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Generalized Decomposition

Extends the MOEA Framework with a version of MOEA/D using weights produced by Generalized Decomposition (GD).

Giagkiozis, I., R. C. Purshouse, and P. J. Fleming (2013). "Generalized Decomposition." Evolutionary Multi-Criterion Optimization, 7th International Conference, pp. 428-442.

Very briefly, MOEA/D typically uses randomly-generated weights that aim to produce a diverse set of solutions. While newer algorithms like NSGA-III have the option to supply "target points" where the algorithm can focus search, picking weights for MOEA/D that produce solutions near a given target is non-trivial. This is further complicated when the Pareto front shape is disjoint / multimodal.

With GD, we can take a target point (or points) and compute the ideal weights for MOEA/D or any other algorithm using the Chebychev / Tchebycheff scalarizing function. Alternatively, we can use GD to compute a set of weights that should yield better and more uniformly-distributed results than randomly-generated weights.

Installation

Add the following dependency to your pom.xml:

<dependency>
    <groupId>org.moeaframework</groupId>
    <artifactId>gd</artifactId>
    <version>2.0</version>
</dependency>

Usage

Reference the GD-MOEA/D algorithm as you would any other:

NondominatedPopulation result = new Executor()
		.withProblem("DTLZ2_3")
		.withAlgorithm("GD-MOEA/D")
		.withProperty("targets", "pf/DTLZ2.3D.pf")  // Target Pareto-optimal points
		.withMaxEvaluations(10000)
		.run();

There is an optional targets property. When set, it will use the target points defined in a file. If unset, it will default to uniformly-spaced points generated using the Normal Boundary Intersection method.

License

Copyright 2009-2024 David Hadka and other contributors. All rights reserved.

The MOEA Framework is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

The MOEA Framework is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with the MOEA Framework. If not, see http://www.gnu.org/licenses/.