Definição de regiões de interesse em problemas multiobjetivo utilizando hiper-elipses

• Patrick P. F. Ferreira Unimontes
• Luciana B. Cosme IFNMG
• Allysson S. M. Lacerda Unimontes

DOI: https://doi.org/10.5753/eniac.2021.18270

Abstract

This paper presents a new methodology to incorporate preferences in multiobjective problems through the definition of an ellipsoid-shapped region of interest. This new layer aplied to the optimization algorithm aims to help the decision making, as the method shows solutions according to the defined preferences.Futhermore, the ellipsoid shape allows the user to change the quantity of selected elements by changing the ellipsoid focus, expanding or shrinking the coverage area of the Pareto frontier.

References

Aguilera, A. and Pérez-Aguila, R. (2004). General n-dimensional rotations.

Bechikh, S., Kessentini, M., Said, L. B., and Ghédira, K. (2015). Chapter four preference incorporation in evolutionary multiobjective optimization: A survey of the state-of-theart. volume 98 of Advances in Computers, pages 141–207. Elsevier.

Branke, J. and Deb, K. (2005). Integrating User Preferences into Evolutionary MultiObjective Optimization, pages 461–477. Springer Berlin Heidelberg, Berlin, Heidelberg.

Branke, J., Kaußler, T., and Schmeck, H. (2001). Guidance in evolutionary multiobjective optimization. Advances in Engineering Software, 32(6):499–507.

Coello, C. A. C., Lamont, G. B., and Veldhuizen, D. A. V. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems. Springer-Verlag, Berlin, Heidelberg.

Costa, N. R., Lourenço, J., and Pereira, Z. L. (2011). Desirability function approach: A review and performance evaluation in adverse conditions. Chemometrics and Intelligent Laboratory Systems, 107(2):234–244.

Deb, K. (2001). Multiobjective Optimization Using Evolutionary Algorithms. Wiley, New York.

Deb, K. (2003). Multi-objective Evolutionary Algorithms: Introducing Bias Among Pareto-optimal Solutions, pages 263–292. Springer Berlin Heidelberg, Berlin, Heidelberg.

Deb, K., Sinha, A., Korhonen, P. J., and Wallenius, J. (2010). An interactive evolutionary multiobjective optimization method based on progressively approximated value functions. IEEE Transactions on Evolutionary Computation, 14(5):723–739.

Deb, K., Thiele, L., Laumanns, M., and Zitzler, E. (2002). Scalable multi-objective optimization test problems. In Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No.02TH8600), volume 1, pages 825–830 vol.1.

Duffin, K. and Barrett, W. (1994). Spiders: a new user interface for rotation and visualization of n-dimensional point sets. In Proceedings Visualization ’94, pages 205–211.

Filatovas, E., Kurasova, O., Redondo, J. L., and Fernández, J. (2020). A reference pointbased evolutionary algorithm for approximating regions of interest in multiobjective problems. TOP, 28:402–423.

Meneghini, I. R., Guimarães, F. G., Gaspar-Cunha, A., and Cohen, M. W. (2021). Incorporation of Region of Interest in a Decomposition-Based Multi-objective Evolutionary Algorithm, pages 35–50. Springer International Publishing, Cham.

Qi, Y., Li, X., Yu, J., and Miao, Q. (2019). User-preference based decomposition in moea/d without using an ideal point. Swarm and Evolutionary Computation, 44:597– 611.

Rachmawati, L. and Srinivasan, D. (2010). Incorporating the notion of relative importance of objectives in evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation, 14(4):530–546.

Santos, W., Silva, L., and Britto, A. (2019). Incorporation of restriction treatment techniques based on the particle swarm optimization metaheuristic in the software project scheduling problem in software projects. In Anais do XVI Encontro Nacional de Inteligência Artificial e Computacional, pages 503–514, Porto Alegre, RS, Brasil. SBC.

Tee, G. (2005). Surface area and capacity of ellipsoids in n dimensions. (citr). volume 34, pages 165–198.

Wagner, T. and Trautmann, H. (2010). Integration of preferences in hypervolume-based multiobjective evolutionary algorithms by means of desirability functions. IEEE Transactions on Evolutionary Computation, 14(5):688–701.

Wolbert, G. (1988). Geometric transformation techniques for digital images: A survey. Columbia University Computer Science Technical Reports, CUCS-390-88. Department of Computer Science, Columbia University.