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Financioneroncios/Julia_STSP_SDP.ipynb

Created April 24, 2025 05:26
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Julia_STSP_SDP.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": []
},
"kernelspec": {
"name": "julia",
"display_name": "Julia"
},
"language_info": {
"name": "julia"
}
},
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "_y6a0XWlXdSk",
"outputId": "3fefe1cd-84fa-42aa-9b1c-262e907d6401"
},
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m SCS_jll ──────── v3.2.7+0\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m SCS ──────────── v2.1.0\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m OpenBLAS32_jll ─ v0.3.24+0\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
" \u001b[90m[c946c3f1] \u001b[39m\u001b[92m+ SCS v2.1.0\u001b[39m\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
" \u001b[90m[c946c3f1] \u001b[39m\u001b[92m+ SCS v2.1.0\u001b[39m\n",
"\u001b[33m⌅\u001b[39m \u001b[90m[656ef2d0] \u001b[39m\u001b[92m+ OpenBLAS32_jll v0.3.24+0\u001b[39m\n",
" \u001b[90m[f4f2fc5b] \u001b[39m\u001b[92m+ SCS_jll v3.2.7+0\u001b[39m\n",
"\u001b[36m\u001b[1m Info\u001b[22m\u001b[39m Packages marked with \u001b[33m⌅\u001b[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`\n",
"\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n",
" 918.6 ms\u001b[32m ✓ \u001b[39m\u001b[90mOpenBLAS32_jll\u001b[39m\n",
" 1001.9 ms\u001b[32m ✓ \u001b[39m\u001b[90mSCS_jll\u001b[39m\n",
" 49966.5 ms\u001b[32m ✓ \u001b[39mSCS\n",
" 3 dependencies successfully precompiled in 53 seconds. 469 already precompiled.\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m UnsafeArrays ────── v1.0.7\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m QDLDL ───────────── v0.4.1\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m COSMOAccelerators ─ v0.1.0\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m COSMO ───────────── v0.8.9\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
" \u001b[90m[1e616198] \u001b[39m\u001b[92m+ COSMO v0.8.9\u001b[39m\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
" \u001b[90m[1e616198] \u001b[39m\u001b[92m+ COSMO v0.8.9\u001b[39m\n",
" \u001b[90m[bbd8fffe] \u001b[39m\u001b[92m+ COSMOAccelerators v0.1.0\u001b[39m\n",
" \u001b[90m[bfc457fd] \u001b[39m\u001b[92m+ QDLDL v0.4.1\u001b[39m\n",
" \u001b[90m[c4a57d5a] \u001b[39m\u001b[92m+ UnsafeArrays v1.0.7\u001b[39m\n",
"\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n",
" 1663.1 ms\u001b[32m ✓ \u001b[39m\u001b[90mUnsafeArrays\u001b[39m\n",
" 1981.5 ms\u001b[32m ✓ \u001b[39m\u001b[90mQDLDL\u001b[39m\n",
" 2006.9 ms\u001b[32m ✓ \u001b[39m\u001b[90mCOSMOAccelerators\u001b[39m\n",
" 3570.3 ms\u001b[32m ✓ \u001b[39mCOSMO\n",
" 4 dependencies successfully precompiled in 6 seconds. 472 already precompiled.\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Match ── v1.2.0\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m TSPLIB ─ v0.1.2\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
" \u001b[90m[b1c258e7] \u001b[39m\u001b[92m+ TSPLIB v0.1.2\u001b[39m\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
"\u001b[33m⌅\u001b[39m \u001b[90m[7eb4fadd] \u001b[39m\u001b[92m+ Match v1.2.0\u001b[39m\n",
" \u001b[90m[b1c258e7] \u001b[39m\u001b[92m+ TSPLIB v0.1.2\u001b[39m\n",
