Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems
H. Trautmann, G. Rudolph, C. Dominguez-Medina, O. Schütze, in: O. Schütze, C.C. Coello, A. Tantar, E. Tantar, P. Bouvry, M.P. Del, P. Legrand (Eds.), EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II, Springer Berlin Heidelberg, 2013, pp. 89–105.
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Book Chapter
| English
Author
Trautmann, HeikeLibreCat 
;
Rudolph, G;
Dominguez-Medina, C;
Schütze, O
;
Rudolph, G;
Dominguez-Medina, C;
Schütze, OBook Editor
Schütze, O;
Coello, Coello CA;
Tantar, A;
Tantar, E;
Bouvry, P;
Del, Moral P;
Legrand, P
Abstract
The averaged Hausdorff distance Δ p is a performance indicator in multi-objective evolutionary optimization which simultaneously takes into account proximity to the true Pareto front and uniform spread of solutions. Recently, the multi-objective evolutionary algorithm Δ p -EMOA was introduced which successfully generates evenly spaced Pareto front approximations for bi-objective problems by integrating an external archiving strategy into the SMS-EMOA based on Δ p . In this work a conceptual generalization of the Δ p -EMOA for higher objective space dimensions is presented and experimentally compared to state-of-the art EMOA as well as specialized EMOA variants on three-dimensional optimization problems.
Publishing Year
Book Title
EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II
Series Title / Volume
Advances in Intelligent Systems and Computing
Volume
175
Page
89–105
ISBN
LibreCat-ID
Cite this
Trautmann H, Rudolph G, Dominguez-Medina C, Schütze O. Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems. In: Schütze O, Coello CC, Tantar A, et al., eds. EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II. Vol 175. Advances in Intelligent Systems and Computing. Springer Berlin Heidelberg; 2013:89–105. doi:10.1007/978-3-642-31519-0_6
Trautmann, H., Rudolph, G., Dominguez-Medina, C., & Schütze, O. (2013). Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems. In O. Schütze, C. C. Coello, A. Tantar, E. Tantar, P. Bouvry, M. P. Del, & P. Legrand (Eds.), EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II (Vol. 175, pp. 89–105). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-31519-0_6
@inbook{Trautmann_Rudolph_Dominguez-Medina_Schütze_2013, series={Advances in Intelligent Systems and Computing}, title={Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems}, volume={175}, DOI={10.1007/978-3-642-31519-0_6}, booktitle={EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II}, publisher={Springer Berlin Heidelberg}, author={Trautmann, Heike and Rudolph, G and Dominguez-Medina, C and Schütze, O}, editor={Schütze, O and Coello, Coello CA and Tantar, A and Tantar, E and Bouvry, P and Del, Moral P and Legrand, P}, year={2013}, pages={89–105}, collection={Advances in Intelligent Systems and Computing} }
Trautmann, Heike, G Rudolph, C Dominguez-Medina, and O Schütze. “Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems.” In EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II, edited by O Schütze, Coello CA Coello, A Tantar, E Tantar, P Bouvry, Moral P Del, and P Legrand, 175:89–105. Advances in Intelligent Systems and Computing. Springer Berlin Heidelberg, 2013. https://doi.org/10.1007/978-3-642-31519-0_6.
H. Trautmann, G. Rudolph, C. Dominguez-Medina, and O. Schütze, “Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems,” in EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II, vol. 175, O. Schütze, C. C. Coello, A. Tantar, E. Tantar, P. Bouvry, M. P. Del, and P. Legrand, Eds. Springer Berlin Heidelberg, 2013, pp. 89–105.
Trautmann, Heike, et al. “Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems.” EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II, edited by O Schütze et al., vol. 175, Springer Berlin Heidelberg, 2013, pp. 89–105, doi:10.1007/978-3-642-31519-0_6.
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