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Experimental Analysis of Algebraic Modelling Languages for Mathematical Optimization
Volume 32, Issue 2 (2021), pp. 283–304
Pub. online: 23 March 2021      Type: Research Article      Open accessOpen Access
Received
1 October 2020
Accepted
1 March 2021
Published
23 March 2021

Abstract

In this work, we perform an extensive theoretical and experimental analysis of the characteristics of five of the most prominent algebraic modelling languages (AMPL, AIMMS, GAMS, JuMP, and Pyomo) and modelling systems supporting them. In our theoretical comparison, we evaluate how the reviewed modern algebraic modelling languages match the current requirements. In the experimental analysis, we use a purpose-built test model library to perform extensive benchmarks. We provide insights on which algebraic modelling languages performed the best and the features that we deem essential in the current mathematical optimization landscape. Finally, we highlight possible future research directions for this work.

References

 
Abhishek, K., Leyffer, S., Linderoth, J. (2010). FilMINT: an outer approximation-based solver for convex mixed-integer nonlinear programs. INFORMS Journal on Computing, 22(4), 555–567. https://doi.org/10.1287/ijoc.1090.0373.
 
Achterberg, T., Bixby, R.E., Gu, Z., Rothberg, E., Weninger, D. (2019). Presolve reductions in mixed integer programming. INFORMS Journal on Computing. https://doi.org/10.1287/ijoc.2018.0857.
 
Cosma, O., Pop, P.C., Dănciulescu, D. (2020). A parallel algorithm for solving a two-stage fixed-charge transportation problem. Informatica, 31(4), 681–706. https://doi.org/10.15388/20-INFOR432.
 
Dantzig, G.B. (1963). The classical transportation problem. In: Linear Programming and Extensions. Princeton University Press, Princeton, NJ, pp. 299–315. https://doi.org/10.1515/9781400884179-015.
 
Dunning, I., Huchette, J., Lubin, M. (2017). JuMP: a modeling language for mathematical optimization. SIAM Review, 59(2), 295–320. https://doi.org/10.1137/15m1020575.
 
Fernández, P., Lančinskas, A., Pelegrín, B., Žilinskas, J. (2020). A discrete competitive facility location model with minimal market share constraints and equity-based ties breaking rule. Informatica, 31(2), 205–224. https://doi.org/10.15388/20-INFOR410.
 
Fourer, R. (2003). AMPL: A Modeling Language for Mathematical Programming. Thomson/Brooks/Cole, Pacific Grove, CA.
 
Fourer, R. (2013). Algebraic modeling languages for optimization. In: Encyclopedia of Operations Research and Management Science. Springer, US, pp. 43–51. https://doi.org/10.1007/978-1-4419-1153-7.
 
Fourer, R. (2017). Linear programming: software survey. OR/MS Today, 44(3).
 
Fragniere, E., Gondzio, J. (2002). Optimization modeling languages. In: Handbook of Applied Optimization, pp. 993–1007.
 
Gay, D.M. (2005). Writing .nl files. Optimization and Uncertainty Estimation.
 
Groër, C., Golden, B., Wasil, E. (2011). A parallel algorithm for the vehicle routing problem. INFORMS Journal on Computing, 23(2), 315–330. https://doi.org/10.1287/ijoc.1100.0402.
 
Gómez, F.J.O., López, G.O., Filatovas, E., Kurasova, O., Garzón, G.E.M. (2019). Hyperspectral image classification using isomap with SMACOF. Informatica, 30(2), 349–365. https://doi.org/10.15388/Informatica.2019.209.
 
Hart, W.E., Watson, J.-P., Woodruff, D.L. (2011). Pyomo: modeling and solving mathematical programs in Python. Mathematical Programming Computation, 3(3), 219–260.
 
Hart, W.E., Laird, C.D., Watson, J.-P., Woodruff, D.L., Hackebeil, G.A., Nicholson, B.L., Siirola, J.D. (2017). Pyomo–Optimization Modeling in Python, Vol. 67, 2nd ed. Springer Science & Business Media, US.
 
Hürlimann, T. (1999). Mathematical Modeling and Optimization. Applied Optimization, Vol. 31. Springer US, Boston, MA. 978-1-4419-4814-4 978-1-4757-5793-4. https://doi.org/10.1007/978-1-4757-5793-4.
 
Jusevičius, V., Paulavičius, R. (2019). Algebraic Modeling Language Benchmark. GitHub. https://github.com/vaidasj/alg-mod-rev/.
 
Kallrath, J. (2004). Modeling Languages in Mathematical Optimization, Vol. 88. Springer Science & Business Media, US. https://doi.org/10.1007/978-1-4613-0215-5.
 
Lee, K.-Y., Lim, J.-S., Ko, S.-S. (2019). Endosymbiotic evolutionary algorithm for an integrated model of the vehicle routing and truck scheduling problem with a cross-docking system. Informatica, 30(3), 481–502. https://doi.org/10.15388/Informatica.2019.215.
 
