Disjunct constraints cannot contain binary or integer variables.

[schlichtanders]

Disjunct constraints cannot contain binary or integer variables.

[hdavid16]

@schlichtanders In general, if you can avoid creating discontinuous variables for an optimization model, this will significantly improve solution performance. I don't think you will want to use the modulo function over an optimization variable, though. I may be wrong, but it sounds like your optimization model could be formulated better, which can reduce the combinatorics. If you can provide the simplest form of your model, we can discuss if it is necessary to support mixed-integer constraints inside disjuncts. However, the theory here for reformulating a disjunctive program to mip would need to be reviewed, especially in the case of the Hull reformulation. Also, Indicator reformulation would fail, but you could still do BigM.

---

As a note to us devs @pulsipher @hdavid16: https://johnhooker.tepper.cmu.edu/milpmodeling2.pdf has some theory on mixed-integer disjunct constraints in Chapter 3, but it is not clear if this extends to nonlinear systems.

[hdavid16]

@hdavid16 can you give an example how to distinguish the day and the time-of-the-day without using Integer variables?

I haven't tested this code, but here's a quick example:

using DisjunctiveProgramming

m=GDPModel()
@variable(m,0<=start[1:2])
@variable(m,0<=finish[1:2])
@variable(m,0<=duration[1:2])
@variable(m,precedence[1:2],Logical) #precedence relation
@variable(m,start_day[1:10,1:2],Logical) #day task 1 or 2 starts (between 1 and 10)

#duration constraint
@constraint(m,[i in 1:2],duration[i] = finish[i] - start[i])

#disjunction to establish precedence between task 1 or task 2
@constraint(m,finish[1] <= start[2],Disjunct(precedence[1])) #task 1 goes first
@constraint(m,finish[2] <= start[1],Disjunct(precedence[2])) #task 2 goes first
@disjunction(m,precedence)

#disjunction to select what day each task starts
@constraint(m,[i in 1:10, j in 1:2], (i + 9/24) <= start[j] <= (i + 18/24), Disjunct(start_day[i,j])) #task j must be between 9:00 and 18:00 on the day it starts
@disjunction(m,[j in 1:2], start_day[:,j])

[hdavid16]

It may often be beneficial to have more variables (https://or.stackexchange.com/questions/3209/how-to-choose-between-high-number-of-binary-variables-or-fewer-number-of-integer). However, we will look into supporting this feature.

[pulsipher]

Hi @schlichtanders, can you please provide a short code example of what you would like to model exactly?

Most GDP reformulation techniques theoretically require that the constraints inside of disjunctions only contain continuous variables to be exact. This is why we enforce that condition. With a concrete example, we can try and see if there is a workaround.

[schlichtanders]

Thank you for your help.

Here an example definition which throws the error Disjunct constraints cannot contain binary or integer variables.

using Jump
using DisjunctiveProgramming
n = 2
seconds_per_day = 24*60*60

model = GDPModel(HiGHS.Optimizer)
@variable(model, 0 <= start[1:n])  # this could also be split similar to durations

# unixepochs duration definition
@variable(model, 0 <= duration_days[1:n], Int)
@variable(model, 0 <= duration_secondsofday[1:n] <= seconds_per_day)
@expression(model, duration, seconds_per_day .* duration_days .+ duration_secondsofday)
# @variable(model, 0 <= duration)

# unixepochs end duration
@expression(model, finish, start .+ duration)

# disjunction
@variable(model, Y[1:2], Logical)
@constraint(model, finish[1] <= start[2], Disjunct(Y[1]))
@constraint(model, finish[2] <= start[1], Disjunct(Y[2]))
@disjunction(model, Y)

[hdavid16]

Why not define a variable finish that is continuous and constrained to be greater than the start variable of its same index? Can you elaborate why you are defining the number of days and adding a float to it instead of just having the start, finish, and duration variables be continuous and nonnegative?

[schlichtanders]

Sure, it is about saving some constraints.

I need to know the number of days of the duration for some other constraints of mine. I could extract these from the difference between finish and start by some extra variables and constraints (using something like modulo).

Alternatively, I can put them into the definition like done, and avoid the extra constraints, which hopefully simplifys the model overall. But this approach fails when using Disjuncts

[pulsipher]

As a note to us devs @pulsipher @hdavid16: https://johnhooker.tepper.cmu.edu/milpmodeling2.pdf has some theory on mixed-integer disjunct constraints in Chapter 3, but it is not clear if this extends to nonlinear systems.

Based on this theory, we could potentially relax the requirement that all variables are continuous and provide an opt-out keyword that users would have to enable to disable the check at their own risk if the model is nonlinear.

[hdavid16]

Yes. However, I think there are many cases where a mixed integer constraint can be avoided in a disjunct, especially if it is being added to a continuous variable as in days + seconds.

[schlichtanders]

I am now falling back to the following modulo MIP rewrite from JuMP Tips&Tricks
https://jump.dev/JuMP.jl/stable/tutorials/linear/tips_and_tricks/#Modulo

[hdavid16]

@schlichtanders feel free to share the simplest version of your model and we can discuss if this is necessary.

[hdavid16]

Based on this theory, we could potentially relax the requirement that all variables are continuous and provide an opt-out keyword that users would have to enable to disable the check at their own risk if the model is nonlinear.

@pulsipher if we decide to relax this, we will need to review the code for the BigM and Hull reformulations as any binaries (from nested disjuncts) are currently not disaggregated and binary bounds are also ignored when calculating tight M values (also for nested case)

[schlichtanders]

@schlichtanders feel free to share the simplest version of your model and we can discuss if this is necessary.

There is actually not so much more to it.

Concretely, I have multiple time intervals which I want to make non-overlapping. I am using Disjuncts for this to model both possibilities that one interval is before or after the other.

In addition I would like to restrict the time-of-the-day of a respective interval, e.g. to start after 09:00 and end before 18:00 of an arbitrary day.
The modelling is a bit different than above, but also comes down to having an integer variable for the days.

[pulsipher]

@pulsipher if we decide to relax this, we will need to review the code for the BigM and Hull reformulations as any binaries (from nested disjuncts) are currently not disaggregated and binary bounds are also ignored when calculating tight M values (also for nested case)

Making it work for BigM should be straightforward at least.

[hdavid16]

@schlichtanders based on your description, I would greatly discourage using integer variables as they are not necessary. Using proper variable bounds and constraint definitions should allow you to model this as a linear GDP which will be more performant than if you start introducing integer variables.

[schlichtanders]

@hdavid16 can you give an example how to distinguish the day and the time-of-the-day without using Integer variables?

[schlichtanders]

Thank you very much for sharing this approach.

In terms of variables and constraints it adds a massive amount of extra constraints compared to the modulus version using Integer variables. I don't know about the precise implications for performance, but I guess that using Integer Variables in Disjuncts could still be an attractive alternative.