Evenly spaced Pareto front approximations for tricriteria problems based on triangulation

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7811 LNCS, Issue , 2013, Pages 443-458

  Rudolph, Günter ^a   Trautmann, Heike ^a   Sengupta, Soumyadip ^b   Schütze, Oliver ^c  

^a TU DORTMUND UNIVERSITY   (Germany)

^b JADAVPUR UNIVERSITY   (India)

^c DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

averaged Hausdorff measure; evenly spaced Pareto front approximation; evolutionary multiobjective algorithm; multiobjective optimization; triangulation

Indexed keywords

EVOLUTIONARY MULTI-OBJECTIVE ALGORITHMS; EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION; HAUSDORFF MEASURES; MULTI OBJECTIVE; OFFLINE MODES; ON-LINE CONTROLS; PARETO FRONT; TECHNICAL APPLICATIONS;

APPROXIMATION ALGORITHMS; EVOLUTIONARY ALGORITHMS; MULTIOBJECTIVE OPTIMIZATION; TRIANGULATION;

PARETO PRINCIPLE;

EID: 84875495403     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-37140-0_34     Document Type: Conference Paper

References (23)

1. Zitzler, E., Knowles, J., Thiele, L.: Quality Assessment of Pareto Set Approximations. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 373-404. Springer, Heidelberg (2008)
2. Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653-1669 (2007)
3. Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Theory of the Hypervolume Indicator: Optimal ì-Distributions and the Choice of the Reference Point. In: Foundations of Genetic Algorithms (FOGA 2009), pp. 87-102. ACM, New York (2009)
4. Brockhoff, D., Wagner, T., Trautmann, H.: On the properties of the R2 indicator. In: Soule, T., et al. (eds.) Proc. 14th Int'l Genetic and Evolutionary Computation Conference (GECCO 2012), pp. 465-472. ACM (2012)
5. Liu, G., Yang, J., Whidborne, J.: Multiobjective Optimisation and Control. Research Studies Press Ltd., Baldock (UK) (2003)
6. Schütze, O., Esquivel, X., Lara, A., Coello Coello, C.A.: Using the averaged Hausdorff distance as a performance measure in evolutionary multi-objective optimization. IEEE Transactions on Evolutionary Computation 16(4), 504-522 (2012)
7. Gerstl, K., Rudolph, G., Schütze, O., Trautmann, H.: Finding evenly spaced fronts for multiobjective control via averaging Hausdorff-measure. In: Proceedings of 8th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), pp. 1-6. IEEE Press (2011)
8. Trautmann, H., Rudolph, G., Dominguez-Medina, C., Schütze, O.: Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems. In: Schütze, O., Coello Coello, C.A., Tantar, A.-A., Tantar, E., Bouvry, P., Del Moral, P., Legrand, P. (eds.) EVOLVE - A Bridge Between Probability. AISC, vol. 175, pp. 89-105. Springer, Heidelberg (2013)
9. Pareto, V.: Manual of Political Economy. The MacMillan Press (1971)
10. Veldhuizen, D.A.V.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering. Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1999)
11. Coello Coello, C.A., Cruz Cortés, N.: Solving Multiobjective Optimization Problems using an Artificial Immune System. Genetic Programming and Evolvable Machines 6(2), 163-190 (2005)
12. De Loera, J.A., Rambau, J., Santos, F.: Triangulations - Structures for Algorithms and Applications. Springer, Berlin (2010)
13. Pateiro-Lopez, B., Rodriguez-Casal, A.: Generalizing the convex hull of a sample: The R package alphahull. Journal of Statistical Software 34(5), 1-28 (2010)
14. Bertsimas, D., Tsitsiklis, J.: Introduction to Linear Optimization, 1st edn. Athena Scientific (1997)
15. Mersmann, O., Bischl, B., Bossek, J., Trautmann, H., Wagner, M., Neumann, F.: Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness. In: Hamadi, Y., Schoenauer, M. (eds.) LION 6. LNCS, vol. 7219, pp. 115-129. Springer, Heidelberg (2012)
16. Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: A case study in local optimization. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization. Wiley (1997)
17. Applegate, D., Cook, W.J., Dash, S., Rohe, A.: Solution of a min-max vehicle routing problem. INFORMS Journal on Computing 14(2), 132-143 (2002)
18. Jain, A.K., Dubes, R.C.: Algorithms for clustering data. Prentice-Hall, Inc., Upper Saddle River (1988)
19. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Fogel, D., et al. (eds.) Proc. Int'l Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 825-830. IEEE press (2002)
20. Viennet, R., Fontiex, C., Marc, I.: Multicriteria optimization using a genetic algorithm for determining a pareto set. International Journal of Systems Science 27(2), 255-260 (1996)
21. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182-197 (2002)
22. Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evolutionary Computation 11(6), 712-731 (2007)
23. Kukkonen, S., Deb, K.: Improved pruning of non-dominated solutions based on crowding distance for bi-objective optimization problems. In: Proc. Congress on Evolutionary Computation (CEC 2006), vol. 1, pp. 1179-1186. IEEE Press, Piscataway (2006)