How to set std value as objective?

Specific Domains Optimization (Mathematical)
,
1 
function solution()
    model = Model(Gurobi.Optimizer);set_silent(model)
    @variable(model,x[1:3000,1:125],Bin)
    @constraint(model,[i=1:3000],sum(x[i,:]) == 5)
    @constraint(model,[i=1:125],sum(x[:,i]) == 120)
    @NLobjective(model,Min,std(sum(x[:,i] .* x[:,j]) for i in 1:125 for j in (i+1):125))
#     println(model)
    optimize!(model)
    value.(x)
end

Here I wanna minimize the std value ,but I don’t know how to code it correctly.Can someone help me fix it ?

LoadError: Unsupported generator `:std`
in expression starting at In[13]:6

Stacktrace:
 [1] error(s::String)
   @ Base .\error.jl:35
 [2] _parse_generator_expression(code::Expr, x::Expr, operators::Set{Tuple{Symbol, Int64}})
   @ JuMP C:\Users\ASUS\.julia\packages\JuMP\KiENn\src\macros.jl:2382
 [3] _parse_nonlinear_expression_inner(code::Expr, x::Expr, operators::Set{Tuple{Symbol, Int64}})
   @ JuMP C:\Users\ASUS\.julia\packages\JuMP\KiENn\src\macros.jl:2342
 [4] _parse_nonlinear_expression(model::Expr, x::Expr)
   @ JuMP C:\Users\ASUS\.julia\packages\JuMP\KiENn\src\macros.jl:2250
 [5] var"@NLobjective"(__source__::LineNumberNode, __module__::Module, model::Any, sense::Any, x::Any)
   @ JuMP C:\Users\ASUS\.julia\packages\JuMP\KiENn\src\macros.jl:2813
1 Like
2

Which version of JuMP are you using? I think starting with 1.15 nonlinear modeling like the kind you’re doing has become much easier: JuMP 1.15.0 is released | JuMP

1 Like
3

Gurobi.jl doesn’t support nonlinear functions directly, so you can’t use something like std or sqrt.

You could write your model like this:

using JuMP, Gurobi
M, N = 3000, 125
model = Model(Gurobi.Optimizer)
set_silent(model)
@variable(model, x[1:M, 1:N], Bin)
@constraint(model, [i=1:M], sum(x[i, :]) == 5)
@constraint(model, [i=1:N], sum(x[:, i]) == 120)
@variable(model, y[i=1:N, j=(i+1):N])
@constraint(model, [i=1:N, j=(i+1):N], y[i, j] == sum(x[:,i] .* x[:,j]))
@variable(model, μ)
@constraint(model, μ == sum(y) / length(y))
@objective(model, Min, sum((y[i, j] - μ)^2 for i in 1:N, j in (i+1):N))  # ignore sqrt(...), doesn't change solution
optimize!(model)
value.(x)

but it likely won’t solve (I have’t tried) because you have a large number of bilinear terms.

What is the background of the model and what are you trying to achieve?

4

Seems like my JuMP version is 1.14,I’ll try to update it later.

1 Like
5

v1.15 won’t help in this case.

6

It’s a problem from the Math Modeling Competition,as you said it has a large number of bilinear terms,so I use the Genetic Algorithm to solve it finally.

1 Like
7

But does it have to be Gurobi?

8

No, but the binary variables rule out solvers like Ipopt, and the number of bilinear terms in the expression is very large, so a naive call to Statistics.std didn’t even finish building when I tried to run it.