Abstract
Before Multiobjective Evolutionary Algorithms (MOEAs) can be used as a widespread tool for solving arbitrary real world problems there are some salient issues which require further investigation. One of these issues is how a uniform distribution of solutions along the Pareto non-dominated front can be obtained for badly scaled objective functions. This is especially a problem if the bounds for the objective functions are unknown, which may result in the non-dominated solutions found by the MOEA to be biased towards one objective, thus resulting in a less diverse set of tradeoffs. In this paper, the issue of obtaining a diverse set of solutions for badly scaled objective functions will be investigated and the proposed solutions will be implemented using the NSGA-II algorithm.
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
Parmee, I.C., Watson, A.H.: Preliminary airframe design using co-evolutionary multiobjective genetic algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 1657–1665 (1999)
Das, D.B., Patvardhan, C.: New multi-objective stochastic search technique for economic load dispatch. IEEE Proceedings of Generation. Transmission and Distribution 145, 747–752 (1998)
Dozier, G., McCullough, S., Homaifar, A., Tunstel, E., Moore, L.: Multiobjective evolutionary path planning via fuzzy tournament selection. In: Proceedings of 1998 IEEE International Conference on Evolutionary Computation, pp. 684–689 (1998)
Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Genetic Algorithms and Evolutionary Computation. Kluwer Academic Publishers, NewYork (2002)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms, 1st edn. John Wiley & Sons, Ltd., West Sussex (2001)
Deb, K., Pratap, A., Moitra, S.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000) NSGA-II code available at KanGAL website: http://www.iitk.ac.in/kangal/
Obayashi, S.: Pareto genetic algorithm for aerodynamic design using the Navier-Stokes equations. In: Quagliarella, D., Périaux, J., Poloni, C., Winter, G. (eds.) Genetic Algorithms and Evolution Strategies in Engineering and Computer Science, pp. 245–266. John Wiley & Sons, Ltd., Trieste (1997)
Deb, K., Mohan, M., Mishra, S.: A fast multi-objective evolutionary algorithm for finding well-spread pareto-optimal solutions. Technical Report 2003002, Kanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur, Kanpur, PIN 208016, India (2003)
Bentley, P.J., Wakefield, J.P.: Finding acceptable solutions in the pareto-optimal range using multiobjective genetic algorithms. In: Proceedings of the Second Online World Conference on Soft Computing in Engineering Design and Manufacturing (WSC2), vol. 5, pp. 231–240 (1998)
Knowles, J.D., Corne, D.W.: The pareto archived evolution strategy: Anewbaseline algorithm for pareto multiobjective optimisation. In: Proceedings of 1999 IEEE International Conference on Evolutionary Computation, pp. 98–105 (1999)
Corne, D.W., Knowles, J.D., Oates, M.J.: The pareto envelope-based selection algorithm for multiobjective optimization. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 839–848. Springer, Heidelberg (2000)
Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Evolutionary Computation 7, 205–230 (1999)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3, 257–271 (1999)
Deb, K., Jain, S.: Multi-speed gearbox design using multi-objective evolutionary algorithms. Technical Report 2002001, Kanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur, Kanpur, PIN 208016, India (2002)
Deb, K.: Unveiling innovative design principles by means of multiple conflicting objectives. Technical Report 2002007, Kanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur, Kanpur, PIN 208016, India (2002)
Goldberg, D.E.: The Design of Innovation: Lessons from and for Competent Genetic Algorithms. Genetic Algorithms and Evolutionary Computation. Kluwer Academic Publishers, Norwell (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pedersen, G.K.M., Goldberg, D.E. (2004). Dynamic Uniform Scaling for Multiobjective Genetic Algorithms. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-24855-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22343-6
Online ISBN: 978-3-540-24855-2
eBook Packages: Springer Book Archive