Multistart optimization

Hello,

I have a multistart optimization code that generates initial parameter guesses initialps as you can see below and later used every row of them to solve a new optimization problem.

using Distributions, LatinHypercubeSampling, Statistics
p = convert(Array{Float64,1}, 1:3)
bounds = [Vector{Float64}(undef,2) for _ in 1:length(p)]
searchgrid = [1E-9, 1E-1]
for (ipara,para) in enumerate(p)
  bounds[ipara][1] = para * searchgrid[1]
  bounds[ipara][2] = para * searchgrid[2]
end

function latinCube(bounds, dims, nguess = 100)  
    initialps = []
    plan, _ = LHCoptim(nguess, dims, 1000)
    plan /= nguess
    
    for i in 1:dims
        append!(initialps, [quantile(LogUniform(bounds[i][1], bounds[i][2]), plan[:,i])])
    end
    return permutedims(hcat(initialps...))
end

nguess = 100
initialps = latinCube(bounds, length(p), nguess)

My problem is that I do not know how to implement it on p when it is a named tuple in the format of,

p = (p₁ = 1., p₂ = fixed(2.), p₃ = bounded(3., 0, 100))

So my question is how I can do multistart optimization using ParameterHandling.

Start with the issue's p, fixed, bounded, and latinCube examples, then trace the public ParameterHandling API for named tuples and parameter constraints. Determine whether the requested behavior belongs in the library or in user code, and define how free parameters, bounds, and fixed values should be handled before implementing or documenting a multistart workflow.