# JuMP mutually exclusive indices iterated over the same set

**URL:** <https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [March 29, 2021, 11:10pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198 "2021-03-29T23:10:13Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Paris\_Pijuan](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@Paris\_Pijuan](https://discourse.julialang.org/u/Paris_Pijuan)\
**Post date:** [March 29, 2021, 11:10pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198/1 "2021-03-29T23:10:13Z")

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Hello,

I am new here and a relatively new Julia user. I have a constraint in a model I am writing where I have variables twice indexed over the same set, but I need the indices to iterate mutually exclusively. The code is:

(ThreeZH2 is the model name, variables start with ‘v’, constraints start with ‘c’, say ‘vTNUM’ is a variable, ‘cTCAP’ is a constraint)

```
@constraints(ThreeZH2, begin 
    cTCap[t in T, l in L, n in N, m in N],
        transport.max_flow[l,n,m] * (vTNUM[n,m] + vTNUM[m,n]) >= vFLOW[t,l,n,m] + vFLOW[t,l,m,n] 

    cTSym[l in L, n in N, m in M]
        vTNUM[n,m] == vTNUM[m,n]
end)

```

for context, variables start with ‘v’ such as vTNUM is a variable. The indices n and m are both indexed over the set ‘N’ which is say 1:3, or in general 1:p where p is some number (For my model N = 1:3).

**The problem is** if I run this constraint n and m can both equal the same number at the same time, say n = 2 and m = 2. I need the indices n and m to be mutually exclusive where m does not equal n. I’m sorry if I am not explaining this well, I hope the problem statement is clear. I feel like the solution should be simple but I cannot figure it out. Any suggestions would be very helpful! Sorry if there is another post with this solution but I could not find one.

Thank you!

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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:** [March 29, 2021, 11:15pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198/2 "2021-03-29T23:15:02Z")

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Hi there!

Use `; m != n]`:

```nohighlight
model = Model()
@variable(model, x[1:4])
@constraint(model, c[a=1:4, b=1:4; a != b], x[a] + x[b] == 1)

```

Docs: [https://jump.dev/JuMP.jl/stable/constraints/#SparseAxisArrays](https://jump.dev/JuMP.jl/stable/constraints/#SparseAxisArrays)

---

<div class="post-metadata">

**Author:** ![Paris\_Pijuan](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@Paris\_Pijuan](https://discourse.julialang.org/u/Paris_Pijuan)\
**Post date:** [March 29, 2021, 11:20pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198/3 "2021-03-29T23:20:44Z")

</div>

Thank you for such a quick reply! Goodness, I knew it would be something simple, I tried  
`m != n in N` but of course didn’t work so wasn’t sure that was the right way. I’ll use `cTCap[t in T, l in L, n in N, m != n]`.

Just to check for concept purposes… this means `m` is also indexed by the same set as `n` but not equal to the `n`? Straightforward, thank you again!

---

<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:** [March 29, 2021, 11:25pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198/4 "2021-03-29T23:25:40Z")

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You want `cTCap[t in T, l in L, n in N, m in N; m != n]`. (The semicolon `;` is important.) You can read this as “for t in T, l in L, n in N, and m in N, where `m` is not equal to `n`”.

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<div class="post-metadata">

**Author:** ![Paris\_Pijuan](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@Paris\_Pijuan](https://discourse.julialang.org/u/Paris_Pijuan)\
**Post date:** [March 29, 2021, 11:26pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198/5 "2021-03-29T23:26:24Z")

</div>

Perfect, I am glad I checked. Still learning, and I appreciate all the help. That makes a lot of sense.

---

<div class="post-metadata">

**Author:** ![Paris\_Pijuan](https://avatars.discourse-cdn.com/v4/letter/p/bcef8e/32.png) [@Paris\_Pijuan](https://discourse.julialang.org/u/Paris_Pijuan)\
**Post date:** [April 7, 2021, 5:05pm UTC](https://discourse.julialang.org/t/jump-mutually-exclusive-indices-iterated-over-the-same-set/58198/6 "2021-04-07T17:05:01Z")

</div>

To anyone curious, I found another iteration of this problem.

In a new iteration of this problem, I have the variable `vFLOW[t,l,n,m]` where `n` and `m` are indices both defined over the set `N`. I have a constraint that is defined over `n in N` but not over the index `m`. Instead, I sum over `m` for the variable` vFLOW[t,l,n,m]` within the constraint. However, since I have defined the variable `vFLOW[t,l,n,m]` as `vFLOW[t in T, l in L, n in N, m in N; m != n] >= 0`, I must sum over `m in N; m != n`.

When I run this constraint I get the error:

ERROR: syntax: invalid keyword argument syntax “(m != n)” around /Users/parispijuan/.julia/packages/MutableArithmetics/bPWR4/src/rewrite.jl:276  
Stacktrace:  
[1] top-level scope at REPL[93]:1

However, if I remove the the `m != n` I get an error telling me there is now `vFLOW[1,1,1,1]`, because, of course, I have defined the variable so that `m != n`.

I guess one work around is to define the variable `vFLOW[t,l,n,m`] to be zero for `n = m` and just sum normally but I was wondering if there was another way.

The full constraint is:

```julia
STARTS and INTERIORS are subsets of the full time of the model, set T. hpp is "hours_per_period". These are wrapping constraints for time reduction. But the problem is actually in the sum. 

    # -- G) State of Charge constraint + Wrap
    @constraints(ThreeZH2, begin
        cSOC[t in INTERIORS, s in S, n in N],
            vSOC[t,s,n] == vSOC[t-1,s,n] + in_eff * sum(vGENG[t,g,n] for g in G) - out_eff * vGENS[t,s,n] + sum(vFLOW[t-1,l,n,m] - vFLOW[t,l,m,n] for l in L, m in N; m != n)

        cSOC[t in STARTS, s in S, n in N],
            vSOC[t,s,n] == vSOC[t+hpp-1,s,n] + in_eff * sum(vGENG[t,g,n] for g in G) - out_eff * vGENS[t,s,n] + sum(vFLOW[t+hpp-1,l,n,m] - vFLOW[t,l,m,n] for l in L, m in N; m != n)
    end)

```