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314 results on '"Deutz, André"'

1. Comparative Analysis of Indicators for Multiobjective Diversity Optimization

Author

Pereverdieva, Ksenia, Deutz, André, Ezendam, Tessa, Bäck, Thomas, Hofmeyer, Hèrm, and Emmerich, Michael T. M.

Subjects
Computer Science - Neural and Evolutionary Computing, Mathematics - Optimization and Control, I.2.8
Abstract

Indicator-based (multiobjective) diversity optimization aims at finding a set of near (Pareto-)optimal solutions that maximizes a diversity indicator, where diversity is typically interpreted as the number of essentially different solutions. Whereas, in the first diversity-oriented evolutionary multiobjective optimization algorithm, the NOAH algorithm by Ulrich and Thiele, the Solow Polasky Diversity (also related to Magnitude) served as a metric, other diversity indicators might be considered, such as the parameter-free Max-Min Diversity, and the Riesz s-Energy, which features uniformly distributed solution sets. In this paper, focusing on multiobjective diversity optimization, we discuss different diversity indicators from the perspective of indicator-based evolutionary algorithms (IBEA) with multiple objectives. We examine theoretical, computational, and practical properties of these indicators, such as monotonicity in species, twinning, monotonicity in distance, strict monotonicity in distance, uniformity of maximizing point sets, computational effort for a set of size~n, single-point contributions, subset selection, and submodularity. We present new theorems -- including a proof of the NP-hardness of the Riesz s-Energy Subset Selection Problem -- and consolidate existing results from the literature. In the second part, we apply these indicators in the NOAH algorithm and analyze search dynamics through an example. We examine how optimizing with one indicator affects the performance of others and propose NOAH adaptations specific to the Max-Min indicator., Comment: 14 pages

Published
2024

2. Multicriteria Optimization and Decision Making: Principles, Algorithms and Case Studies

Author

Emmerich, Michael and Deutz, André

Subjects
Mathematics - Optimization and Control, Mathematics - Numerical Analysis, 90C29, G.1.6
Abstract

Real-world decision and optimization problems, often involve constraints and conflicting criteria. For example, choosing a travel method must balance speed, cost, environmental footprint, and convenience. Similarly, designing an industrial process must consider safety, environmental impact, and cost efficiency. Ideal solutions where all objectives are optimally met are rare; instead, we seek good compromises and aim to avoid lose-lose scenarios. Multicriteria optimization offers computational techniques to compute Pareto optimal solutions, aiding decision analysis and decision making. This reader offers an introduction to this topic and has been developed on the basis of the revised edition of the reader for the MSc computer science course "Multicriteria Optimization and Decision Analysis" at the Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands. This course was taught annually by the first author from 2007 to 2023 as a single semester course with lectures and practicals. Our aim was to make the material accessible to MSc students who do not study mathematics as their core discipline by introducing basic numerical analysis concepts when necessary and providing numerical examples for interesting cases. The introduction is organized in a unique didactic manner developed by the authors, starting from more simple concepts such as linear programming and single-point methods, and advancing from these to more difficult concepts such as optimality conditions for nonlinear optimization and set-oriented solution algorithms. Besides, we focus on the mathematical modeling and foundations rather than on specific algorithms, though not excluding the discussion of some representative examples of solution algorithms., Comment: 102 pages, Lecture notes

Published
2024

3. A Newton Method for Hausdorff Approximations of the Pareto Front within Multi-objective Evolutionary Algorithms

Author

Wang, Hao, Rodriguez-Fernandez, Angel E., Uribe, Lourdes, Deutz, André, Cortés-Piña, Oziel, and Schütze, Oliver

