# Modeling constraints with CPLEXCP.jl
**URL:** https://discourse.julialang.org/t/modeling-constraints-with-cplexcp-jl/102360
**Category:** Optimization (Mathematical)
**Tags:** question, math, cplex
**Created:** [August 1, 2023, 4:08pm UTC](https://discourse.julialang.org/t/modeling-constraints-with-cplexcp-jl/102360 "2023-08-01T16:08:43Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Matheus\_Diogenes\_And](https://discourse.julialang.org/u/Matheus_Diogenes_And)
#### Post date: [August 1, 2023, 4:08pm UTC](https://discourse.julialang.org/t/modeling-constraints-with-cplexcp-jl/102360/1 "2023-08-01T16:08:43Z")
Hello everyone.
I am trying to model some constraints through constraint programming, by using [CPLEXCP.jl](https://github.com/JuliaConstraints/CPLEXCP.jl). But I am having some issues with regards to translating the constraints into functions available by the library. So, the constraint I am trying to model is this:
```julia
if x = 10 then p + 5 = q
```
However, I am struggling to find a way to express this by using the functions given by library. One straightforward solution, would be to create a variable `r`.
```julia
r = q - p
if x = 10 then r = 5
```
The above logic could be implemented as below:
```julia
# r - (q - p) = r - q + p
r_eq = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1, -1, 1], [r, q, p]), 0)
# r - q + p = 0
MOI.add_constraint(model, r_eq, MOI.EqualsTo(0))
# if x = 10 then r = 5
MOI.add_constraint(model,
MOI.VectorOfVariables([x, r]),
CP.Implication(MOI.EqualTo(10), MOI.EqualTo(5))
# github.com/JuliaConstraints/ConstraintProgrammingExtensions.jl/blob/master/src/Test/test_implication.jl#L16
)
```
However, by doing so, for each `p` and `q` we want to impose such constraint, we would have to create another variable `r`. I would like to know other ways of doing this without imposing a new variable to the model.
Case there is any confusing point, please, let me know. Thanks and regards.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [August 1, 2023, 9:55pm UTC](https://discourse.julialang.org/t/modeling-constraints-with-cplexcp-jl/102360/2 "2023-08-01T21:55:51Z")
I don’t have CPLEXCP so I can’t test, but perhaps:
```julia
# x == 10 => p - q == -5
MOI.add_constraint(
model,
MOI.Utilities.operate(vcat, Int, x, 1 * p + -1 * q),
CP.Implication(MOI.EqualTo(10), MOI.EqualTo(-5)),
)
```
---
### Author:  [@Matheus\_Diogenes\_And](https://discourse.julialang.org/u/Matheus_Diogenes_And)
#### Post date: [August 2, 2023, 5:28pm UTC](https://discourse.julialang.org/t/modeling-constraints-with-cplexcp-jl/102360/3 "2023-08-02T17:28:32Z")
Thank you very much.
Actually, it seems to be a little bit more complex, although I do not have the answer, at least not yet. I created an environment for running the above code [here](https://github.com/matheusdiogenesandrade/CPLEXCP_example/blob/main/test_conditional.jl). Basically, in order to make the command ` MOI.Utilities.operate(vcat, Int, x, 1 * p + -1 * q),` to work, we have to take so concerns:
```julia
affine::MOI.ScalarAffineFunction{Float64} = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm{Float64}.([1, -1], [p, q]), 0.0)
MOI.add_constraint(
model,
MOI.Utilities.operate(vcat, MOI.ScalarAffineFunction{Float64}, MOI.SingleVariable(x), affine),
CP.Implication(MOI.EqualTo(10), MOI.EqualTo(-5)),
)
```
However tha avobe code still presents errors:
```julia
ERROR: LoadError: MethodError: no method matching _build_constraint(::CPLEXCP.Optimizer, ::MathOptInterface.VectorAffineFunction{MathOptInterface.ScalarAffineFunction{Float64}}, ::ConstraintProgrammingExtensions.Implication{MathOptInterface.EqualTo{Int64}, MathOptInterface.EqualTo{Int64}})
Closest candidates are:
_build_constraint(::CPLEXCP.Optimizer, ::Union{MathOptInterface.VectorAffineFunction{T}, MathOptInterface.VectorOfVariables}, ::ConstraintProgrammingExtensions.AllDifferent) where T at ~/.julia/packages/CPLEXCP/jbgSe/src/MOI/wrapper_constraints_cp.jl:14
_build_constraint(::CPLEXCP.Optimizer, ::Union{MathOptInterface.VectorAffineFunction{T}, MathOptInterface.VectorOfVariables}, ::ConstraintProgrammingExtensions.Implication{S1, S2}) where {T<:Int64, S1<:MathOptInterface.AbstractSet, S2<:MathOptInterface.AbstractSet} at ~/.julia/packages/CPLEXCP/jbgSe/src/MOI/wrapper_constraints_cp_reification.jl:234
_build_constraint(::CPLEXCP.Optimizer, ::Union{MathOptInterface.VariableIndex, MathOptInterface.ScalarAffineFunction{T}}, ::ConstraintProgrammingExtensions.AntiDomain{T}) where T<:Int64 at ~/.julia/packages/CPLEXCP/jbgSe/src/MOI/wrapper_constraints_cp.jl:60
...
Stacktrace:
[1] add_constraint(model::CPLEXCP.Optimizer, f::MathOptInterface.VectorAffineFunction{MathOptInterface.ScalarAffineFunction{Float64}}, s::ConstraintProgrammingExtensions.Implication{MathOptInterface.EqualTo{Int64}, MathOptInterface.EqualTo{Int64}})
@ CPLEXCP ~/.julia/packages/CPLEXCP/jbgSe/src/MOI/wrapper_constraints.jl:29
[2] top-level scope
@ test_conditional.jl:30
[3] include(fname::String)
@ Base.MainInclude ./client.jl:476
[4] top-level scope
@ REPL[1]:1
in expression starting at test_conditional.jl:30
```
The [README](https://github.com/matheusdiogenesandrade/CPLEXCP_example/blob/main/README.md) of the project gives the step-by-step for setting up CPLEXCP locally.
Thanks for the support. Regards.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [August 2, 2023, 9:17pm UTC](https://discourse.julialang.org/t/modeling-constraints-with-cplexcp-jl/102360/4 "2023-08-02T21:17:47Z")
Your use of `operate` is incorrect. It should be something like:
```julia
affine = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1.0, -1.0], [p, q]), 0.0)
MOI.add_constraint(
model,
MOI.Utilities.operate(vcat, Float64, MOI.SingleVariable(x), affine),
CP.Implication(MOI.EqualTo(10.0), MOI.EqualTo(-5.0)),
)
```
> [@Matheus\_Diogenes\_And](#):
>
> The [README](https://github.com/matheusdiogenesandrade/CPLEXCP_example/blob/main/README.md) of the project gives the step-by-step for setting up CPLEXCP locally.
I don’t have a license.