Gurobi seems to think there are small coefficients somewhere, or large coefficients

[IainNZ]

I have a fairly simple & small model, and when I solve it with Gurobi it says:

Optimize a model with 20 rows, 40 columns and 75 nonzeros
Coefficient statistics:
  Matrix range    [0e+00, 5e+02]
  Objective range [2e-01, 5e+01]
  Bounds range    [1e+00, 1e+00]
  RHS range       [7e+01, 1e+02]
Warning: Model contains large matrix coefficient range
         Consider reformulating model or setting NumericFocus parameter
         to avoid numerical issues.

However, printing the A matrix after prepConstrMatrix reveals nothing out of the ordinary, and printing the model to an LP and loading that with gurobipy also doesn't trigger the warning. Sebastien reported to me a similar message where Gurobi said it was removing variables with very small coefficients, even though he couldn't find any by printing out. Is there somewhere we could be injecting noise?

[mlubin]

Try calling getconstrmatrix on the gurobi model instance?

[IainNZ]

I just did something similar, got Gurobi.jl to do writeproblem, nothing weird. Here is JuMP's output

Maximize
 obj: 3 VAR36 + 3 VAR37 + 3 VAR38 + 3 VAR39 + 3 VAR40 + 0 VAR11 - .64 VAR16 - .21 VAR21 - .91 VAR26 - .72 VAR31 - .64 VAR12 + 0 VAR17 - .49 VAR22 - .67 VAR27 - 1.14 VAR32 - .21 VAR13 - .49 VAR18 + 0 VAR23 - .91 VAR28 - .91 VAR33 - .91 VAR14 - .67 VAR19 - .91 VAR24 + 0 VAR29 - .91 VAR34 - .72 VAR15 - 1.14 VAR20 - .91 VAR25 - .91 VAR30 + 0 VAR35 - 50 VAR6 - 50 VAR7 - 50 VAR8 - 50 VAR9 - 50 VAR10 - 1 VAR1 - 1 VAR2 - 1 VAR3 - 1 VAR4 - 1 VAR5
Subject To
 c1: 1 VAR11 = 0
 c2: 1 VAR1 - 524 VAR6 <= 0
 c3: 1 VAR36 <= 94
 c4: 1 VAR36 - 1 VAR1 - 1 VAR11 - 1 VAR16 - 1 VAR21 - 1 VAR26 - 1 VAR31 + 1 VAR11 + 1 VAR12 + 1 VAR13 + 1 VAR14 + 1 VAR15 <= 0
 c5: 1 VAR17 = 0
 c6: 1 VAR2 - 524 VAR7 <= 0
 c7: 1 VAR37 <= 95
 c8: 1 VAR37 - 1 VAR2 - 1 VAR12 - 1 VAR17 - 1 VAR22 - 1 VAR27 - 1 VAR32 + 1 VAR16 + 1 VAR17 + 1 VAR18 + 1 VAR19 + 1 VAR20 <= 0
 c9: 1 VAR23 = 0
 c10: 1 VAR3 - 524 VAR8 <= 0
 c11: 1 VAR38 <= 116
 c12: 1 VAR38 - 1 VAR3 - 1 VAR13 - 1 VAR18 - 1 VAR23 - 1 VAR28 - 1 VAR33 + 1 VAR21 + 1 VAR22 + 1 VAR23 + 1 VAR24 + 1 VAR25 <= 0
 c13: 1 VAR29 = 0
 c14: 1 VAR4 - 524 VAR9 <= 0
 c15: 1 VAR39 <= 71
 c16: 1 VAR39 - 1 VAR4 - 1 VAR14 - 1 VAR19 - 1 VAR24 - 1 VAR29 - 1 VAR34 + 1 VAR26 + 1 VAR27 + 1 VAR28 + 1 VAR29 + 1 VAR30 <= 0
 c17: 1 VAR35 = 0
 c18: 1 VAR5 - 524 VAR10 <= 0
 c19: 1 VAR40 <= 148
 c20: 1 VAR40 - 1 VAR5 - 1 VAR15 - 1 VAR20 - 1 VAR25 - 1 VAR30 - 1 VAR35 + 1 VAR31 + 1 VAR32 + 1 VAR33 + 1 VAR34 + 1 VAR35 <= 0
Bounds
 0 <= VAR1 <= +inf
 0 <= VAR2 <= +inf
 0 <= VAR3 <= +inf
 0 <= VAR4 <= +inf
 0 <= VAR5 <= +inf
 0 <= VAR6 <= 1
 0 <= VAR7 <= 1
 0 <= VAR8 <= 1
 0 <= VAR9 <= 1
 0 <= VAR10 <= 1
 0 <= VAR11 <= +inf
 0 <= VAR12 <= +inf
 0 <= VAR13 <= +inf
 0 <= VAR14 <= +inf
 0 <= VAR15 <= +inf
 0 <= VAR16 <= +inf
 0 <= VAR17 <= +inf
 0 <= VAR18 <= +inf
 0 <= VAR19 <= +inf
 0 <= VAR20 <= +inf
 0 <= VAR21 <= +inf
 0 <= VAR22 <= +inf
 0 <= VAR23 <= +inf
 0 <= VAR24 <= +inf
 0 <= VAR25 <= +inf
 0 <= VAR26 <= +inf
 0 <= VAR27 <= +inf
 0 <= VAR28 <= +inf
 0 <= VAR29 <= +inf
 0 <= VAR30 <= +inf
 0 <= VAR31 <= +inf
 0 <= VAR32 <= +inf
 0 <= VAR33 <= +inf
 0 <= VAR34 <= +inf
 0 <= VAR35 <= +inf
 0 <= VAR36 <= +inf
 0 <= VAR37 <= +inf
 0 <= VAR38 <= +inf
 0 <= VAR39 <= +inf
 0 <= VAR40 <= +inf
General
 VAR6
 VAR7
 VAR8
 VAR9
 VAR10
End

