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.
Highlights
Many real-world problems are routinely solved using modern optimization tools (e.g. Abhishek et al, 2010; Fragniere and Gondzio, 2002; Groër et al, 2011; Paulavičius and Žilinskas, 2014; Paulavičius et al, 2020a, 2020b; Pistikopoulos et al, 2015)
It should be noted that GAMS, JuMP, and Pyomo allow initiating data structures during their declaration, while AIMMS and AMPL only support it as a separate step in the model instance building process
We can conclude that AMPL allows us to formulate an optimization problem in the shortest and potentially easiest way while providing the best performance in model instance loading times
Summary
Many real-world problems are routinely solved using modern optimization tools (e.g. Abhishek et al, 2010; Fragniere and Gondzio, 2002; Groër et al, 2011; Paulavičius and Žilinskas, 2014; Paulavičius et al, 2020a, 2020b; Pistikopoulos et al, 2015). Abhishek et al, 2010; Fragniere and Gondzio, 2002; Groër et al, 2011; Paulavičius and Žilinskas, 2014; Paulavičius et al, 2020a, 2020b; Pistikopoulos et al, 2015) These tools use the combination of a mathematical model with an appropriate solution algorithm Model formulation and the proper solution technique (Fragniere and Gondzio, 2002) They enable the formulation of a mathematical model as a human-readable set of equations while not requiring to specify how the described model should be solved or what specific solver should be used. Models written in an AML are known for the high degree of similarity to the mathematical formulation This aspect distinguishes AMLs from other types of modelling languages, like object-oriented (e.g. OptimJ), solver specific (e.g. LINGO), or generalpurpose (e.g. TOMLAB) modelling languages.
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