Help with constraints to select and/or insert columns to a matrix

Specific Domains Optimization (Mathematical)
3

Perhaps it is the right solution?

Does your formulation provide sensible results? Or is there something wrong with it?

I haven’t looked at your question in detail, but to the “simple context free” part of your question:

model = Model()
@variable(model, select[1:10], Bin)
@variable(model, 0 <= insert[1:10] <= 10, Int)
@variable(model, insert_zero[1:10], Bin)

# insert[i] == 0 if insert_zero[i] == 1
@constraint(model, [i=1:10], insert[i] <= 10 * insert_zero[i])
# Monotonicity of insert_zero
@constraint(model, [i=2:10], insert_zero[i] <= insert_zero[i-1])
#   i > sum(select) + sum(insert) ⟹ insert_zero[i] == 0
# ⟺
#   sum(select) + sum(insert) == sum(insert_zero)
@constraint(model, sum(select) + sum(insert) == sum(insert_zero))

A few JuMP/style points:

model = JuMP.Model(JuMP.with_optimizer(Cbc.Optimizer, loglevel=0))

You should update to the latest version of JuMP.

model =  JuMP.Model(Cbc.Optimizer)
JuMP.set_silent(model)

select = JuMP.@variable(model, select[1:10], Bin)

No need for select = . JuMP.@variable(model, select[1:10], Bin) is the same by itself.

JuMP.@variable(model, insert[1:10], Int, upper_bound=maxins, lower_bound = 0)

JuMP.@variable(model, 0 <= insert[1:10] <= maxins, Int)

JuMP.@constraint(model, [i=2:10], 0 <= colast[i] - colast[i-1] <= 1)

This simplifies to

JuMP.@constraint(model, [i=2:10], colast[i] >= colast[i-1])
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