Problems

ZDT family

  • Number of problems: 6 (ZDT1 - ZDT6)
  • Reference: Zitzler, E., Deb, K., Thieler, L. Comparison of multiobjective evolutionary algorithms: Empirical results. IEEE Trans. on Evol. Computation 8 (2000) 173-195.
  • Pareto fronts: ZDT.tar.gz

DTLZ family

  • Number of problems: 7 (DTLZ1 - DTLZ7)
  • Reference: K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. Scalable Test Problems for Evolutionary Multi-Objective Optimization, Zurich, Switzerland, Tech. Rep. 112, 2001.
  • Pareto fronts (2D formulation): DTLZ.2D.tar.gz
  • Pareto fronts (3D formulation): DTLZ.3D.tar.gz

WFG family

  • Number of problems: 9 (WFG1 - WFG9)
  • Reference: 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 2007.
  • Pareto fronts (2D formulation): WFG.2D.tar.gz
  • Pareto fronts (3D formulation): WFG.3D.tar.gz

LZ09 family

  • Number of problems: 9 (LZ09_F1 - LZ09_F9)
  • Reference: H. Li and Q. Zhang. Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II, IEEE Trans on Evolutionary Computation, 2(12):284-302, April 2009.
  • Pareto fronts: LZ09.tar.gz

Classical Problems

  • Schaffer
    • Features: two objectives, one variable
    • Reference:.D. Schaffer. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In J.J. Grefensttete, editor, Proc. of the First International Conference on Genetic Algorithms (ICGA), pages 93–100, Hillsdale, NJ, 1987.
    • Pareto front: Schaffer.pf
  • Kursawe
    • Features: two objectives, N numbers of variables (default: N = 3)
    • Reference:F. Kursawe. A Variant of Evolution Strategies for Vector Optimization. In H.P. Schwefel and R. M¨nner, editors, Parallel Problem Solving for Nature, volume 496 of Lecture Notes in Computer Science, pages 193-197, Berlin, Germany, 1990. Springer-Verlag.
    • Pareto front (3 variables): Kursawe.pf
  • Fonseca
    • Features: two objectives, three variables
    • Reference: C.M. Fonseca and P.J. Flemming. Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms - Part II: Application Example. IEEE Transactions on Systems, Man and Cybernetics, 28:38-47, 1998.
    • Pareto front: Fonseca.pf