"\u001b[36m\u001b[1m Info\u001b[22m\u001b[39m Packages marked with \u001b[33m⌅\u001b[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`\n",
"\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n",
" 939.9 ms\u001b[32m ✓ \u001b[39m\u001b[90mMatch\u001b[39m\n",
" 1209.7 ms\u001b[32m ✓ \u001b[39mTSPLIB\n",
" 2 dependencies successfully precompiled in 3 seconds. 476 already precompiled.\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m ArnoldiMethod ─ v0.4.0\n",
"\u001b[32m\u001b[1m Installed\u001b[22m\u001b[39m Graphs ──────── v1.12.1\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Project.toml`\n",
" \u001b[90m[86223c79] \u001b[39m\u001b[92m+ Graphs v1.12.1\u001b[39m\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/.julia/environments/v1.10/Manifest.toml`\n",
" \u001b[90m[ec485272] \u001b[39m\u001b[92m+ ArnoldiMethod v0.4.0\u001b[39m\n",
" \u001b[90m[86223c79] \u001b[39m\u001b[92m+ Graphs v1.12.1\u001b[39m\n",
"\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m packages...\n",
" 2401.0 ms\u001b[32m ✓ \u001b[39m\u001b[90mArnoldiMethod\u001b[39m\n",
" 5131.3 ms\u001b[32m ✓ \u001b[39mGraphs\n",
" 2 dependencies successfully precompiled in 8 seconds. 478 already precompiled.\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n"
]
}
],
"source": [
"using Pkg\n",
"Pkg.add(\"Convex\")\n",
"Pkg.add(\"SCS\")\n",
"Pkg.add(\"COSMO\")\n",
"Pkg.add(\"TSPLIB\")\n",
"Pkg.add(\"Graphs\")\n",
"Pkg.add(\"Plots\")"
]
},
{
"cell_type": "code",
"source": [
"using Convex, SCS, COSMO, TSPLIB, Random, LinearAlgebra\n",
"using Graphs, SparseArrays, Plots\n",
"import Convex: MOI"
],
"metadata": {
"id": "VPSknvsBXyua"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"####################################################################################\n",
"# Part of this script is taken from the very nice tutorial by Piotr Zakrzewski:\n",
"# https://github.com/PiotrZakrzewski/julia-tsp/blob/main/TSP.ipynb\n",
"####################################################################################\n",
"\n",
"struct Delivery\n",
" x::Float64\n",
" y::Float64\n",
"end;\n",
"\n",
"function random_delivery(width=100, height=100)\n",
" x = rand(0.0:0.1:width)\n",
" y = rand(0.0:0.1:height)\n",
" return Delivery(x, y)\n",
"end;\n",
"\n",
"struct TSProblem\n",
" deliveries::Array{Delivery}\n",
"end;\n",
"\n",
"function random_instance(n_deliveries, width=100, height=100, seed=1234)\n",
" Random.seed!(seed)\n",
" deliveries = [random_delivery(width, height) for _=1:n_deliveries]\n",
" problem = TSProblem(deliveries)\n",
" return problem\n",
"end;\n",
"\n",
"function display_problem(problem)\n",
" x_pos = [c.x for c in problem.deliveries]\n",
" y_pos = [c.y for c in problem.deliveries]\n",
" return scatter(x_pos, y_pos, shape = :circle, markersize = 6, label= \"City\")\n",
"end;\n",
"\n",
"function dist(del1::Delivery, del2::Delivery)\n",
" return sqrt((del1.x - del2.x)^2 + (del1.y - del2.y)^2)\n",
"end;\n",
"\n",
"function calc_travelmatrix(deliveries::Array{Delivery})\n",
" tm = zeros(Float64, length(deliveries), length(deliveries))\n",
" for i = 1:length(deliveries)\n",
" for j = 1:length(deliveries)\n",
" tm[i, j] = dist(deliveries[i], deliveries[j])\n",
" end\n",
" end\n",
" return tm\n",
"end\n",
"\n",
"\n",
"function display_solution(problem, route)\n",
" x_pos = [c.x for c in problem.deliveries]\n",