Subjects
Computer Science - Neural and Evolutionary Computing
Abstract

A common goal in evolutionary multi-objective optimization is to find suitable finite-size approximations of the Pareto front of a given multi-objective optimization problem. While many multi-objective evolutionary algorithms have proven to be very efficient in finding good Pareto front approximations, they may need quite a few resources or may even fail to obtain optimal or nearly approximations. Hereby, optimality is implicitly defined by the chosen performance indicator. In this work, we propose a set-based Newton method for Hausdorff approximations of the Pareto front to be used within multi-objective evolutionary algorithms. To this end, we first generalize the previously proposed Newton step for the performance indicator for the treatment of constrained problems for general reference sets. To approximate the target Pareto front, we propose a particular strategy for generating the reference set that utilizes the data gathered by the evolutionary algorithm during its run. Finally, we show the benefit of the Newton method as a post-processing step on several benchmark test functions and different base evolutionary algorithms.

Published
2024

4. The Hypervolume Indicator Hessian Matrix: Analytical Expression, Computational Time Complexity, and Sparsity

Author

Deutz, André H., Emmerich, Michael T. M., and Wang, Hao

Subjects
Mathematics - Optimization and Control, Computer Science - Machine Learning
Abstract

The problem of approximating the Pareto front of a multiobjective optimization problem can be reformulated as the problem of finding a set that maximizes the hypervolume indicator. This paper establishes the analytical expression of the Hessian matrix of the mapping from a (fixed size) collection of $n$ points in the $d$-dimensional decision space (or $m$ dimensional objective space) to the scalar hypervolume indicator value. To define the Hessian matrix, the input set is vectorized, and the matrix is derived by analytical differentiation of the mapping from a vectorized set to the hypervolume indicator. The Hessian matrix plays a crucial role in second-order methods, such as the Newton-Raphson optimization method, and it can be used for the verification of local optimal sets. So far, the full analytical expression was only established and analyzed for the relatively simple bi-objective case. This paper will derive the full expression for arbitrary dimensions ($m\geq2$ objective functions). For the practically important three-dimensional case, we also provide an asymptotically efficient algorithm with time complexity in $O(n\log n)$ for the exact computation of the Hessian Matrix' non-zero entries. We establish a sharp bound of $12m-6$ for the number of non-zero entries. Also, for the general $m$-dimensional case, a compact recursive analytical expression is established, and its algorithmic implementation is discussed. Also, for the general case, some sparsity results can be established; these results are implied by the recursive expression. To validate and illustrate the analytically derived algorithms and results, we provide a few numerical examples using Python and Mathematica implementations. Open-source implementations of the algorithms and testing data are made available as a supplement to this paper.

Published
2022

5. The Prism-Net Search Space Representation for Multi-objective Building Spatial Design

Author

Pereverdieva, Ksenia, Emmerich, Michael, Deutz, André, Ezendam, Tessa, Bäck, Thomas, Hofmeyer, Hèrm, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Emmerich, Michael, editor, Deutz, André, editor, Wang, Hao, editor, Kononova, Anna V., editor, Naujoks, Boris, editor, Li, Ke, editor, Miettinen, Kaisa, editor, and Yevseyeva, Iryna, editor

Published
2023
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6. The Hypervolume Indicator Hessian Matrix: Analytical Expression, Computational Time Complexity, and Sparsity

Author

Deutz, André, Emmerich, Michael, Wang, Hao, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Emmerich, Michael, editor, Deutz, André, editor, Wang, Hao, editor, Kononova, Anna V., editor, Naujoks, Boris, editor, Li, Ke, editor, Miettinen, Kaisa, editor, and Yevseyeva, Iryna, editor

Published
2023
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7. Many-Criteria Dominance Relations

Author

Deutz, Andre H., Emmerich, Michael, Wang, Yali, Rozenberg, Grzegorz, Founding Editor, Bäck, Thomas, Series Editor, Kari, Lila, Series Editor, Stepney, Susan, Series Editor, Brockhoff, Dimo, editor, Emmerich, Michael, editor, Naujoks, Boris, editor, and Purshouse, Robin, editor

Published
2023
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8. Improving Many-Objective Evolutionary Algorithms by Means of Edge-Rotated Cones

