The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume
H.V. Sosa, O. Schütze, G. Rudolph, H. Trautmann, in: M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, A. Tantar, P. Moral, P. Legrand, P. Bouvry, C. Coello (Eds.), EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, Springer International Publishing, 2013, pp. 189–205.
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Book Chapter
| English
Author
Sosa, Hernández V;
Schütze, O;
Rudolph, G;
Trautmann, HeikeLibreCat 
Book Editor
Emmerich, M;
Deutz, A;
Schuetze, O;
Bäck, T;
Tantar, A;
Moral, PD;
Legrand, P;
Bouvry, P;
Coello, CA
Abstract
In many applications one is faced with the problem that multiple objectives have to be optimized at the same time. Since typically the solution set of such multi-objective optimization problems forms a manifold which cannot be computed analytically, one is in many cases interested in a suitable finite size approximation of this set. One widely used approach is to find a representative set that maximizes the dominated hypervolume that is defined by the images in objective space of these solutions and a given reference point.
In this paper, we propose a new point-wise iterative search procedure, Hypervolume Directed Search (HVDS), that aims to increase the hypervolume of a given point in an archive for bi-objective unconstrained optimization problems. We present the HVDS both as a standalone algorithm and as a local searcher within a specialized evolutionary algorithm. Numerical results confirm the strength of the novel approach.
Publishing Year
Book Title
EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV
Series Title / Volume
Advances in Intelligent Systems and Computing
Volume
227
Page
189–205
ISBN
LibreCat-ID
Cite this
Sosa HV, Schütze O, Rudolph G, Trautmann H. The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume. In: Emmerich M, Deutz A, Schuetze O, et al., eds. EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV. Vol 227. Advances in Intelligent Systems and Computing. Springer International Publishing; 2013:189–205. doi:10.1007/978-3-319-01128-8_13
Sosa, H. V., Schütze, O., Rudolph, G., & Trautmann, H. (2013). The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume. In M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, A. Tantar, P. Moral, P. Legrand, P. Bouvry, & C. Coello (Eds.), EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV (Vol. 227, pp. 189–205). Springer International Publishing. https://doi.org/10.1007/978-3-319-01128-8_13
@inbook{Sosa_Schütze_Rudolph_Trautmann_2013, series={Advances in Intelligent Systems and Computing}, title={The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume}, volume={227}, DOI={10.1007/978-3-319-01128-8_13}, booktitle={EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV}, publisher={Springer International Publishing}, author={Sosa, Hernández V and Schütze, O and Rudolph, G and Trautmann, Heike}, editor={Emmerich, M and Deutz, A and Schuetze, O and Bäck, T and Tantar, A and Moral, PD and Legrand, P and Bouvry, P and Coello, CA}, year={2013}, pages={189–205}, collection={Advances in Intelligent Systems and Computing} }
Sosa, Hernández V, O Schütze, G Rudolph, and Heike Trautmann. “The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume.” In EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, edited by M Emmerich, A Deutz, O Schuetze, T Bäck, A Tantar, PD Moral, P Legrand, P Bouvry, and CA Coello, 227:189–205. Advances in Intelligent Systems and Computing. Springer International Publishing, 2013. https://doi.org/10.1007/978-3-319-01128-8_13.
H. V. Sosa, O. Schütze, G. Rudolph, and H. Trautmann, “The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume,” in EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, vol. 227, M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, A. Tantar, P. Moral, P. Legrand, P. Bouvry, and C. Coello, Eds. Springer International Publishing, 2013, pp. 189–205.
Sosa, Hernández V., et al. “The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume.” EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, edited by M Emmerich et al., vol. 227, Springer International Publishing, 2013, pp. 189–205, doi:10.1007/978-3-319-01128-8_13.
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