Add an example of column generation

[dourouc05]

Follows #2004 and #2008. Supersedes #2006.

I cleaned up the history from the previous PR, and took into account the remaining comments. There is one outstanding issue (line 140 of this PR; this was https://github.com/JuliaOpt/JuMP.jl/pull/2006/files#diff-46229f75b87dbb3f6099492776c892edR143):

Why does a dual value of 0.0 cause GLPK to crash? That shouldn't happen.

Actually, it's more GPLK.jl that gives an error (Cbc.jl too):

ERROR: LoadError: AssertionError: dual >= 0.0
Stacktrace:
 [1] __assert_dual_sense__ at C:\Users\…\.julia\packages\LinQuadOptInterface\ZMx9f\src\solve.jl:210 [inlined]
 [2] get at C:\Users\…\.julia\packages\LinQuadOptInterface\ZMx9f\src\solve.jl:217 [inlined]
 [3] get(::MathOptInterface.Bridges.LazyBridgeOptimizer{GLPK.Optimizer,MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Bridges.AllBridgedConstraints{Float64}}}, ::MathOptInterface.ConstraintDual, ::MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64},MathOptInterface.GreaterThan{Float64}}) at C:\Users\…\.julia\packages\MathOptInterface\C3lip\src\Bridges\bridgeoptimizer.jl:236
 [4] get(::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.AbstractOptimizer,MathOptInterface.Utilities.UniversalFallback{JuMP._MOIModel{Float64}}}, ::MathOptInterface.ConstraintDual, ::MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64},MathOptInterface.GreaterThan{Float64}}) at C:\Users\…\.julia\packages\MathOptInterface\C3lip\src\Utilities\cachingoptimizer.jl:453
 [5] _moi_get_result(::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.AbstractOptimizer,MathOptInterface.Utilities.UniversalFallback{JuMP._MOIModel{Float64}}}, ::MathOptInterface.ConstraintDual, ::Vararg{Any,N} where N) at C:\Users\…\.julia\dev\JuMP\src\JuMP.jl:618
 [6] get(::Model, ::MathOptInterface.ConstraintDual, ::ConstraintRef{Model,MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64},MathOptInterface.GreaterThan{Float64}},ScalarShape}) at C:\Users\…\.julia\dev\JuMP\src\JuMP.jl:649
 [7] _constraint_dual(::ConstraintRef{Model,MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64},MathOptInterface.GreaterThan{Float64}},ScalarShape}) at C:\Users\…\.julia\dev\JuMP\src\constraints.jl:545
 [8] dual(::ConstraintRef{Model,MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64},MathOptInterface.GreaterThan{Float64}},ScalarShape}) at C:\Users\…\.julia\dev\JuMP\src\constraints.jl:538
 [9] _broadcast_getindex_evalf at .\broadcast.jl:625 [inlined]
 [10] _broadcast_getindex at .\broadcast.jl:598 [inlined]
 [11] getindex at .\broadcast.jl:558 [inlined]
 [12] copyto_nonleaf!(::Array{Float64,1}, ::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1},Tuple{Base.OneTo{Int64}},typeof(dual),Tuple{Base.Broadcast.Extruded{Array{ConstraintRef{Model,C,Shape} where Shape<:AbstractShape where C,1},Tuple{Bool},Tuple{Int64}}}}, ::Base.OneTo{Int64}, ::Int64, ::Int64) at .\broadcast.jl:982
 [13] copy at .\broadcast.jl:836 [inlined]
 [14] materialize at .\broadcast.jl:798 [inlined]
 [15] #example_cutting_stock#3(::Int64, ::typeof(example_cutting_stock)) at C:\Users\…\Desktop\a.jl:126
 [16] example_cutting_stock() at C:\Users\…\Desktop\a.jl:88
 [17] top-level scope at C:\Users\…\Desktop\a.jl:175

[codecov]

Codecov Report

Merging #2010 into master will increase coverage by 0.43%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master    #2010      +/-   ##
==========================================
+ Coverage   91.41%   91.84%   +0.43%     
==========================================
  Files          33       33              
  Lines        4217     4771     +554     
==========================================
+ Hits         3855     4382     +527     
- Misses        362      389      +27

Impacted Files	Coverage Δ
src/constraints.jl	90.5% <0%> (-1.11%)	⬇️
src/objective.jl	91.07% <0%> (-0.11%)	⬇️
src/operators.jl	86.89% <0%> (-0.05%)	⬇️
src/_Derivatives/forward.jl	97.61% <0%> (-0.01%)	⬇️
src/nlp.jl	92.2% <0%> (+0.27%)	⬆️
src/variables.jl	97.66% <0%> (+2.42%)	⬆️
src/JuMP.jl	87.01% <0%> (+2.45%)	⬆️
src/copy.jl	97.67% <0%> (+2.67%)	⬆️
src/parse_nlp.jl	95.19% <0%> (+4.22%)	⬆️

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[mlubin]

The assertion error will be fixed by jump-dev/GLPK.jl#101, so let's hold off on merging this before that's released.

[dourouc05]

Nice! What about Cbc/Clp, as there is the same assertion?

[mlubin]

Clp will be fixed when either a new LinQuadOptInterface is released or the wrapper is rewritten without LinQuadOptInterface like we're doing for GLPK.

[chriscoey]

This would also be great in notebook format in https://github.com/barpit20/JuMPTutorials.jl (which will be moved under the JuMP repos umbrella soon)

[mlubin]

Just reran the tests, and it looks like this PR has drifted a bit from master:

 LoadError: UndefVarError: set_standard_form_coefficient not defined
368  Stacktrace:
369   [1] #example_cutting_stock#8(::Int64, ::Function) at /home/travis/build/JuliaOpt/JuMP.jl/examples/cutting_stock_column_generation.jl:158
370   [2] example_cutting_stock() at /home/travis/build/JuliaOpt/JuMP.jl/examples/cutting_stock_column_generation.jl:98

I'll merge once CI passes.

[dourouc05]

This should be corrected.