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More information
Author: Dimo Brockhoff
Most of the available multiobjective evolutionary algorithms (MOEA) for approximating the Pareto set have been designed for and tested on low dimensional problems (≤3 objectives). However, it is known that problems with a high number of objectives cause additional difficulties in terms of the quality of the Pareto set approximation and running time. Furthermore, the decision making process becomes the harder the more objectives are involved.
In this context, the question arises whether all objectives are necessary to preserve the problem characteristics. One may also ask under which conditions such an objective reduction is feasible, and how a minimum set of objectives can be computed. On this web page, we provide both greedy and exact algorithms proposed in [bz2006d], [bz2007a], and [bz2007d] to answer these three questions.
A more detailed description of how to use the algorithms and how to compile the code is provided in a README file within the downloadable archives.
For more details about the algorithms, see the README file or the corresponding papers listed below.
Computes all minimal sets for a given set of individuals with the exact algorithm of [bz2006d].
Provides both the greedy and the exact algorithms of [bz2006d].
Computes the delta error for a given set of solutions according to two objective (sub)sets.
Performs the experiments with the random problem in [bz2007d].
Calculates the nondominated or dominated points in a given set of individuals.
Performs the greedy delta-MOSS algorithm of [bz2006d] for a given delta and a set of individuals.
Performs the greedy k-EMOSS algorithm of [bz2006d] for a given k and a set of individuals.
Computes a tree-like visualization of the hierarchical clustering based greedy algorithm for both delta-MOSS and kEMOSS, see [bz2007a] for details.
Computes the maximal spread max_spread = max_i [ max_p (f_i(p)) - min_p (f_i(p)) ] of a given population.
All algorithms available on this website can be used for academic purposes without fee. If you publish research results achieved using the following objective reduction algorithms please remember to cite the corresponding papers [bz2006a], [bz2006c], [bz2006d], [bz2007a], and [bz2007d]. The following copyright notice applies:
Copyright (c) 2006-2007 Swiss Federal Institute of Technology, Computer Engineering and Networks Laboratory. All rights reserved.
Permission to use, copy, modify, and distribute this software and its documentation for any purpose, without fee, and without written agreement is hereby granted, provided that the above copyright notice and the following two paragraphs appear in all copies of this software.
IN NO EVENT SHALL THE SWISS FEDERAL INSTITUTE OF TECHNOLOGY, COMPUTER ENGINEERING AND NETWORKS LABORATORY BE LIABLE TO ANY PARTY FOR DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF THE SWISS FEDERAL INSTITUTE OF TECHNOLOGY, COMPUTER ENGINEERING AND NETWORKS LABORATORY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
THE SWISS FEDERAL INSTITUTE OF TECHNOLOGY, COMPUTER ENGINEERING AND NETWORKS LABORATORY, SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS ON AN "AS IS" BASIS, AND THE SWISS FEDERAL INSTITUTE OF TECHNOLOGY, COMPUTER ENGINEERING AND NETWORKS LABORATORY HAS NO OBLIGATION TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
The following archives provide all algorithms described above and used in the publications listed below as Java 1.5 source code. Note, that you need a Java compiler for Java 1.5 or later. The corresponding JDK can be downloaded on the web page of Sun microsystems.
Source code for the objective reduction algorithms as zip file (177 KB)
Source code for the objective reduction algorithms as tar file (387 KB)
