# Binary integer variable returned as float64

**URL:** <https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [November 23, 2020, 7:36pm UTC](https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647 "2020-11-23T19:36:07Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![bvilmann](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bvilmann/32/19775_2.png) [@bvilmann](https://discourse.julialang.org/u/bvilmann)\
**Post date:** [November 23, 2020, 7:36pm UTC](https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647/1 "2020-11-23T19:36:07Z")

</div>

I have a mixed-integer optimization problem with two variables: A binary integer, `x`, and a float, `P_G`  
I was a little surprised that the value matrix of the binary integer variable was of type float64 and not int64:

```julia
julia> value.(x)
10×100 Array{Float64,2}:
 0.0 1.0 1.0 0.0 0.0 -0.0 0.0 … 1.0 1.0 1.0 1.0 1.0 1.0
...
 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 1.0 

```

This is immediately no problem, but I also get “actual floats” in between (e.g. values \> 0 and \< 1):

```julia
value.(x)[value.(x) .>0]
489-element Array{Float64,1}:
 1.0
 1.0
 1.0
 1.0
 0.9999999999999999
 1.0
...

```

Should I provide further inputs for my solver or is this unintended performance?

My model is of a simple “unit commitment” problem:

```julia
# Data
P_C = [50 200; # Power capacity
    25 250;
    75 300;
    100 400;
    125 500;
    150 600;
    175 700;
    200 800;
    225 900;
    250 1000;]
P_D = LinRange(0, sum(P_C[:,2]), 100) # Power demand
F = rand(100:500,10) # Random prod. prices
T = length(P_D) # Number of time steps
N = length(P_C[:,1]) # Number of generators

# Model
m = Model(CPLEX.Optimizer) # Model
@variable(m, x[1:N,1:T], Bin,start=0) # Unit activation
@variable(m, P_G[i=1:N,1:T]) # Power generation
for i in 1:T # Load balance
    @constraint(m, sum(P_G[:,i]) == P_D[i])
end
for i in 1:N # Unit generation limit
    for j in 1:T
        @constraint(m, P_C[i,1]*x[i,j] <= P_G[i,j])
        @constraint(m,P_G[i,j] <= P_C[i,2]*x[i,j])
    end
end
@objective(m,Min,sum((P_G[:,1:T].*x[1:N,1:T]).*F[1:N])) # Objective function
optimize!(m) # Solve

```

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [November 23, 2020, 8:02pm UTC](https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647/2 "2020-11-23T20:02:55Z")

</div>

This is expected behavior. All variables are `Float64` and solvers use tolerances for checking integrality. Read more:

> **[Documentation - Gurobi Optimization](https://www.gurobi.com/documentation/9.0/refman/num_tolerances_and_user_sc.html)**
>
> Est. reading time: 1 minute

---

<div class="post-metadata">

**Author:** ![bvilmann](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bvilmann/32/19775_2.png) [@bvilmann](https://discourse.julialang.org/u/bvilmann)\
**Post date:** [November 23, 2020, 8:38pm UTC](https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647/3 "2020-11-23T20:38:30Z")

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Thanks for your answer! It makes sense - and I guess it might be the best way to return data back from the solver like that.

However, it just occurred counter-intuitive to me that a plot did not show correct properties because I could not use an obvious logical expression to create an array from the “binary” variable: `colors = [i == 1 ? "green" : "red" for i in value.(x)]`.

But yet again, thanks for your answer 🙂

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [November 23, 2020, 10:32pm UTC](https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647/4 "2020-11-23T22:32:02Z")

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```julia
colors = [round(Int, i) == 1 ? "green" : "red" for i in value.(x)]

```

---

<div class="post-metadata">

**Author:** ![bvilmann](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bvilmann/32/19775_2.png) [@bvilmann](https://discourse.julialang.org/u/bvilmann)\
**Post date:** [November 23, 2020, 10:53pm UTC](https://discourse.julialang.org/t/binary-integer-variable-returned-as-float64/50647/5 "2020-11-23T22:53:39Z")

</div>

Yep. That would be the proper way to do it. It is approximate 10 days since I started to learn Julia and JuMP and I have fallen in love with the syntax, performance, and intuition - so like with any other romance, the veil of love slowly disappears and you begin to see flaws (even though it might not even be). I am glad that you took your time to point out the purpose of the Float64. All the best!