Abstract
In this paper, we elaborate how decision space diversity can be integrated into indicator-based multiobjective search. We introduce DIOP, the diversity integrating multiobjective optimizer, which concurrently optimizes two set-based diversity measures, one in decision space and the other in objective space. We introduce a possibility to improve the diversity of a solution set, where the minimum proximity of these solutions to the Pareto-front is user-defined. Experiments show that DIOP is able to optimize both diversity measures and that the decision space diversity can indeed be improved if the required maximum distance of the solutions to the front is relaxed.
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References
Conover, W.J.: Practical Nonparametric Statistics, 3rd edn. John Wiley, Chichester (1999)
Deb, K., Agrawal, S.: A niched-penalty approach for constraint handling in genetic algorithms. In: ICANNGA (1999)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multi-Objective Optimization. TIK Report 112, ETH Zurich (2001)
Deb, K., Tiwari, S.: Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization. EJOR 185(3), 1062–1087 (2008)
Gaston, K.J., Spicer, J.I.: Biodiversity: An Introduction, 2nd edn. Wiley-Blackwell, Chichester (2004)
Izsák, J., Papp, L.: A link between ecological diversity indices and measures of biodiversity. Ecological Modelling 130(1-3), 151–156 (2000)
Li, X., Zheng, J., Xue, J.: A Diversity Metric for Multi-objective Evolutionary Algorithms. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 68–73. Springer, Heidelberg (2005)
Rudolph, G., Naujoks, B., Preuss, M.: Capabilities of EMOA to detect and preserve equivalent pareto subsets. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 36–50. Springer, Heidelberg (2007)
Sarma, J., Jong, K.A.D.: An analysis of the effects of neighborhood size and shape on local selection algorithms. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 236–244. Springer, Heidelberg (1996)
Shimodaira, H.: A diversity-control-oriented genetic algorithm (dcga): Performance in function optimization. In: Genetic and Evolutionary Computation Conference, p. 366 (2000)
Shir, O.M., Preuss, M., Naujoks, B., Emmerich, M.: Enhancing decision space diversity in evolutionary multiobjective algorithms. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 95–109. Springer, Heidelberg (2009)
Solow, A.R., Polasky, S.: Measuring biological diversity. Environmental and Ecological Statistics 1(2), 95–103 (1994)
Squillero, G., Tonda, A.P.: A novel methodology for diversity preservation in evolutionary algorithms. In: GECCO, pp. 2223–2226. ACM, New York (2008)
Srinivas, N., Deb, K.: Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation 2(3), 221–248 (1994)
Toffolo, A., Benini, E.: Genetic diversity as an objective in multi-objective evolutionary algorithms. Evolutionary Computation 11(2), 151–167 (2003)
Tsutsui, S., Fujimoto, Y., Ghosh, A.: Forking genetic algorithms: Gas with search space division schemes. Evolutionary Computation 5(1), 61–80 (1997)
Ulrich, T., Bader, J., Zitzler, E.: Integrating Decision Space Diversity into Hypervolume-based Multiobjective Search. In: Genetic and Evolutionary Computation Conference (to appear, 2010)
Ursem, R.K.: Diversity-guided evolutionary algorithms. In: Congress on Evolutionary Computation, pp. 1633–1640 (2002)
Weitzman, M.: On diversity. The Quarterly Journal of Economics 107(2), 363–405 (1992)
Zhou, A., Zhang, Q., Jin, Y.: Approximating the set of pareto optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Transactions on Evolutionary Computation (2009) (accepted)
Zitzler, E., Thiele, L., Bader, J.: On Set-Based Multiobjective Optimization (Revised Version). TIK Report 300, ETH Zurich (2008)
Zitzler, E., Thiele, L., Bader, J.: On Set-Based Multiobjective Optimization. IEEE Transactions on Evolutionary Computation (2009) (to appear)
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Ulrich, T., Bader, J., Thiele, L. (2010). Defining and Optimizing Indicator-Based Diversity Measures in Multiobjective Search. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_71
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DOI: https://doi.org/10.1007/978-3-642-15844-5_71
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