Problems included in jMetal

Problem families

ZDT benchmark

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

DTLZ benchmark

  • 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.
  • Reference Pareto fronts (2D): DTLZ.2D.tar.gz
  • Reference Pareto fronts (3D): DTLZ.3D.tar.gz

WFG benchmark

  • 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
  • Reference Pareto fronts (2D): WFG.2D.tar.gz
  • Reference Pareto fronts (3D): WFG.3D.tar.gz

LZ09 benchmark

  • 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.
  • Reference Pareto fronts: LZ09.tar.gz

CEC2009 competition benchmark (unconstrained problems)

  • Number of problems: 10 (UF1 - UF10)
  • Reference: Q. Zhang, A. Zhou, S. Zhao, P.N. Suganthan, W. Liu, S. Tiwari, Multiobjective optimization test instances for the CEC 2009 special session and competition, Tech. Rep. CES-487, University of Essex and Nanyang Technological University, 2008.
  • Reference Pareto fronts: UF.tar.gz

Combinatorial problems

Multi-objective Quadratic Assignment Problem (mQAP)

Unconstrained problems

Fonseca

  • Features: two objectives, 3 variables
  • Reference: BIBTEX.
  • Reference Pareto front: Fonseca.pf

Kursawe

  • Features: two objectives, N numbers of variables (default: N = 3)
  • Reference: BIBTEX.
  • Reference Pareto front: Kursawe.pf

Schaffer

  • Features: two objectives, 1 variables
  • Reference: BIBTEX.
  • Reference Pareto front: Schaffer.pf

Viennet2

  • Features: 3 objectives, 2 variables
  • Reference: BIBTEX.
  • Reference Pareto front: Viennet2.pf

Viennet3

  • Features: 3 objectives, 2 variables
  • Reference: BIBTEX.
  • Reference Pareto front: Viennet3.pf

Constrained problems

Binh2

  • Features: 2 objectives, 2 variables, 2 constraints
  • Reference: BIBTEX.
  • Reference Pareto front: Binh2.pf

Contr_Ex

  • Features: two objectives, 1 variable
  • Reference: BIBTEX.
  • Reference Pareto front: Constr_Ex.pf

Golinski

  • Features: 2 objectives, 7 variables , 11 constraints
  • Reference: BIBTEX.
  • Reference Pareto front: Golinski.pf

Ozyczka2

  • Features: 2 objectives, 6 variables, 6 constraints
  • Reference: BIBTEX.
  • Reference Pareto front: Osyczka2.pf

Tanaka

  • Features: 2 objectives, 2 variable, 2 constraints
  • Reference: BIBTEX.
  • Reference Pareto front: Tanaka.pf

Srinivas

  • Features: two objectives, 1 variable
  • Reference: BIBTEX.
  • Reference Pareto front: Srinivas.pf

Water

  • Features: 5 objectives, 1 variable
  • Reference: BIBTEX.
  • Reference Pareto front: Water.pf