GitHub

Problem Families

MOProblems.jl groups benchmark constructors by their source family or publication. Each constructor returns an MOProblem instance with effective dimensions, objective and constraint evaluators, variable and constraint bounds when available, and registered analytical derivatives when implemented.

Documented families

  • Amaral–Assunção–Souza (AAS): two fixed-dimension problems from Amaral, Assunção, and Souza [1].
  • Ansary–Panda (AP): four fixed-dimension problems from Md. A. T. Ansary and G. Panda [2].
  • Binh–Korn (BK): one fixed-dimension problem from To Thanh Binh and Ulrich Korn [3].
  • Das–Dennis (DD): one constrained, fixed-dimension problem from Indraneel Das and J. E. Dennis. [4].
  • Dumitrescu-Grosan-Oltean (DGO): three fixed-dimension problems from Crina Grosan, Dan Dumitrescu, and Mihai Oltean [5].
  • Deb–Thiele–Laumanns–Zitzler (DTLZ): scalable test problems from Deb, Thiele, Laumanns, and Zitzler [6].
  • Farhang-Mehr-Azarm (FA): one fixed-dimension problem from A. Farhang-Mehr and S. Azarm [7].
  • Farina (Far): one fixed-dimension problem originating in M. Farina [8], using the corrected formulation cataloged by Huband et al. [9].
  • Fliege–Drummond–Svaiter (FDS): one scalable, three-objective problem introduced by J. Fliege, L. M. Graña Drummond, and B. F. Svaiter [10].
  • Fonseca–Fleming (FF): one fixed-dimension problem from Carlos M. Fonseca and Peter J. Fleming [11].
  • Hillermeier (Hil): one unconstrained, fixed-dimension academic problem from C. Hillermeier [12].
  • Ikeda–Kita–Kobayashi (IKK): one fixed-dimension problem from K. Ikeda, H. Kita, and S. Kobayashi [13].
  • Ishibuchi–Murata (IM): one fixed-dimension problem from H. Ishibuchi and T. Murata [14].
  • Jin–Olhofer–Sendhoff (JOS): two variable-dimension problems from Yaochu Jin, Markus Olhofer, and Bernhard Sendhoff [15], using source-order numbering and documenting the alternative Huband catalog name.
  • Kim–de Weck (KW): one fixed-dimension problem from the second numerical example of I. Y. Kim and O. L. de Weck [16], expressed in the package's minimization convention.
  • Lis–Eiben (LE): one fixed-dimension problem from Test 1 of J. Lis and A. E. Eiben [17].
  • Lovison (Lov): six fixed-dimension examples from Alberto Lovison [18], including a smooth regularization of ZDT3 [19], with documented minimization conventions.
  • Laumanns–Thiele–Deb–Zitzler (LTDZ): one fixed-dimension, three-objective problem from Laumanns, Thiele, Deb, and Zitzler [20], using the formulation and LTDZ1 name given in Table XVI of Huband et al. [9].
  • Moré–Garbow–Hillstrom (MGH): four problems derived from the nonlinear least-squares collection of Moré, Garbow, and Hillstrom [21], using duly documented extensions of the multiobjective formulations based on Mita, Fukuda, and Yamashita [22].
  • Mao–Hirasawa–Hu–Murata (MHHM): two fixed-dimension, three-objective problems from the numerical simulations of Jiangming Mao, K. Hirasawa, Jinlu Hu, and J. Murata [23].
  • Molyneaux–Leyland–Favrat (MLF): two fixed-dimension problems from A. K. Molyneaux, G. B. Leyland, and D. Favrat [24], including the corrected MLF1 formulation cataloged by Huband et al. [9].
  • Miglierina–Molho–Recchioni (MMR): four fixed-dimension problems from Tests 1–4 of E. Miglierina, E. Molho, and M. C. Recchioni [25].
  • Preuss–Naujoks–Rudolph (PNR): the fixed-dimension Case 1 specialization of the TWO-ON-ONE test problem by Mike Preuss, Boris Naujoks, and Günter Rudolph [26].
  • Quagliarella–Vicini (QV): one variable-dimension problem introduced by D. Quagliarella and A. Vicini [27] and subsequently cataloged by Huband et al. [9].
  • Stadler–Dauer (SD): one fixed-dimension truss-design problem from the “Elastic Trusses” example of W. Stadler and J. Dauer [28], implemented in its normalized instance.
  • Socha–Kisiel-Dorohinicki (SK): two fixed-dimension problems used as test cases by K. Socha and M. Kisiel-Dorohinicki [29], including the corrected SK1 formulation cataloged by Huband et al. [9], with documented minimization conventions.
  • Schütze–Laumanns–Coello Coello–Dellnitz–Talbi (SLCDT): two fixed-dimension problems from Oliver Schütze, Marco Laumanns, Carlos A. Coello Coello, Michael Dellnitz, and El-Ghazali Talbi [30], with the perturbation coefficient λ of SLCDT1 exposed as a constructor parameter.
  • Sefrioui–Perlaux (SP): one fixed-dimension problem from the simple mathematical example of M. Sefrioui and J. Perlaux [31].
  • Shim–Suh–Furukawa–Yagawa–Yoshimura (SSFYY): the fixed-dimension Test problem 2 of Mun-Bo Shim, Myung-Won Suh, Tomonari Furukawa, Genki Yagawa, and Shinobu Yoshimura [32].
  • Tan–Khor–Lee–Yang (TKLY): the fixed-dimension Test problem 2 of K. C. Tan, E. F. Khor, T. H. Lee, and Y. J. Yang [33].
  • Toint (Toi): four problems derived from the partially separable collection of Ph. L. Toint [34], whose element functions are taken as objectives in the multiobjective adaptations of Mita, Fukuda, and Yamashita [22].
  • Valenzuela-Rendón–Uresti-Charre (VU): two fixed-dimension problems from M. Valenzuela-Rendón and E. Uresti-Charre [35], using the formulations cataloged by Huband et al. [9].
  • Van Veldhuizen (VV): five problems of the test suite assembled by David A. Van Veldhuizen [36] and cataloged by Huband et al. [9].
  • Zitzler–Deb–Thiele (ZDT): five variable-dimension, two-objective problems from the real-valued test functions of Eckart Zitzler, Kalyanmoy Deb, and Lothar Thiele [19]; the source's binary-encoded test function is not implemented.
  • Zitzler–Laumanns–Thiele (ZLT): one independent-dimension problem from the test suite of Eckart Zitzler, Marco Laumanns, and Lothar Thiele [37], where it is named SPH-m, using the ZLT1 name and the general objective count cataloged by Huband et al. [9].