Author

Wang, Yali, Deutz, André, Bäck, Thomas, and Emmerich, Michael

Subjects
Computer Science - Neural and Evolutionary Computing
Abstract

Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and dominating) region decreases proportionally to $1/2^{m-1}$, i.e., the volume of the Pareto dominating orthant as compared to all other volumes. Due to this reason, it gets increasingly unlikely that dominating points can be found by random, isotropic mutations. As a remedy to stagnation of search in many objective optimization, in this paper, we suggest to enhance the Pareto dominance order by involving an obtuse convex dominance cone in the convergence phase of an evolutionary optimization algorithm. We propose edge-rotated cones as generalizations of Pareto dominance cones for which the opening angle can be controlled by a single parameter only. The approach is integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and tested on benchmark problems with four, five, six and eight objectives. Computational experiments demonstrate the ability of these edge-rotated cones to improve the performance of MOEAs on many-objective optimization problems.

Published
2020

9. Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms

Author

Yang, Kaifeng, Emmerich, Michael, Deutz, André, and Bäck, Thomas

Subjects
Computer Science - Machine Learning, Statistics - Machine Learning
Abstract

In the field of multi-objective optimization algorithms, multi-objective Bayesian Global Optimization (MOBGO) is an important branch, in addition to evolutionary multi-objective optimization algorithms (EMOAs). MOBGO utilizes Gaussian Process models learned from previous objective function evaluations to decide the next evaluation site by maximizing or minimizing an infill criterion. A common criterion in MOBGO is the Expected Hypervolume Improvement (EHVI), which shows a good performance on a wide range of problems, with respect to exploration and exploitation. However, so far it has been a challenge to calculate exact EHVI values efficiently. In this paper, an efficient algorithm for the computation of the exact EHVI for a generic case is proposed. This efficient algorithm is based on partitioning the integration volume into a set of axis-parallel slices. Theoretically, the upper bound time complexities are improved from previously $O (n^2)$ and $O(n^3)$, for two- and three-objective problems respectively, to $\Theta(n\log n)$, which is asymptotically optimal. This article generalizes the scheme in higher dimensional case by utilizing a new hyperbox decomposition technique, which was proposed by D{\"a}chert et al, EJOR, 2017. It also utilizes a generalization of the multilayered integration scheme that scales linearly in the number of hyperboxes of the decomposition. The speed comparison shows that the proposed algorithm in this paper significantly reduces computation time. Finally, this decomposition technique is applied in the calculation of the Probability of Improvement (PoI).

Published
2019

13. Diversity-Indicator Based Multi-Objective Evolutionary Algorithm: DI-MOEA

Author

Wang, Yali, Emmerich, Michael, Deutz, André, Bäck, Thomas, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Deb, Kalyanmoy, editor, Goodman, Erik, editor, Coello Coello, Carlos A., editor, Klamroth, Kathrin, editor, Miettinen, Kaisa, editor, Mostaghim, Sanaz, editor, and Reed, Patrick, editor

Published
2019
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14. The Expected R2-Indicator Improvement for Multi-objective Bayesian Optimization

Author

Deutz, André, Emmerich, Michael, Yang, Kaifeng, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Deb, Kalyanmoy, editor, Goodman, Erik, editor, Coello Coello, Carlos A., editor, Klamroth, Kathrin, editor, Miettinen, Kaisa, editor, Mostaghim, Sanaz, editor, and Reed, Patrick, editor

Published
2019
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16. Faster Computation of Expected Hypervolume Improvement

Author

Hupkens, Iris, Emmerich, Michael, and Deutz, André

Subjects
Computer Science - Data Structures and Algorithms, G.1.6, F.2.1
Abstract

