Abstract
Research within the area of Evolutionary Multi-objective Optimization (EMO) focused on two- and three-dimensional objective functions, so far. Most algorithms have been developed for and tested on this limited application area. To broaden the insight in the behavior of EMO algorithms (EMOA) in higher dimensional objective spaces, a comprehensive benchmarking is presented, featuring several state-of-the-art EMOA, as well as an aggregative approach and a restart strategy on established scalable test problems with three to six objectives. It is demonstrated why the performance of well-established EMOA (NSGA-II, SPEA2) rapidly degradates with increasing dimension. Newer EMOA like ε-MOEA, MSOPS, IBEA and SMS-EMOA cope very well with high-dimensional objective spaces. Their specific advantages and drawbacks are illustrated, thus giving valuable hints for practitioners which EMOA to choose depending on the optimization scenario. Additionally, a new method for the generation of weight vectors usable in aggregation methods is presented.
Keywords
- Weight Vector
- Pareto Front
- Objective Space
- Target Vector
- Extremal Solution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Farina, M., Amato, P.: On the optimal solution definition for many-criteria optimization problems. In: Keller, J., Nasraoui, O. (eds.) Proc. of the NAFIPS-FLINT Int’l Conf. 2002, pp. 233–238. IEEE Computer Society Press, Piscataway (2002)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)
Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, New York (2002)
Purshouse, R.C., Fleming, P.J.: Evolutionary Multi-Objective Optimisation: An Exploratory Analysis. In: Proc. of the 2003 Congress on Evolutionary Computation (CEC’2003), vol. 3, Canberra, Australia, pp. 2066–2073. IEEE Press, Los Alamitos (2003)
Hughes, E.J.: Evolutionary Many-Objective Optimisation: Many Once or One Many? In: Evolutionary Computation ’Congress (CEC’05), Edinburgh, UK, vol. 1, pp. 222–227. IEEE Press, Piscataway (2005)
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)
Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA — a platform and programming language independent interface for search algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 494–508. Springer, Heidelberg (2003)
Deb, K., Mohan, M., Mishra, S.: A Fast Multi-objective Evolutionary Algorithm for Finding Well-Spread Pareto-Optimal Solutions. KanGAL report 2003002, Indian Institute of Technology, Kanpur, India (2003)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-objective Optimization Test Problems. In: Proc. of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 825–830. IEEE Press, Piscataway (2002)
Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms—A Comparative Case Study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN V. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Naujoks, B., Beume, N., Emmerich, M.: Multi-objective optimisation using S-metric selection: Application to three-dimensional solution spaces. In: Evolutionary Computation Congress (CEC’05), Edinburgh, UK, pp. 1282–1289. IEEE Press, Piscataway (2005)
Jensen, M.T.: Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms. IEEE Transactions On Evolutionary Computation 7(5), 503–515 (2003)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zürich, Switzerland (2001)
Silverman, B.W.: Density estimation for statistics and data analysis. Chapman and Hall, London (1986)
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation 10(3), 263–282 (2002)
Rudolph, G., Agapie, A.: Convergence properties of some multi-objective evolutionary algorithms. In: Zalzala, A., Eberhart, R. (eds.) Congress on Evolutionary Computation (CEC2000), vol. 2, pp. 1010–1016. IEEE Press, Piscataway (2000)
Hughes, E.J.: Multiple Single Objective Pareto Sampling. In: Congress on Evolutionary Computation (CEC’03), IEEE Press, Piscataway (2003)
Ostermeier, A., Gawelczyk, A., Hansen, N.: Step-size adaptation based on non-local use of selection information. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN III. LNCS, vol. 866, pp. 189–198. Springer, Heidelberg (1994)
Hansen, N., Ostermeier, A.: Completely Derandomized Self-Adaptation in Evolution Strategies. IEEE Computational Intelligence Magazine 9(2), 159–195 (2001)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN VIII. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005)
Beume, N., Rudolph, G.: Faster S-Metric Calculation by Considering Dominated Hypervolume as Klee’s Measure Problem. In: International Conference on Computational Intelligence (CI (2006) (in print, 2006)
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Wagner, T., Beume, N., Naujoks, B. (2007). Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_56
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DOI: https://doi.org/10.1007/978-3-540-70928-2_56
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