Abstract
This work discusses robustness assessment during multi-objective optimization with a Multi-Objective Evolutionary Algorithm (MOEA) using a combination of two types of robustness measures. Expectation quantifies simultaneously fitness and robustness, while variance assesses the deviation of the original fitness in the neighborhood of the solution. Possible equations for each type are assessed via application to several benchmark problems and the selection of the most adequate is carried out. Diverse combinations of expectation and variance measures are then linked to a specific MOEA proposed by the authors, their selection being done on the basis of the results produced for various multi-objective benchmark problems. Finally, the combination preferred plus the same MOEA are used successfully to obtain the fittest and most robust Pareto optimal frontiers for a few more complex multi-criteria optimization problems.
Similar content being viewed by others
References
Schaffer, J.D.: Some experiments in machine learning using vector evaluated genetic algorithms. Ph.D. thesis, Vanderbilt University, Nashville, TN (1984)
Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423. Morgan Kauffman, Los Altos (1993)
Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2, 221–248 (1995)
Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched Pareto genetic algorithm for multiobjective optimization, In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 82–87 (1994)
Deb, K., Pratap, A., Agrawal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGAII. IEEE Trans. Evol. Comput. 6, 182–197 (2002)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm. TIK report no. 103, Swiss Federal Institute of Technology, Zurich, Switzerland (2001)
Knowles, J.D., Corne, D.W.: Approximating the non-dominated front using the Pareto archived evolutionary strategy. Evol. Comput. J. 8, 149–172 (2000)
Deb, K.: Multi-Objective Optimisation Using Evolutionary Algorithms. Wiley, New York (2001)
Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, Dordrecht (2002)
Ray, T.: Constrained robust optimal design using a multiobjective evolutionary algorithm. In: Proceedings of the 2002 Congress on Evolutionary Computation—CEC’02, pp. 419–424 (2002)
Jin, Y., Sendhoff, B.: Trade-off between performance and robustness: an evolutionary multiobjective approach. In: Second International Conference on Evolutionary Multi-Objective Optimization—EMO’2003, Faro, Portugal, pp. 237–251 (2003)
Jin, Y., Branke, J.: Evolutionary optimization in uncertain environments—a survey. IEEE Trans. Evol. Comput. 9, 303–317 (2005)
Wiesmann, D., Hammel, U., Bäck, T.: Robust design of multilayer optical coatings by means of evolutionary algorithms. IEEE Trans. Evol. Comput. 2, 162–167 (1998)
Das, I.: Nonlinear multicriteria optimization and robust optimality. Ph.D. thesis, Rice University, Houston, TX, USA (1997)
Tsutsui, S., Ghosh, A.: Genetic algorithms with a robust solution scheme. IEEE Trans. Evol. Comput. 1, 201–208 (1997)
Chen, W., Sahai, A., Messac, A., Sundararaj, G.J.: Physical programming for robust design. In: 40th Structures, Structural Dynamics and Materials Conference, St. Louis, USA (1999)
Deb, K., Gupta, H.: Searching for robust Pareto-optimal solutions in multi-objective optimization. In: Proceedings of the Third International Conference on Evolutionary Multi-Criterion Optimization (EMO-2005), Guanajuato, Mexico. Lecture Notes in Computer Science, vol. 3410, pp. 150–164. Springer, Berlin (2005)
Gaspar-Cunha, A., Oliveira, P., Covas, J.A.: Use of genetic algorithms in multicriteria optimization to solve industrial problems. In: Seventh International Conference on Genetic Algorithms, Michigan, USA, pp. 682–688 (1997)
Gaspar-Cunha, A., Covas, J.A.: RPSGAe—a multiobjective genetic algorithm with elitism: application to polymer extrusion. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’kindt, V. (eds.) Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, pp. 221–249. Springer, Berlin (2004)
Goldberg, D.E.: Genetic Algorithms in Search, Optimisation and Machine Learning. Addison-Wesley, Reading (1989)
Gaspar-Cunha, A.: Modelling and optimisation of single screw extrusion. Ph.D. thesis, University of Minho, Guimarães, Portugal (2000)
Roseman, M.A., Gero, J.S.: Reducing the Pareto optimal set in multicriteria optimization. Eng. Optim. 8, 189–206 (1985)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8, 173–195 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gaspar-Cunha, A., Covas, J.A. Robustness in multi-objective optimization using evolutionary algorithms. Comput Optim Appl 39, 75–96 (2008). https://doi.org/10.1007/s10589-007-9053-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10589-007-9053-9