The expected improvement algorithm (or efficient global optimization) aims for global continuous optimization with a limited budget of black-box function evaluations. It is based on a statistical model of the function learned from previous evaluations and an infill criterion - the expected improvement - used to find a promising point for a new evaluation. The `expected improvement' infill criterion takes into account the mean and variance of a predictive multivariate Gaussian distribution. The expected improvement algorithm has recently been generalized to multiobjective optimization. In order to measure the improvement of a Pareto front quantitatively the gain in dominated (hyper-)volume is used. The computation of the expected hypervolume improvement (EHVI) is a multidimensional integration of a step-wise defined non-linear function related to the Gaussian probability density function over an intersection of boxes. This paper provides a new algorithm for the exact computation of the expected improvement to more than two objective functions. For the bicriteria case it has a time complexity in $O(n^2)$ with $n$ denoting the number of points in the current best Pareto front approximation. It improves previously known algorithms with time complexity $O(n^3 \log n)$. For tricriteria optimization we devise an algorithm with time complexity of $O(n^3)$. Besides discussing the new time complexity bounds the speed of the new algorithm is also tested empirically on test data. It is shown that further improvements in speed can be achieved by reusing data structures built up in previous iterations. The resulting numerical algorithms can be readily used in existing implementations of hypervolume-based expected improvement algorithms., Comment: LIACS Technical Report

Published
2014

18. Community Detection in NK Landscapes - An Empirical Study of Complexity Transitions in Interactive Networks

Author

Maulana, Asep, Deutz, André H., Schultes, Erik, Emmerich, Michael T. M., Kacprzyk, Janusz, Series editor, Pal, Nikhil R., Advisory editor, Bello Perez, Rafael, Advisory editor, Corchado, Emilio S., Advisory editor, Hagras, Hani, Advisory editor, Kóczy, László T., Advisory editor, Kreinovich, Vladik, Advisory editor, Lin, Chin-Teng, Advisory editor, Lu, Jie, Advisory editor, Melin, Patricia, Advisory editor, Nedjah, Nadia, Advisory editor, Nguyen, Ngoc Thanh, Advisory editor, Wang, Jun, Advisory editor, Tantar, Alexandru-Adrian, editor, Tantar, Emilia, editor, Emmerich, Michael, editor, Legrand, Pierrick, editor, Alboaie, Lenuta, editor, and Luchian, Henri, editor

Published
2018
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19. On Gradient-Based and Swarm-Based Algorithms for Set-Oriented Bicriteria Optimization

Author

Verhoef, Wilco, Deutz, André H., Emmerich, Michael T. M., Kacprzyk, Janusz, Series editor, Pal, Nikhil R., Advisory editor, Bello Perez, Rafael, Advisory editor, Corchado, Emilio S., Advisory editor, Hagras, Hani, Advisory editor, Kóczy, László T., Advisory editor, Kreinovich, Vladik, Advisory editor, Lin, Chin-Teng, Advisory editor, Lu, Jie, Advisory editor, Melin, Patricia, Advisory editor, Nedjah, Nadia, Advisory editor, Nguyen, Ngoc Thanh, Advisory editor, Wang, Jun, Advisory editor, Tantar, Alexandru-Adrian, editor, Tantar, Emilia, editor, Emmerich, Michael, editor, Legrand, Pierrick, editor, Alboaie, Lenuta, editor, and Luchian, Henri, editor

Published
2018
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24. Computing 3-D Expected Hypervolume Improvement and Related Integrals in Asymptotically Optimal Time

Author

Yang, Kaifeng, Emmerich, Michael, Deutz, André, Fonseca, Carlos M., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Trautmann, Heike, editor, Rudolph, Günter, editor, Klamroth, Kathrin, editor, Schütze, Oliver, editor, Wiecek, Margaret, editor, Jin, Yaochu, editor, and Grimme, Christian, editor

Published
2017
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25. Hypervolume Indicator Gradient Ascent Multi-objective Optimization

Author

Wang, Hao, Deutz, André, Bäck, Thomas, Emmerich, Michael, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Trautmann, Heike, editor, Rudolph, Günter, editor, Klamroth, Kathrin, editor, Schütze, Oliver, editor, Wiecek, Margaret, editor, Jin, Yaochu, editor, and Grimme, Christian, editor

