Wanted: better error messages

In [1] a user tries the following constraint:

mdl.addConstrs((t[i,k] * X[i,j,k] - te1[i] <= 5) >> (z1[i,k] == 1) for i,j,k in arcos if i != 0 and i != 23)

(t and X and variables). This is not accepted, and the following error message is issued:

AttributeError: 'gurobipy.QuadExpr' object has no attribute 'getVar'

This is a terrible error message. It does not describe the real, underlying problem, and it does not tell the user what to do next. Developers typically do not pay much attention to error messages. Often they seem more aimed to make life easy for the developer than providing assistance to an already confused user. In this case, I believe the modeling tool did not even issue an error message, but rather made assumptions without checking, and left it to the Python run-time system to complain. 

This constraint has two problems: 

• Indicator constraints have a simple binary variable as condition, not a general (boolean) expression
• Only linear constraints are supported in indicator constraints

Maybe a better message is:

Indicator constraints have the form:

        binary variable == 0 ==> linear constraint

or

        binary variable == 1 ==> linear constraint 

Your constraint does not have this form. You need to reformulate it to fit this format, or use a different (big-M) formulation.

Well-formed and meaningful error messages are very important. The user is already confused, otherwise (s)he would formulate a correct constraint. Adding confusing error messages to this confusion is not a good idea. A good error message could have prevented this post. We can think of error messages as the UI (User Interface) when it really matters: when the user needs help. Developers should pay much more attention to this.

A question for another day is of course: why are only linear constraints supported?

References

1. AttributeError: 'gurobipy.QuadExpr' object has no attribute 'getVar', https://stackoverflow.com/questions/71153625/attributeerror-gurobipy-quadexpr-object-has-no-attribute-getvar/71158372

SLSQP original paper

This is somewhat hard to find (although I did), so I share it. This is the original paper[1] describing the SLSQP solver used in scipy[2]:

Visualization: Animating flow along an edge

In a large network, it is a bit of a pain to visualize the flow. Here is an attempt to show the shortest path in a random sparse directed graph. The shortest path is of course a min-cost flow of one unit. I used cytoscape.js [1] to generate the picture.

4-color maps: another model

In [1], I discussed coloring all US counties (3,221 of them) such that neighboring counties have a different color. The famous 4-color theorem says we can do this with just 4 colors. After some adventures with the data, I was indeed able to produce maps with 4 colors.

 

Model 1: US Counties colored with minimum number of colors

An interesting part is the color count table. That table shows the number of counties colored by each color. This is a bit unbalanced. So an obvious question is:

Can we find a 4-coloring that has a more equal use of colors?