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.

Add the following dependency to your pom.xml:

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

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.

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