or-tools VS pyomo

Small NP-hard problems aren't actually that bad. You can usually formulate them as eg a integer programming problem or a SMT problem, and throw an off-the-shelf solver at them.

You only need to learn the solver once, and you can re-use it for all kinds of problems. (Assuming that your instances don't have to be solved with low latency. Eg only as part of your level generation process, or at most when loading a randomly generated level, but not every frame or so.)

https://developers.google.com/optimization has a decent collection of tools.

Just saw that it looks like an upcoming release of OR-Tools might include reified tables: https://github.com/google/or-tools/commit/94f3d9b46870e7ea04...

Google OR - Tried to represent a solution to be a 5 dimensional matrix with an hour granularity. Dimensions are stations, program, project manager, day and time. If matrix[station][program][project manager][day][time] = 1, then that set is assigned, otherwise not. The main issue encountered here is about time slots, as they are not necessarily on a per hour basis. We tried time slots to be in a 5-minute interval. However, constructing the constraints that would adhere to each programs duration was proven to be difficult.

If you are just interested in getting a solution or for having a reference solver: There is a sudoku example in the OR-Tools package that uses constraint programming.

Not sql, but check out google’s OR-Tools. Hardly ever gets mentioned but looks very capable for some applications. https://developers.google.com/optimization

Then there's also the Google's solution: https://developers.google.com/optimization/

start enumerating the properties you think the solution to your problem should have. once you have this, you should be able to reformulate those properties as constraints and then you can just plug this into a combinatorial solver such as https://developers.google.com/optimization

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/