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.
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 |
| 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) |
- [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.