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Problem Families

MultiObjectiveProblems.jl groups benchmark constructors by their source family or publication. Each constructor returns a MultiObjectiveProblem 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].