[IainNZ]

and Gurobi.jl

Maximize
  - C0 - C1 - C2 - C3 - C4 - 50 C5 - 50 C6 - 50 C7 - 50 C8 - 50 C9
   - 0.64 C11 - 0.21 C12 - 0.91 C13 - 0.72 C14 - 0.64 C15 - 0.49 C17
   - 0.67 C18 - 1.14 C19 - 0.21 C20 - 0.49 C21 - 0.91 C23 - 0.91 C24
   - 0.91 C25 - 0.67 C26 - 0.91 C27 - 0.91 C29 - 0.72 C30 - 1.14 C31
   - 0.91 C32 - 0.91 C33 + 3 C35 + 3 C36 + 3 C37 + 3 C38 + 3 C39
Subject To
 R0: C10 = -0
 R1: C0 - 524 C5 <= -0
 R2: C35 <= 94
 R3: - C0 - 0 C10 + C11 + C12 + C13 + C14 - C15 - C20 - C25 - C30 + C35
   <= -0
 R4: C16 = -0
 R5: C1 - 524 C6 <= -0
 R6: C36 <= 95
 R7: - C1 - C11 + C15 - 0 C16 + C17 + C18 + C19 - C21 - C26 - C31 + C36
   <= -0
 R8: C22 = -0
 R9: C2 - 524 C7 <= -0
 R10: C37 <= 116
 R11: - C2 - C12 - C17 + C20 + C21 - 0 C22 + C23 + C24 - C27 - C32 + C37
   <= -0
 R12: C28 = -0
 R13: C3 - 524 C8 <= -0
 R14: C38 <= 71
 R15: - C3 - C13 - C18 - C23 + C25 + C26 + C27 - 0 C28 + C29 - C33 + C38
   <= -0
 R16: C34 = -0
 R17: C4 - 524 C9 <= -0
 R18: C39 <= 148
 R19: - C4 - C14 - C19 - C24 - C29 + C30 + C31 + C32 + C33 - 0 C34 + C39
   <= -0
Bounds
Binaries
 C5 C6 C7 C8 C9
End

[mlubin]

There's cancellation happening here, leading to zero (or near zero) coefficients.

[IainNZ]

There was cancellation in Seb's thing too. But isn't it 1-1 cancellation?

[mlubin]

Yeah, not sure why gurobi would complain about coefficients that are exactly zero.

[IainNZ]

using JuMP, Gurobi, Distributions
    n = 5
    srand(1000)
    μ = rand(50:150, n)
    σ = 0.5 * μ
    p = 3
    locs = rand(Uniform(0,1),(n,2))
    t = Matrix{Float64}(round([norm(locs[i,:]-locs[j,:]) for i in 1:n, j in 1:n],2))
    C = 50
    D = rand(5)
    m = Model(solver=GurobiSolver())
    @defVar(m, x[1:n] >= 0)
    @defVar(m, B[1:n], Bin)
    @defVar(m, y[1:n,1:n] >= 0)
    @defVar(m, S[1:n] >= 0)

    @setObjective(m, Max, p*sum(S) - sum(t.*y) - C*sum(B) - sum(x) )

    for i in 1:n
        @addConstraint(m, y[i,i] == 0)
        @addConstraint(m, x[i] <= sum(D)*B[i])
        @addConstraint(m, S[i] <= D[i])
        @addConstraint(m, S[i] <= x[i] + sum{y[j,i],j=1:n}
                                       - sum{y[i,j],j=1:n})
    end
    solve(m)

[IainNZ]

So is this a Gurobi bug then arguably?

[mlubin]

We could add a check for exact zeros here: https://github.com/JuliaOpt/JuMP.jl/blob/bb1e072630e6c4e1f5468e45ba5068a2bae383f7/src/solvers.jl#L713

[IainNZ]

Yeah, true, one pass to get true number of nnzs, then fill in second. Probably wouldn't hurt performance much.

[IainNZ]

Or one pass with push!

[mlubin]

one pass with sizehint! should be fine