PULP在求解后添加更多变量。 如何在不重建的情况下使用它们更新obj和约束？

Question

if I want to add more variables to a problem already in memory in PULP, do I need to redefine/re-declare the objective function and constraints to include/use these new variables? Or is there some streamlined method to add them and have the prob do that for me?

Now, I see in PULP documentation that the LpVariable class has a paremeter option: "e – Used for column based modelling: relates to the variable's existence in the objective function and constraints"

And I also see in the doc that there is a command: "addVariableToConstraints(e)"

Does anyone have an example of the usage of these? I am not very good at using source code to deduce usage. Also, I don't see a similar function for adding a variable to objective, and when I tried to do it with prob += lpSum(...) , I got the message "Overwriting previously set objective"

Answer 1

So in PuLP the constraints of your problem are stored in an Ordered Dictionary object. Of course, this means you can alter it as you required. Your question is a little unclear, but here's all the ways you can modify your current problem with the different situations it would work in. For the sake of explanation, let's assume the two variables you're trying to add are called var1 and var2.

1. Alter the objective

In this case, it seems like your objective was a lpSum() method, although I'm not sure since you've not been specific enough in your question.

problem += problem.objective + 2*var1 - 3*var2 

This ensures you don't have to recalculate the current problem objective and call lpSum() again, since it's a heavy calculation overhead if you're doing it over and over again. Of course, anytime you alter the objective, you would get a notification saying that you're overwriting the previously set objective.

2. Alter an existing constraint

Again, assume this was your original constraint: var3 + 5*var4 >= 20 . And let's assume you want to change the constraint to: var3 + 5*var4 + var1 - 2*var2 >= 20

Then the simplest way to do that would be to previously label all the constraints as you add them in. So while creating the original constraint, you would have done the following:

problem += var3 + 5*var4 >= 20, "ConstraintName #1" 

Then to change the constraint and add in additional variables, you'd do:

problem.constraints["ConstraintName #1"] = var3 + 5*var4 + var1 - 2*var2 >= 20

Note: The method you proposed above in your question, where you add a new constraint to the original problem, instead of altering an existing constraint may not always work. This is because if the Older Constraint was more constricting/restricting, and you planned to loosen the constraint or make it more elastic by adding in additional flexibility with the new variable, then it wold fail. Because the solver would obtain both old & new constraints, and then choose the more constraining one (ie. the Older Constraint). And therefore, nothing would change.