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# Untitled

a guest Nov 17th, 2019 114 Never
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1. function optimization(data, n, k, ρ)
2.     data_mean = mean(data)
3.     data_std = std(data)
4.     norm_data = (data .- data_mean) ./ data_std
5.
6.     m = Model(solver=GurobiSolver(OutputFlag=0))
7.     @variable(m, d)
8.     @variable(m, x1[1:n], Bin)
9.     @variable(m, x2[1:n], Bin)
10.     mu1 = 1 / k * sum(norm_data .* x1)
11.     mu2 = 1 / k * sum(norm_data .* x2)
12.     sigma1 = 1 / k * sum((norm_data .^ 2) .* x1)
13.     sigma2 = 1 / k * sum((norm_data .^ 2) .* x2)
14.     @constraint(m, d >= mu1 - mu2 + ρ*sigma1 - ρ*sigma2)
15.     @constraint(m, d >= mu1 - mu2 + ρ*sigma2 - ρ*sigma1)
16.     @constraint(m, d >= mu2 - mu1 + ρ*sigma1 - ρ*sigma2)
17.     @constraint(m, d >= mu2 - mu1 + ρ*sigma2 - ρ*sigma1)
18.     @constraint(m, sum(x1) == k)
19.     @constraint(m, sum(x2) == k)
20.     @constraint(m, x1 .+ x2 .== 1)
21.     @constraint(m, x1[1] == 0)
22.     @objective(m, Min, d)
23.     @show status=solve(m)
24.     x1 = getvalue(x1)
25.     x2 = getvalue(x2)
26.
27.     first_group, second_group = zeros(0), zeros(0)
28.     for i = 1:n
29.         if x1[i] == 1
30.             append!(first_group, data[i])
31.         else
32.             append!(second_group, data[i])
33.         end
34.     end
35.     return first_group, second_group
36. end
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