Published
2017
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27. Towards Analyzing Multimodality of Continuous Multiobjective Landscapes

Author

Kerschke, Pascal, Wang, Hao, Preuss, Mike, Grimme, Christian, Deutz, André, Trautmann, Heike, Emmerich, Michael, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Handl, Julia, editor, Hart, Emma, editor, Lewis, Peter R., editor, López-Ibáñez, Manuel, editor, Ochoa, Gabriela, editor, and Paechter, Ben, editor

Published
2016
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30. Faster Exact Algorithms for Computing Expected Hypervolume Improvement

Author

Hupkens, Iris, Deutz, André, Yang, Kaifeng, Emmerich, Michael, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Gaspar-Cunha, António, editor, Henggeler Antunes, Carlos, editor, and Coello, Carlos Coello, editor

Published
2015
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36. On Quality Indicators for Black-Box Level Set Approximation

Author

Emmerich, Michael T. M., Deutz, André H., Kruisselbrink, Johannes W., Tantar, Emilia, editor, Tantar, Alexandru-Adrian, editor, Bouvry, Pascal, editor, Del Moral, Pierre, editor, Legrand, Pierrick, editor, Coello Coello, Carlos A., editor, and Schütze, Oliver, editor

Published
2013
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37. A Theoretical Analysis of Curvature Based Preference Models

Author

Shukla, Pradyumn Kumar, Emmerich, Michael, Deutz, André, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Purshouse, Robin C., editor, Fleming, Peter J., editor, Fonseca, Carlos M., editor, Greco, Salvatore, editor, and Shaw, Jane, editor

Published
2013
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38. Cone-Based Hypervolume Indicators: Construction, Properties, and Efficient Computation

Author

Emmerich, Michael, Deutz, André, Kruisselbrink, Johannes, Shukla, Pradyumn Kumar, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Purshouse, Robin C., editor, Fleming, Peter J., editor, Fonseca, Carlos M., editor, Greco, Salvatore, editor, and Shaw, Jane, editor

Published
2013
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40. On Expected-Improvement Criteria for Model-based Multi-objective Optimization

Author

Wagner, Tobias, Emmerich, Michael, Deutz, André, Ponweiser, Wolfgang, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Schaefer, Robert, editor, Cotta, Carlos, editor, Kołodziej, Joanna, editor, and Rudolph, Günter, editor

Published
2010
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41. Exploiting Overlap When Searching for Robust Optima

Author

Kruisselbrink, Johannes, Emmerich, Michael, Deutz, André, Bäck, Thomas, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Schaefer, Robert, editor, Cotta, Carlos, editor, Kołodziej, Joanna, editor, and Rudolph, Günter, editor

Published
2010
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47. High Spies (or How to Win a Programming Contest)

Author

Deutz, André, van Vliet, Rudy, Hoogeboom, Hendrik Jan, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Crescenzi, Pierluigi, editor, Prencipe, Giuseppe, editor, and Pucci, Geppino, editor

Published
2007
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48. Test Problems Based on Lamé Superspheres

Author

Emmerich, Michael T. M., Deutz, André H., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Obayashi, Shigeru, editor, Deb, Kalyanmoy, editor, Poloni, Carlo, editor, Hiroyasu, Tomoyuki, editor, and Murata, Tadahiko, editor

Published
2007
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49. Gradient-Based/Evolutionary Relay Hybrid for Computing Pareto Front Approximations Maximizing the S-Metric

Author

Emmerich, Michael, Deutz, André, Beume, Nicola, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Bartz-Beielstein, Thomas, editor, Blesa Aguilera, María José, editor, Blum, Christian, editor, Naujoks, Boris, editor, Roli, Andrea, editor, Rudolph, Günter, editor, and Sampels, Michael, editor

Published
2007
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