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pyomo
An object-oriented algebraic modeling language in Python for structured optimization problems.
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For modelling libraries in general-purpose languages, Gurobi's python bindings have the best reputation. But of course Gurobi is very expensive (I have heard about $50k for a fully unrestricted license, plus $10k yearly for support). On the open-source side, besides Google's OR-Tools, there is Pyomo [1] and PuLP [2] in Python (as the article mentions). In Julia, there is JuMP [3], whose development community is extremely enthusiastic.
Traditionally, however, mathematical models were encoded in domain-specific languages. The most prominent one is AMPL [4] which is proprietary. The glpk [5] people have developed a very neat open source clone of AMPL: the GNU MathProg language. For a more modern take on AMPL-type modelling DSLs, look at ZIMPL [6], which is open source as well.
[1] http://www.pyomo.org/
[2] https://coin-or.github.io/pulp/
[3] https://jump.dev/JuMP.jl/stable/
[4] https://ampl.com
[5] https://www.gnu.org/software/glpk/
[6] https://zimpl.zib.de/
For modelling libraries in general-purpose languages, Gurobi's python bindings have the best reputation. But of course Gurobi is very expensive (I have heard about $50k for a fully unrestricted license, plus $10k yearly for support). On the open-source side, besides Google's OR-Tools, there is Pyomo [1] and PuLP [2] in Python (as the article mentions). In Julia, there is JuMP [3], whose development community is extremely enthusiastic.
Traditionally, however, mathematical models were encoded in domain-specific languages. The most prominent one is AMPL [4] which is proprietary. The glpk [5] people have developed a very neat open source clone of AMPL: the GNU MathProg language. For a more modern take on AMPL-type modelling DSLs, look at ZIMPL [6], which is open source as well.
[1] http://www.pyomo.org/
[2] https://coin-or.github.io/pulp/
[3] https://jump.dev/JuMP.jl/stable/
[4] https://ampl.com
[5] https://www.gnu.org/software/glpk/
[6] https://zimpl.zib.de/