Lubin, M., Dunning, I. (2015). Computing in operations research using Julia. INFORMS Journal on Computing, 27(2), 238–248. https://doi.org/10.1287/ijoc.2014.0623.
 
McCarl, B.A., Meeraus, A., van der Eijk, P., Bussieck, M., Dirkse, S., Nelissen, F. (2016). McCarl Expanded GAMS User Guide. Citeseer, US.
 
Paulavičius, R., Žilinskas, J. (2014). Simplicial Global Optimization. SpringerBriefs in Optimization. Springer, New York. 978-1-4614-9092-0. https://doi.org/10.1007/978-1-4614-9093-7.
 
Paulavičius, R., Adjiman, C.S. (2020). New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm. Journal of Global Optimization, 77(2), 197–225. https://doi.org/10.1007/s10898-020-00874-3.
 
Paulavičius, R., Sergeyev, Y.D., Kvasov, D.E., Žilinskas, J. (2014). Globally-biased DISIMPL algorithm for expensive global optimization. Journal of Global Optimization, 59(2-3), 545–567. https://doi.org/10.1007/s10898-014-0180-4.
 
Paulavičius, R., Gao, J., Kleniati, P.-M., Adjiman, C.S. (2020a). BASBL: branch-and-sandwich BiLevel solver: implementation and computational study with the BASBLib test set. Computers & Chemical Engineering, 132, 106609. https://doi.org/10.1016/j.compchemeng.2019.106609.
 
Paulavičius, R., Sergeyev, Y.D., Kvasov, D.E., Žilinskas, J. (2020b). Globally-biased BIRECT algorithm with local accelerators for expensive global optimization. Expert Systems with Applications, 144, 113052. https://doi.org/10.1016/j.eswa.2019.113052.
 
Pistikopoulos, E.N., Diangelakis, N.A., Oberdieck, R., Papathanasiou, M.M., Nascu, I., Sun, M. (2015). PAROC—an integrated framework and software platform for the optimisation and advanced model-based control of process systems. Chemical Engineering Science, 136, 115–138. https://doi.org/10.1016/j.ces.2015.02.030.
 
Puranik, Y., Sahinidis, N.V. (2017). Domain reduction techniques for global NLP and MINLP optimization. Constraints, 22(3), 338–376. https://doi.org/10.1007/s10601-016-9267-5.
 
Rothberg, E. (2020). How A Mathematical Optimization Model Can Help Your Business Deal With Disruption. https://forbes.com/sites/forbestechcouncil/2020/08/24/how-a-mathematical-optimization-model-can-help-your-business-deal-with-disruption.
 
Stripinis, L., Paulavičius, R., Žilinskas, J. (2019). Penalty functions and two-step selection procedure based DIRECT-type algorithm for constrained global optimization. Structural and Multidisciplinary Optimization, 59(6), 2155–2175. https://doi.org/10.1007/s00158-018-2181-2.
 
Stripinis, L., Žilinskas, J., Casado, L.G., Paulavičius, R. (2021). On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization. Applied Mathematics and Computation, 390, 125596. https://doi.org/10.1016/j.amc.2020.125596.

Biographies

Jusevičius Vaidas
vaidas.jusevicius@mif.vu.lt

V. Jusevičius received the master’s degree in software engineering from Vilnius University, Vilnius, Lithuania, in 2011. In 2017 he started PhD studies in computer science at Vilnius University, Institute of Data Science and Digital Technologies. His thesis title “Research and Development of an Open Source System for Algebraic Modeling Languages”. He is working as a partnership associate professor in Vilnius University, Institute of Computer Science, and as a Chief Software Architect for Danske Bank A/S.

Oberdieck Richard
https://orcid.org/0000-0002-8685-8694
oberdieck@gurobi.com

R. Oberdieck obtained his bachelor and MSc degrees from ETH Zurich in Switzerland (2009–1013), before pursuing a PhD in Chemical Engineering at Imperial College London, UK, which he completed in 2017. After using his knowledge in mathematical modelling and optimization in the space of renewable energies at the world leader in offshore wind energy, Ørsted A/S, he is now helping companies around the world to unlock business value through mathematical optimization as a Technical Account Manager for Gurobi Optimization, LLC.

Paulavičius Remigijus
https://orcid.org/0000-0003-2057-2922
remigijus.paulavicius@mif.vu.lt

R. Paulavičius received the PhD degree in computer science from Vytautas Magnus University, Kaunas, Lithuania, in 2010. He was a postdoctoral researcher with Vilnius University, Vilnius, Lithuania, and a research associate with Imperial College London, London, UK. He is currently a professor and the Head of the Blockchain Technologies Group, Institute of Data Science and Digital Technologies, Vilnius University. His research interests include optimization, distributed ledger technologies, parallel and distributed computing, machine learning, and the development and application of various operation research techniques.


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Keywords
algebraic modelling languages optimization AMPL AIMMS GAMS JuMP Pyomo

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