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Web-Based Tool for Algebraic Modeling and Mathematical Optimization

Author

Listed:
  • Vaidas Jusevičius

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos Str. 4, LT-08412 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Remigijus Paulavičius

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos Str. 4, LT-08412 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

In this article, we present a new open-source tool for algebraic modeling and mathematical optimization. We begin by distilling the main gaps within the existing algebraic modeling languages and tools (varying performance, limited cross-compatibility, complex syntax, and different solver, feature, and problem type support). Later, we propose a state-of-the-art web-based tool (WebAML and Optimization System) for algebraic modeling languages and mathematical optimization. The tool does not require specific algebraic language knowledge, allows solving problems using different solvers, and utilizes the best characteristics of existing algebraic modeling languages. We also provide clear extension points and ideas on how we could further improve such a tool.

Suggested Citation

  • Vaidas Jusevičius & Remigijus Paulavičius, 2021. "Web-Based Tool for Algebraic Modeling and Mathematical Optimization," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2751-:d:668001
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    References listed on IDEAS

    as
    1. Michael R. Bussieck & Michael C. Ferris & Alexander Meeraus, 2009. "Grid-Enabled Optimization with GAMS," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 349-362, August.
    2. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    3. Chris Groër & Bruce Golden & Edward Wasil, 2011. "A Parallel Algorithm for the Vehicle Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 315-330, May.
    4. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    5. Miles Lubin & Iain Dunning, 2015. "Computing in Operations Research Using Julia," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 238-248, May.
    6. Stripinis, Linas & Žilinskas, Julius & Casado, Leocadio G. & Paulavičius, Remigijus, 2021. "On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization," Applied Mathematics and Computation, Elsevier, vol. 390(C).
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