Support constant values in objective

[0wenwu]

1. if the problem need to convert multi-objectives to singe-objective, it's necessary to make normalization involving some constant variables.
   It's not conveniet to construct objective containing constant, such as x+1
   Here is a trick to add constant
   constant_1=m.add_variables(lower=1, upper=1,name="constant_1")
2. class Variable only have sum function, other operations are also needed, such as std

[FabianHofmann]

@0wenwu, you are right, the current objective class does not support carrying constants. Let's leave this open and see whether there is more people who wish for this feature.

The std could be easily introduced as function. PRs are always welcome :)

[mal84emma]

Supporting constants in the objective would be really helpful. It's just very fiddly to figure out what the constants are and when they need to be put back into the cost terms (e.g. when they appear in constraints). It'd save a bunch of headache to be able to keep the constants in for consistency. Though perhaps a warning would be appreciated.

[ManOntheWindows]

Supporting constants in the objective would be really helpful. It's just very fiddly to figure out what the constants are and when they need to be put back into the cost terms (e.g. when they appear in constraints). It'd save a bunch of headache to be able to keep the constants in for consistency. Though perhaps a warning would be appreciated.

Agree

[RobbieKiwi]

A constant in the objective cost function has no impact on the optimisation itself, so if the final value of the ocf (including constant) is important to you, would it not be possible to simply add it at the end?

[mal84emma]

For simple cases I agree, but for some tasks (e.g. certain stochastic programming problems) encapsulating objective contributions which may contain constants is really useful, e.g. for compound objectives or including objective contributions in constraints. Having to manually track where objective constants can and can't be used and make adjustments gets messy quickly and breaks encapsulation, so supporting them would be helpful.
Unless there's already a nice way of accessing and removing the constant part of the objective directly before optimisation?

[RobbieKiwi]

Maybe we could add a method to get the constant part of a linear expression.
Would something like this work for you?

x: LinearExpression = ...
x_const = x.get_constant()
model.add_objective(x - x_const)
model.solve()
objective_value = x.solution
#or
objective_value = (model.objective + x_const).solution

[mal84emma]

That would be super helpful!
I think the question for me would be, is there a reason not to include this behaviour in model.solve?
It would be smoother from the user's side not to have to manage this manually. But perhaps a warning could be provided that the constant isn't being passed to the solver so the objective logs will be offset?

[RobbieKiwi]

I am a little worried that removing the constant before solving might make debugging more difficult, but perhaps with enough warning logs we could reduce the chance of confusion. I will make a PR in the coming days

[mal84emma]

That's a great point, I hadn't thought about that. Maybe a hint about removing the constant to improve debugging could be included in the warning message (with the syntax)?
PR would be greatly appreciated 😁