fminslp VS pyomo

You can get some inspiration here. It is an SLP optimizer, wrapped around a convergence filter combined with an adaptive move limit scheme. You could in theory replace the linear optimizer with your mma version, and utilize the rest of the framework (convergence filter + adaptive move limits) I also handle constraints in a similar fashion as mma, so you should be able to see some similarities 😉

Pyomo: We tried pyomo still using the same matrix representation as above (5-minutes timeslot interval), but still encountered the same difficulty of expressing program durations as constraint. I seem to not able to make a condition inside the constraint declaration such that if this matrix entry is 1, then do this operation.

Alternative: pyomo

I’m looking for something similar to Pyomo for Python. Something that connects on the backend to something like GLPK, CBC, IPOPT. Using Google, I’ve only been able to find a few linear programming libraries. If anyone could point me the right direction, it would be greatly appreciated!

Pyomo, it even has its own book. Additionally, CVXOPT focuses on convex optimization, PuLP on linear programming (it has lots of interfaces for other solvers).

There are some optimization modeling tools, Pulp andScipy are known for linear programming (LP) modeling, CVXOPT and Pyomo for quadratic programming (QP).

To rephrase this in math terms, you're looking for the least expensive possible path that covers every node in your yard. As for tools, if you don't mind programming in python, maybe try this: http://www.pyomo.org/.

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/