Abstract.
Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables, collected from the literature.
The test problems are available online in AMPL and were translated into the input formats of the various solvers using routines from the COCONUT environment. These translators are available online, too.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Barr, R.S., Golden, B.L., Kelly, J.P., Resende, M.G.C., Stewart, W.R.: Designing and reporting on computational experiments with heuristic methods. J. Heuristics 1, 9–32 (1995) http://www.research.att.com/~mgcr/abstracts/guidelines.html
Benhamou, F., Goualard, F.: Universally Quantified Interval Constraints. In: Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming (CP’2000), 2000, pp. 67–82
COCONUT test results, WWW-directory, 2004, http://www.mat.univie.ac.at/~neum/glopt/coconut/tests/figures/
Crowder, H.P., Dembo, R.S., Mulvey, J.M.: On reporting Computational Experiments with Mathematical Software. ACM Transactions on Mathematical Software 5, 193–203 (1979)
Gould, N.I.M., Orban, D., Toint, Ph.L.: CUTEr, a constrained and unconstrained testing environment, revisited. WWW-document, 2001. http://cuter.rl.ac.uk/cuter-www/problems.html
Dixon, L.C.W., Szegö, G.P.: The Global Optimization Problem: An Introduction. In: Towards Global Optimization 2, North-Holland, Amsterdam 1978, pp. 1–15
Dolan, E.D., Moré, J.J.: Benchmarking Optimization Software with COPS. Tech. Report ANL/MCS-246, Argonne Nat. Lab., November 2000. http://www-unix.mcs.anl.gov/~more/cops
Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Programming 91, 201–213 (2002), http://www-unix.mcs.anl.gov/~more/cops
Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. Duxbury Press, Brooks/Cole Publishing Company, 1993, http://www.ampl.com/cm/cs/what/ampl/
Frontline Systems, Inc., Solver Technology - Global Optimization, WWW-document (2003), http://www.solver.com/technology5.htm
GAMS Solver descriptions, GAMS/OQNLP, WWW-document, 2003, http://www.gams.com/solvers/solvers.htm#OQNLP
GAMS World, WWW-document, 2002, http://www.gamsworld.org
GLOBAL Library, WWW-document, 2002, http://www.gamsworld.org/global/globallib.htm
Greenberg, H.J.: Computational testing: Why, how, and how much. ORSA J. Comput. 2, 94–97 (1990)
Huyer, W.: A comparison of some algorithms for bound constrained global optimization. WWW-document, 2004, http://www.mat.univie.ac.at/~neum/glopt/contrib/compbound.pdf
ILOG: ILOG Solver. Reference Manual, 2002
Jackson, R.H.F., Boggs, P.T., Nash, S.G., Powell, S.: Guidelines for reporting results of computational experiments. Report of the ad hoc committee. Math. Program. 49, 413–426 (1990/91)
Janka, E.: Vergleich stochastischer Verfahren zur globalen Optimierung. Diplomarbeit, Mathematisches Inst., Universität Wien, 1999 A shorter online version in English language is at http://www.mat.univie.ac.at/~neum/glopt/janka/gopt_eng.html.
Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht 1996, http://www.mscs.mu.edu/~globsol
Lebbah, Y.: ICOS (Interval COnstraints Solver), WWW-document (2003), http://www-sop.inria.fr/coprin/ylebbah/icos/
Lindo Systems, Inc., New LINGO 8.0, WWW-document, 2003, http://www.lindo.com/table/lgofeatures8t.html
Mittelmann, H.: Benchmarks. WWW-document, 2002, http://plato.la.asu.edu/topics/benchm.html
Mongeau, M., Karsenty, H., Rouzé, V., Hiriart-Urruty,J.-B.: Comparison of public-domain software for black box global optimization. Optimization Methods and Software 13, 203–226 (2000) http://mip.ups-tlse.fr/publi/rapp99/99.50.html
Murtagh, B.A., Saunders, M.A.: MINOS 5.4 User’s Guide, Report SOL 83-20R, Systems Optimization Laboratory. Stanford University, December 1983 (revised February 1995), http://www.sbsi-sol-optimize.com/Minos.htm
Neumaier, A.: Complete Search in Continuous Global Optimization and Constraint Satisfaction. In: Acta Numerica 2004, A. Iserles (ed.), Cambridge University Press 2004, pp. 271–369
Neumaier, A., Shcherbina, O.: Safe bounds in linear and mixed-integer programming. Math. Programming A 99, 283–296 (2004), http://www.mat.univie.ac.at/∼neum/papers.html#mip
Pinter, J.D.: Global Optimization in Action. Kluwer, Dordrecht 1996, http://www.dal.ca/~jdpinter/l_s_d.html
Ratliff, H.D., Pierskalla, W.: Reporting Computational Experience in Operations Research. Operations Research 29 (2), xi–xiv (1981)
Ryoo, H.S., Sahinidis, N.V.: A branch-and-reduce approach to global optimization. J. Global Optim. 8, 107–139 (1996), http://archimedes.scs.uiuc.edu/baron/baron.html
Schichl, H.: Global optimization in the COCONUT project. In: Proceedings of the Dagstuhl Seminar “Numerical Software with Result Verification”. Springer Lecture Notes in Computer Science 2991, Springer, Berlin, 2004
Schichl, H.: Mathematical Modeling and Global Optimization, Habilitation Thesis, 2003, Cambridge Univ. Press, to appear. http://www.mat.univie.ac.at/~herman/papers/habil.ps
Schichl, H.: The COCONUT Environment. Web site, 2004, http://www.mat.univie.ac.at/coconut- environment/
Shcherbina, O., Neumaier, A.: Djamila Sam-Haroud, Xuan-Ha Vu and Tuan-Viet Nguyen, Benchmarking global optimization and constraint satisfaction codes. In: Ch. Bliek, Ch. Jermann, A. Neumaier (eds.), Global Optimization and Constraint Satisfaction, Springer, Berlin 2003
Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, Dordrecht 2002
Tawarmalani, M., Sahinidis, N.V.: Global optimization of mixed-integer nonlinear programs: A theoretical and computational study, Math. Programming 99, 563–591 (2004)
Vanderbei, B.: Nonlinear Optimization Models. WWW-document, http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Neumaier, A., Shcherbina, O., Huyer, W. et al. A comparison of complete global optimization solvers. Math. Program. 103, 335–356 (2005). https://doi.org/10.1007/s10107-005-0585-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10107-005-0585-4