Fix performance issues

[odow]

Cleverly calling update_model! results in an order-of-magnitude improvement.

cc @evanfields

Closes #184. (Note, running the benchmark in #184 yields an identical 10x improvement.)

benchmark_jump.jl is:

using Gurobi, JuMP
function benchmark(n = 150)
	m = JuMP.direct_model(Gurobi.Optimizer())
	@variable(m, f[1:n, 1:n] >= 0)
    return m
end
@time benchmark()
@time benchmark()
@time benchmark()
@time benchmark()
@time benchmark()

The results are

C:\Users\Oscar\.julia\dev\Gurobi>git checkout od/moi_speed
Switched to branch 'od/moi_speed'

C:\Users\Oscar\.julia\dev\Gurobi>julia --color=yes benchmark_jump.jl
Academic license - for non-commercial use only
  2.896283 seconds (5.20 M allocations: 279.623 MiB, 7.16% gc time)
Academic license - for non-commercial use only
  0.314600 seconds (821.42 k allocations: 63.965 MiB, 34.51% gc time)
Academic license - for non-commercial use only
  0.184337 seconds (802.34 k allocations: 62.967 MiB, 13.06% gc time)
Academic license - for non-commercial use only
  0.368996 seconds (802.34 k allocations: 62.967 MiB, 40.08% gc time)
Academic license - for non-commercial use only
  0.242605 seconds (802.34 k allocations: 62.967 MiB, 25.85% gc time)

C:\Users\Oscar\.julia\dev\Gurobi>git checkout master
Switched to branch 'master'
Your branch is up to date with 'origin/master'.

C:\Users\Oscar\.julia\dev\Gurobi>julia --color=yes benchmark_jump.jl
Academic license - for non-commercial use only
  4.386719 seconds (5.49 M allocations: 294.247 MiB, 4.21% gc time)
Academic license - for non-commercial use only
  1.936523 seconds (802.34 k allocations: 62.966 MiB, 3.52% gc time)
Academic license - for non-commercial use only
  1.981247 seconds (821.42 k allocations: 63.966 MiB, 4.13% gc time)
Academic license - for non-commercial use only
  1.925684 seconds (802.34 k allocations: 62.967 MiB, 1.39% gc time)
Academic license - for non-commercial use only
  2.019717 seconds (802.34 k allocations: 62.967 MiB, 6.44% gc time)

[evanfields]

I can confirm this branch gives a huge speedup on our research code - thanks! This is a really big deal for the problem we're working on.

Not sure I have much more to add. It seems like there is still meaningful overhead in solver communication; though surely some of that is inevitable. Is there a (distant) future where models can be passed at once rather than built incrementally, leading to further speedups?

[mlubin]

Is there a (distant) future where models can be passed at once rather than built incrementally, leading to further speedups?

Yes, MOI is structured to allow this. Gurobi would need to implement copy_to efficiently to construct the constraint matrix all together instead of falling back to incrementally adding constraints.

[odow]

Gurobi would need to implement copy_to

LinQuadOptInterface.j should be the one to implement copy_to. The solver wrappers all implement plural arguments. I've opened an issue: JuliaOpt/LinQuadOptInterface.jl#85.

[blegat]

Seems to be the right fix