" y_pos = [c.y for c in problem.deliveries]\n",
" plot_result = scatter(x_pos, y_pos, shape = :circle, markersize = 6)\n",
" for i in 1:length(problem.deliveries)\n",
" for j in 1:length(problem.deliveries)\n",
" val = route[i, j]\n",
" if val > 0\n",
" del1 = problem.deliveries[i]\n",
" del2 = problem.deliveries[j]\n",
" plot!([del1.x, del2.x], [del1.y, del2.y], legend = false)\n",
" end\n",
" end\n",
" end\n",
" return plot_result\n",
"end;"
],
"metadata": {
"id": "XmRZ9YsPZbJm"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"####################################################################################\n",
"# Semidefinite programming TSP based on QAP and GIP proposed by Cajas (2025)\n",
"####################################################################################\n",
"\n",
"function julia_duplication_elimination_matrix(n::Int, diag::Bool = true)\n",
" m = 1\n",
" j = 1\n",
" nsq = n * n\n",
" r = 0\n",
" a = 1\n",
"\n",
" v = zeros(Int, nsq)\n",
" sequence = 0:(n - 1)\n",
" cn = cumsum(sequence)\n",
"\n",
" if diag\n",
" m = div(n * (n + 1), 2)\n",
" else\n",
" m = div(n * (n - 1), 2)\n",
" j = 2\n",
" end\n",
"\n",
" for i in j:n\n",
" r += i - 1\n",
" for k in 0:(n - i)\n",
" v[r + k + 1] = a + k + cn[i]\n",
" end\n",
" r += n - i + 1\n",
" a += n - i + 1\n",
" end\n",
"\n",
" v = filter(!=(0), v)\n",
"\n",
" row_indices = collect(1:m)\n",
" col_indices = v\n",
" values = ones(Float64, m)\n",
"\n",
" return sparse(row_indices, col_indices, values, m, nsq)\n",
"end\n",
"\n",
"function SDP_STSP_Cajas(C_d, solver=\"SCS\")\n",
"\n",
" n = size(C_d, 1)\n",
"\n",
" A_c = adjacency_matrix(cycle_graph(n))\n",
" B = incidence_matrix(complete_graph(n))\n",
" L2 = julia_duplication_elimination_matrix(n, false)\n",
" vec_A_c = reshape(A_c, n^2 ,1)\n",
" vec_C_d = reshape(C_d, n^2 ,1)\n",
"\n",
" ones_n = ones(n, 1)\n",
" ones_n2 = ones(n^2, 1)\n",
"\n",
" Y = Variable((n^2, n^2))\n",
" X = Variable((n, n))\n",
" vec_X = reshape(X, n^2 ,1)\n",
"\n",
" M = [Y vec_X; vec_X' ones(1, 1)]\n",
"\n",
" # Initialize an empty matrix for X_X\n",
" Z = []\n",
"\n",
" # Loop over j (1-based index)\n",
" for j in 1:n\n",
" # Reshape slice X[j * n: j * n + 1] (reshaped to n x n)\n",
" Aj = reshape(Y[(j - 1) * n + 1, :], n, n)\n",
" # Loop over i (1-based index)\n",
" for i in 2:n\n",
" Aij = reshape(Y[(i + (j - 1) * n), :], n, n)\n",
" Aj = vcat(Aj, Aij)\n",
" end\n",
"\n",
" # Concatenate horizontally (X_X = hstack([X_X, Aj]))\n",
" if j == 1\n",
" Z = Aj\n",
" else\n",
" Z = hcat(Z, Aj)\n",
" end\n",
" end\n",
"\n",
" # Defining the objective function\n",
" cost = vec_C_d' * (Z * vec_A_c) / 2\n",
"\n",
" # Defining the constraints\n",
" constraints = []\n",
" push!(constraints, Y == Y')\n",
" push!(constraints, M ⪰ 0)\n",
" push!(constraints, Z * ones_n2 == 1)\n",
" push!(constraints, Z' * ones_n2 == 1)\n",
" push!(constraints, reshape(diag(Y,0), n^2 ,1) - vec_X == 0)\n",
" push!(constraints, Y * ones_n2 - n * vec_X == 0)\n",
" push!(constraints, B * L2 * Z * vec_A_c == 2)\n",
" push!(constraints, X * ones_n == 1)\n",
" push!(constraints, X' * ones_n == 1)\n",
" push!(constraints, X >= 0)\n",
" push!(constraints, X <= 1)\n",
" push!(constraints, Y >= 0)\n",
" push!(constraints, Y <= 1)\n",
" push!(constraints, X[1,2] == 1)\n",
"\n",
" # Solve the problem by calling solve!\n",
