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Mooses: Multiobjective optimization resources

The Mooses project is intended to provide a repository of resources for multiobjective optimization with mateheuristics. It currently contains reference Pareto fronts for benchmark problems and weight vectors taken from the jMetal framework (https://github.com/jMetal/jMetal). We provide the files in TXT and CSF formats.

Weight vector files

The name of the vector files follow the scheme WxD_y.dat, where x represents the number of dimensions or objectives and y is the number of vectors.

Objectives Number of vectors
2 300, 400, 500, 600, 800, 1000
3 91, 300, 500, 600, 800
5 210, 495, 1000, 1200, 1500, 1800, 2000, 2500
8 156
10 220, 275
15 120, 135

Reference Pareto fronts

Problem family: ZDT [1] Objectives (points)
ZDT1 2 (1001)
ZDT2 2 (1000)
ZDT3 2 (1000)
ZDT4 2 (1000)
ZDT6 2 (1000)
Problem family: DTLZ [2] Objectives (points)
DTLZ1 2 (1000), 3 (9901), 4 (183), 6 (264), 8 (370)
DTLZ2 2 (1000), 3 (10000), 4 (216), 6 (254), 8 (380)
DTLZ3 2 (1000), 3 (4000), 4 (216), 6 (254), 8 (380)
DTLZ4 2 (1000), 3 (4000), 4 (216), 6 (254), 8 (380)
DTLZ5 2 (200), 3 (333)
DTLZ6 2 (200), 3 (140)
DTLZ7 2 (101), 3 (676), 4 (214), 6 (203), 8 (354)
Problem family: WFG [3] Objectives (points)
WFG1 2 (1113), 3 (2000)
WFG2 2 (119), 3 (2801)
WFG3 2 (796), 3 (100)
WFG4 2 (1326), 3 (9898)
WFG5 2 (837), 3 (9901)
WFG6 2 (426), 3 (9901)
WFG7 2 (2494), 3 (9716)
WFG8 2 (527), 3 (10009)
WFG9 2 (2600), 3 (10201)
Problem family: MaF [4] Objectives (points)
MaF01 5 (8855), 10 (7007), 15 (6120)
MaF02 5 (190), 10 (7007), 15 (6210)
MaF03 5 (8855), 10 (7007), 15 (6120)
MaF04 5 (8855), 10 (7007), 15 (6120)
MaF05 5 (8855), 10 (7007), 15 (6120)
MaF06 5 (100000), 10 (10000), 15 (10000)
MaF07 5 (100000), 10 (19663), 15 (16384)
MaF08 5 (5826), 10 (7188), 15 (7462)
MaF09 5 (5826), 10 (7188), 15 (7462)

References

  • [1] Zitzler, E., Deb, K., and Thiele, L. (2000). Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2). June 2000. DOI: https://dl.acm.org/doi/10.1162/106365600568202
  • [2] K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. Scalable Test Problems for Evolutionary Multi-Objective Optimization. In Abraham A., Jain L., Goldberg R. (eds) Evolutionary Multiobjective Optimization. Advanced Information and Knowledge Processing. Springer, London. 2005. DOI: https://doi.org/10.1007/1-84628-137-7_6
  • [3] Simon Huband, Phil Hingston, Luigi Barone, and Lyndon While. A Review of Multi-objective Test Problems and a Scalable Test Problem Toolkit. IEEE Transactions on Evolutionary Computation, volume 10, no 5, pages 477-506. IEEE, October 2006. DOI: https://doi.org/10.1109/TEVC.2005.861417
  • [4] Ran Cheng, Miqing Li, Ye Tian, Xingyi Zhang, Shengxiang Yang, Yaochu Jin and Xin Yao " Benchmark Functions for the CEC'2018 Competition on Many-Objective Optimization", Technical Report, University of Birmingham, United Kingdom, 2018.