A method for distributing reference points uniformly along the Pareto front of DTLZ test functions in many-objective evolutionary optimization

Testing and assessing the performance of proposed algorithms in a right way is a very important part in evolutionary optimization. If the number of optimization objectives is more than three, it´s commonly referred as many-objective optimization problem(MaOP). Despite the fact there exists many test functions and assessment metrics, all of which are designed for testing and assessing the performance of evolutionary algorithms, the test functions DTLZ proposed by Deb(2005) and the assessment metrics Inverted Generational Distance(IGD) proposed by Bosman and Thierens(2003) are both widely recognized and used in most of evolutionary optimizations, especially in many-objective evolutionary optimization. When using IGD as a assessment tool, the vital task is to distribute reference points uniformly along the Pareto front of test functions. To overcome it, however, is really difficult with the number of objectives increase. For dealing with such difficulty, this paper introduce an approach called Inverse Transform Technique(ITT) suggested by Fang and Wang(1999) and successfully distributes reference points uniformly along the Pareto front of DTLZ test functions. In the final, three representative evolutionary algorithms: NSGA-II, MOEA/D and MOEA/D-M2M are selected to test their performance in dealing with many-objective optimization. As a result, extensive experiments and analysis are conducted on four DTLZ test functions from five to ten objectives.