" prob = minimize(cost, constraints)\n",
"\n",
" if solver == \"SCS\"\n",
" solver_0 = MOI.OptimizerWithAttributes(SCS.Optimizer, \"max_iters\" => 200000, \"eps_abs\" => 1e-8, \"eps_rel\" => 1e-8 )\n",
" elseif solver == \"COSMO\"\n",
" solver_0 = MOI.OptimizerWithAttributes(COSMO.Optimizer, \"max_iter\" => 30000, \"eps_abs\" => 1e-8, \"eps_rel\" => 1e-8 )\n",
" end\n",
"\n",
" @time begin\n",
" # Step 5: Solve the problem using the SCS solver\n",
" solve!(prob, solver_0)\n",
" end\n",
"\n",
" # Check the status of the problem\n",
" prob.status\n",
"\n",
" X1 = []\n",
" X1 = reshape(evaluate(Z) * vec_A_c, n, n)\n",
" X1 = round.(X1, digits=4)\n",
"\n",
" # Get the optimal value\n",
" return X1, prob.optval\n",
"\n",
"end;"
],
"metadata": {
"id": "OqoCbuvEZeFz"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"####################################################################################\n",
"# Creating a ramdom instance of cities in the plane\n",
"# With Julia in Google Colab I don't recommend to use this\n",
"# code with more than 15 cities\n",
"####################################################################################\n",
"\n",
"ran_points = random_instance(16, 200, 300, 132)\n",
"C_d = calc_travelmatrix(ran_points.deliveries)\n",
"display_problem(ran_points)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 421
},
"id": "V0Ml_lucZkVG",
"outputId": "287bc8b9-849e-4370-d51e-23afbf170dac"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"image/png": 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},
"metadata": {},
"execution_count": 18
}
]
},
{
"cell_type": "code",
"source": [
"####################################################################################\n",
"# Run the optimization process\n",
"####################################################################################\n",
"\n",
"X1, opt_val = SDP_STSP_Cajas(C_d, \"SCS\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "d8DDHkSgZk9g",
"outputId": "ea06f8f4-3135-4766-b1f0-63070ec2fa6c"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39m[Convex.jl] Compilation finished: 30.13 seconds, 10.145 GiB of memory allocated\n"
]
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"------------------------------------------------------------------\n",
"\t SCS v3.2.7 - Splitting Conic Solver\n",
"\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
"------------------------------------------------------------------\n",
"problem: variables n: 65792, constraints m: 263986\n",
"cones: \t z: primal zero / dual free vars: 99249\n",
"\t l: linear vars: 131584\n",
"\t s: psd vars: 33153, ssize: 1\n",
"settings: eps_abs: 1.0e-08, eps_rel: 1.0e-08, eps_infeas: 1.0e-07\n",
"\t alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1\n",
"\t max_iters: 200000, normalize: 1, rho_x: 1.00e-06\n",
"\t acceleration_lookback: 10, acceleration_interval: 10\n",
"\t compiled with openmp parallelization enabled\n",
"lin-sys: sparse-direct-amd-qdldl\n",
"\t nnz(A): 566145, nnz(P): 0\n",
"------------------------------------------------------------------\n",
" iter | pri res | dua res | gap | obj | scale | time (s)\n",
"------------------------------------------------------------------\n",
" 0| 3.40e+02 1.13e+02 2.43e+07 -1.22e+07 1.00e-01 1.20e+00 \n",
