On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front
G. Rudolph, O. Schütze, H. Trautmann, in: G. Squillero, P. Burelli (Eds.), Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II, Springer International Publishing, Cham, 2016, pp. 42–55.
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Author
Rudolph, G;
Schütze, O;
Trautmann, HeikeLibreCat 
Book Editor
Squillero, G;
Burelli, P
Abstract
The averaged Hausdorff distance has been proposed as an indicator for assessing the quality of finitely sized approximations of the Pareto front of a multiobjective problem. Since many set-based, iterative optimization algorithms store their currently best approximation in an internal archive these approximations are also termed archives. In case of two objectives and continuous variables it is known that the best approximations in terms of averaged Hausdorff distance are subsets of the Pareto front if it is concave. If it is linear or circularly concave the points of the best approximation are equally spaced.
Here, it is proven that the optimal averaged Hausdorff approximation and the Pareto front have an empty intersection if the Pareto front is circularly convex. But the points of the best approximation are equally spaced and they rapidly approach the Pareto front for increasing size of the approximation.
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Book Title
Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II
Page
42–55
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Rudolph G, Schütze O, Trautmann H. On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front. In: Squillero G, Burelli P, eds. Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II. Springer International Publishing; 2016:42–55. doi:10.1007/978-3-319-31153-1_4
Rudolph, G., Schütze, O., & Trautmann, H. (2016). On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front. In G. Squillero & P. Burelli (Eds.), Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II (pp. 42–55). Springer International Publishing. https://doi.org/10.1007/978-3-319-31153-1_4
@inbook{Rudolph_Schütze_Trautmann_2016, place={Cham}, title={On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front}, DOI={10.1007/978-3-319-31153-1_4}, booktitle={Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II}, publisher={Springer International Publishing}, author={Rudolph, G and Schütze, O and Trautmann, Heike}, editor={Squillero, G and Burelli, P}, year={2016}, pages={42–55} }
Rudolph, G, O Schütze, and Heike Trautmann. “On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front.” In Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II, edited by G Squillero and P Burelli, 42–55. Cham: Springer International Publishing, 2016. https://doi.org/10.1007/978-3-319-31153-1_4.
G. Rudolph, O. Schütze, and H. Trautmann, “On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front,” in Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II, G. Squillero and P. Burelli, Eds. Cham: Springer International Publishing, 2016, pp. 42–55.
Rudolph, G., et al. “On the Closest Averaged Hausdorff Archive for a Circularly Convex Pareto Front.” Applications of Evolutionary Computation: 19$^th$ European Conference, EvoApplications 2016, Porto, Portugal, March 30 — April 1, 2016, Proceedings, Part II, edited by G Squillero and P Burelli, Springer International Publishing, 2016, pp. 42–55, doi:10.1007/978-3-319-31153-1_4.
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