Abstract
Solving multi-objective problems usually results in a set of Perto-optimal solutions, or a Pareto front. Assessing the quality of these solutions, however, and comparing the performance of different multi-objective optimisers is still not very well understood. Current trends either model the outcome of the optimiser as a probability density function in the objective space, or defines an indicator that quantify the overall performance of the optimiser. Here an approach based on the concept of mutual information is proposed. The approach models the probability density function of the optimisers’ output and use that to define an indicator, namely the amount of shared information among the compared Pareto fronts. The strength of the new approach is not only in better assessment of performance but also the interpretability of the results it provides.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Talbi, E.: Metaheuristics - From Design to Implementation. Wiley (2009)
Coello, C.A.C., Lamont, G.B., Veldhuizen, D.A.V.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Genetic and Evolutionary Computation. Springer, New York (2007)
Deb, K.: Multi-objective optimization. In: Multi-Objective Optimization using Evolutionary Algorithms, pp. 13–46 (2001)
Al Moubayed, N., Hasan, B.A.S., Gan, J.Q., Petrovski, A., McCall, J.: Continuous presentation for multi-objective channel selection in brain-computer interfaces. In: 2012 IEEE Congress on Evolutionary Computation (CEC), pp. 1–7. IEEE (2012)
Fonseca, C.M., Knowles, J.D., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. In: Third International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005), vol. 216 (2005)
Fonseca, C.M., da Fonseca, V.G., Paquete, L.: Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function. In: Coello, C.A.C., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 250–264. Springer, Heidelberg (2005)
Grunert da Fonseca, V., Fonseca, C.M., Hall, A.O.: Inferential performance assessment of stochastic optimisers and the attainment function. In: Zitzler, E., Deb, K., Thiele, L., Coello, C.A.C., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 213–225. Springer, Heidelberg (2001)
Van Veldhuizen, D.A., Lamont, G.B.: Multiobjective evolutionary algorithm research: A history and analysis. Air Force Inst. Technol., Dayton, OH. Tech. Rep. TR-98-03 (1998)
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.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Scott, D.W.: On optimal and data-based histograms. Biometrika 66(3), 605–610 (1979)
Witten, I.H., Frank, E.: Data Mining: Practical machine learning tools and techniques. Morgan Kaufmann (2005)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Evolutionary Multiobjective Optimization, pp. 105–145 (2005)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: Nsga-ii. IEEE Trans. on Evolutionary Computation 6(2), 181–197 (2002)
Zitzler, E., Laumanns, M., Thiele, L.: Spea2: Improving the strength pareto evolutionary algorithm (2001)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moubayed, N.A., Petrovski, A., McCall, J. (2013). Mutual Information for Performance Assessment of Multi Objective Optimisers: Preliminary Results. In: Yin, H., et al. Intelligent Data Engineering and Automated Learning – IDEAL 2013. IDEAL 2013. Lecture Notes in Computer Science, vol 8206. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41278-3_65
Download citation
DOI: https://doi.org/10.1007/978-3-642-41278-3_65
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41277-6
Online ISBN: 978-3-642-41278-3
eBook Packages: Computer ScienceComputer Science (R0)