353-3360, 2006.
[18] D. K. Saxena and K. Deb, “Objective reduction in many-objective optimization: linear and nonlinear algorithm,” Kangal Technique Report, 2010.
[19] T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley Series in Telecommunications, John Wiley & Sons, New York, NY, USA, 1991. · Zbl 0762.94001
[20] W. Li, “Mutual information functions versus correlation functions,” Journal of Statistical Physics, vol. 60, no. 5-6, pp. 823-837, 1990. · Zbl 1086.82554
[21] L. Kaufman and P. J. Rousseeuw, Finding Groups in Data: An Introduction to Cluster Analysis, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, New York, NY, USA, 1990. · Zbl 1345.62009
[22] R. Ng and J. Han, “Effecient and effictive clustering methods for spatial data mining,” in Proceedings of the 20th International Conference on Very Large Data Bases (VLDB ’94), Santiago de Chile, Chile, 1994.
[23] K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable multiobjective optimization test problems,” in Proceedings of IEEE Congress on Evolutionary Computation, pp. 825-830, 2002. · Zbl 1078.90567
[24] K. . Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable test problems for evolutionary multi-objective optimization,” in Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, A. Abraham, R. Jain, and R. Goldberg, Eds., chapter 6, pp. 105-145, Springer, 2005. · Zbl 1078.90567
[25] S. Huband, P. Hingston, L. Barone, and L. While, “A review of multiobjective test problems and a scalable test problem toolkit,” IEEE Transactions on Evolutionary Computation, vol. 10, no. 5, pp. 477-506, 2006. · Zbl 1109.68603
[26] X. Guo, X. Wang, M. Wang, and Y. Wang, “A new objective reduction algorithm for many-objective problems: employing mutual information and clustering algorithm,” in Proceedings of the 8th International Conference on Computational Intelligence and Security (CIS ’12), IEEE Press, 2012.
[27] K. Musselman and J. Talavage, “A tradeoff cut approach to multiple objective optimization,” Operations Research, vol. 28, no. 6, pp. 1424-1435, 1980. · Zbl 0447.90076
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.