" 250| 3.60e-02 6.51e-01 1.04e+02 6.35e+02 9.78e+00 1.35e+01 \n",
" 500| 4.85e-03 8.28e-02 4.40e+01 7.88e+02 9.78e+00 2.53e+01 \n",
" 750| 5.88e-01 6.49e+00 1.49e+01 8.35e+02 9.78e+00 3.69e+01 \n",
" 1000| 2.10e-03 9.15e-02 1.78e+01 8.20e+02 9.78e+00 4.82e+01 \n",
" 1250| 1.45e-03 9.58e-02 1.35e+01 8.25e+02 9.78e+00 6.02e+01 \n",
" 1500| 1.07e-03 8.96e-02 1.07e+01 8.28e+02 9.78e+00 7.21e+01 \n",
" 1750| 8.82e-04 6.98e-02 8.61e+00 8.30e+02 9.78e+00 8.38e+01 \n",
" 2000| 8.13e-04 4.82e-02 7.06e+00 8.31e+02 9.78e+00 9.49e+01 \n",
" 2250| 7.50e-04 3.34e-02 5.92e+00 8.31e+02 9.78e+00 1.05e+02 \n",
" 2500| 7.01e-04 2.51e-02 5.12e+00 8.32e+02 9.78e+00 1.17e+02 \n",
" 2750| 6.42e-04 2.46e-02 4.51e+00 8.33e+02 9.78e+00 1.28e+02 \n",
" 3000| 5.67e-04 2.49e-02 4.04e+00 8.33e+02 9.78e+00 1.39e+02 \n",
" 3250| 5.01e-04 2.56e-02 3.60e+00 8.33e+02 9.78e+00 1.49e+02 \n",
" 3500| 6.62e-02 5.77e+00 3.48e-01 8.35e+02 9.78e+00 1.61e+02 \n",
" 3750| 3.89e-04 2.36e-02 2.84e+00 8.34e+02 9.78e+00 1.72e+02 \n",
" 4000| 3.46e-04 2.20e-02 2.52e+00 8.34e+02 9.78e+00 1.83e+02 \n",
" 4250| 3.09e-04 2.02e-02 2.24e+00 8.34e+02 9.78e+00 1.93e+02 \n",
" 4500| 2.76e-04 1.81e-02 1.99e+00 8.34e+02 9.78e+00 2.05e+02 \n",
" 4750| 2.47e-04 1.64e-02 1.78e+00 8.34e+02 9.78e+00 2.15e+02 \n",
" 5000| 2.19e-04 1.50e-02 1.58e+00 8.34e+02 9.78e+00 2.26e+02 \n",
" 5250| 1.95e-04 1.38e-02 1.41e+00 8.34e+02 9.78e+00 2.36e+02 \n",
" 5500| 1.71e-04 1.26e-02 1.25e+00 8.35e+02 9.78e+00 2.47e+02 \n",
" 5750| 1.50e-04 1.16e-02 1.10e+00 8.35e+02 9.78e+00 2.57e+02 \n",
" 6000| 1.32e-04 1.07e-02 9.67e-01 8.35e+02 9.78e+00 2.68e+02 \n",
" 6250| 1.21e-02 1.36e+00 1.63e+00 8.34e+02 9.78e+00 2.78e+02 \n",
" 6500| 1.01e-04 9.00e-03 7.35e-01 8.35e+02 9.78e+00 2.88e+02 \n",
" 6750| 8.74e-05 8.08e-03 6.35e-01 8.35e+02 9.78e+00 2.98e+02 \n",
" 7000| 7.49e-05 7.21e-03 5.44e-01 8.35e+02 9.78e+00 3.08e+02 \n",
" 7250| 6.36e-05 6.39e-03 4.63e-01 8.35e+02 9.78e+00 3.18e+02 \n",
" 7500| 5.36e-05 5.63e-03 3.90e-01 8.35e+02 9.78e+00 3.28e+02 \n",
" 7750| 4.48e-05 4.95e-03 3.24e-01 8.35e+02 9.78e+00 3.38e+02 \n",
" 8000| 3.69e-05 4.35e-03 2.66e-01 8.35e+02 9.78e+00 3.47e+02 \n",
" 8250| 3.00e-05 3.80e-03 2.15e-01 8.35e+02 9.78e+00 3.57e+02 \n",
" 8500| 2.39e-05 3.25e-03 1.71e-01 8.35e+02 9.78e+00 3.67e+02 \n",
" 8750| 1.85e-05 2.72e-03 1.33e-01 8.35e+02 9.78e+00 3.76e+02 \n",
" 9000| 3.68e-03 4.66e-01 5.02e-01 8.35e+02 9.78e+00 3.86e+02 \n",
" 9250| 1.03e-05 1.87e-03 7.25e-02 8.35e+02 9.78e+00 3.96e+02 \n",
" 9500| 7.13e-06 1.56e-03 4.90e-02 8.35e+02 9.78e+00 4.05e+02 \n",
" 9750| 4.49e-06 1.22e-03 2.97e-02 8.35e+02 9.78e+00 4.15e+02 \n",
" 10000| 3.94e-06 9.46e-04 1.43e-02 8.35e+02 9.78e+00 4.25e+02 \n",
" 10225| 1.77e-09 3.45e-08 6.22e-07 8.35e+02 9.78e+00 4.33e+02 \n",
"------------------------------------------------------------------\n",
"status: solved\n",
"timings: total: 4.33e+02s = setup: 1.07e+00s + solve: 4.32e+02s\n",
"\t lin-sys: 1.29e+02s, cones: 2.62e+02s, accel: 7.80e+00s\n",
"------------------------------------------------------------------\n",
"objective = 834.926714\n",
"------------------------------------------------------------------\n",
"463.494359 seconds (1.58 M allocations: 10.242 GiB, 2.10% gc time)\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"([-0.0 0.0 … -0.0 0.0; 0.0 -0.0 … 0.0 0.0; … ; -0.0 0.0 … -0.0 -0.0; 0.0 0.0 … -0.0 -0.0], 834.926713535438)"
]
},
"metadata": {},
"execution_count": 19
}
]
},
{
"cell_type": "code",
"source": [
"###################################################################################\n",
"# Plot the optimal tour\n",
"#####################################################################################\n",
"\n",
"display_solution(ran_points, X1)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 421
},
"id": "2b5iv_P9Zokb",
"outputId": "604e1f9a-ce7a-442e-f266-29545e2b1939"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"image/png": 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685.7,269.885 \"/>\n<polyline clip-path=\"url(#clip432)\" style=\"stroke:#ed5d92; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"868.397,157.562 1622.33,203.587 \"/>\n<polyline clip-path=\"url(#clip432)\" style=\"stroke:#c68125; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"778.267,918.071 232.609,418.918 \"/>\n<polyline clip-path=\"url(#clip432)\" style=\"stroke:#00a98d; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"778.267,918.071 796.536,1445.72 \"/>\n<polyline clip-path=\"url(#clip432)\" style=\"stroke:#8e971d; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1990.16,87.9763 2066.89,572.335 \"/>\n<polyline clip-path=\"url(#clip432)\" style=\"stroke:#00a8cb; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"1990.16,87.9763 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2291,1172.85 \"/>\n<polyline clip-path=\"url(#clip432)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2194.78,901.086 1362.9,712.054 \"/>\n</svg>\n"
},
"metadata": {},
"execution_count": 20
}
]
},
{
"cell_type": "code",
"source": [
"####################################################################################\n",
"# Plot the adjacency matrix\n",
"####################################################################################\n",
"display(\"Adjacency matrix:\")\n",
"\n",
"display(round.(X1, digits=0))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 323
},
"id": "dfmcEgNUZrQJ",
"outputId": "82990178-11cb-4348-b20e-31d8d67c6102"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"\"Adjacency matrix:\""
]
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"16×16 Matrix{Float64}:\n",
" -0.0 0.0 -0.0 0.0 -0.0 -0.0 … -0.0 1.0 0.0 0.0 -0.0 0.0\n",
" 0.0 -0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0\n",
" -0.0 0.0 -0.0 0.0 -0.0 -0.0 1.0 -0.0 -0.0 0.0 -0.0 0.0\n",
" 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 -0.0 0.0\n",
" -0.0 0.0 -0.0 0.0 -0.0 -0.0 1.0 -0.0 1.0 -0.0 -0.0 0.0\n",
" -0.0 0.0 -0.0 0.0 -0.0 -0.0 … -0.0 -0.0 -0.0 -0.0 1.0 -0.0\n",
" -0.0 0.0 -0.0 0.0 -0.0 -0.0 -0.0 -0.0 -0.0 0.0 1.0 -0.0\n",
" 1.0 0.0 1.0 0.0 -0.0 -0.0 -0.0 0.0 0.0 0.0 -0.0 0.0\n",
" 0.0 0.0 0.0 0.0 -0.0 -0.0 -0.0 0.0 0.0 0.0 -0.0 1.0\n",
" -0.0 0.0 -0.0 0.0 -0.0 1.0 -0.0 1.0 0.0 0.0 -0.0 0.0\n",
" -0.0 0.0 1.0 0.0 1.0 -0.0 … 0.0 -0.0 -0.0 -0.0 -0.0 -0.0\n",
" 1.0 0.0 -0.0 0.0 -0.0 -0.0 -0.0 -0.0 0.0 0.0 -0.0 0.0\n",
" 0.0 1.0 -0.0 0.0 1.0 -0.0 -0.0 0.0 0.0 0.0 -0.0 0.0\n",
" 0.0 0.0 0.0 1.0 -0.0 -0.0 -0.0 0.0 0.0 0.0 -0.0 1.0\n",
" -0.0 0.0 -0.0 -0.0 -0.0 1.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0\n",
" 0.0 0.0 0.0 0.0 0.0 -0.0 … -0.0 0.0 0.0 1.0 -0.0 -0.0"
]
},
"metadata": {}
}
]
}
]
}
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