diff --git a/.ipynb_checkpoints/heldAndKarp-checkpoint.ipynb b/.ipynb_checkpoints/heldAndKarp-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..3907e9630960c50fca0d7e2550b8f5282778031c
--- /dev/null
+++ b/.ipynb_checkpoints/heldAndKarp-checkpoint.ipynb
@@ -0,0 +1,119 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Held \\& Karp algorithm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "┌ Info: Precompiling Graphs [86223c79-3864-5bf0-83f7-82e725a168b6]\n",
+ "â”” @ Base loading.jl:1260\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Modules loaded\n"
+ ]
+ }
+ ],
+ "source": [
+ "using LinearAlgebra\n",
+ "using JuMP\n",
+ "using Cbc\n",
+ "using Graphs\n",
+ "\n",
+ "println(\"Modules loaded\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "function hk(W)\n",
+ " \n",
+ " # Initialization\n",
+ " n = size(W, 1)\n",
+ " \n",
+ " if size(W, 2)!=n\n",
+ " error(\"Weight matrice must be square\")\n",
+ " end\n",
+ " # \n",
+ " \n",
+ " λ = zeros(n)\n",
+ "\n",
+ " g = simple_graph(n-1, is_directed = false)\n",
+ " W_reduced = W[2:n,2:n]\n",
+ " z = 0\n",
+ " while z!=n # While not a tour\n",
+ " \n",
+ " # Minimum spanning tree (span_tree : st)\n",
+ " st = kruskal_minimum_spantree(g, W_reduced)[1]\n",
+ " \n",
+ " # Connect vertex 1\n",
+ " m = Model(Cbc.Optimizer()) # PL(NE) Model\n",
+ " \n",
+ " @variable(m, X[1:n, 1:n], Bin)\n",
+ " \n",
+ " @objective(m, Min, \n",
+ " 2*sum(λ[2:n]) + \n",
+ " sum((W[u,v] - λ[u] - λ[v])*X[u,v] for u ∈ 1:n for v ∈ 1:u)\n",
+ " )\n",
+ " \n",
+ " @constraint(m, degreeRoot, sum(X[1,:]) == 2)\n",
+ " @constraint(m, spanningTree[u ∈ 2:n, v ∈ 2:n], X[u,v] == st[u,v])\n",
+ " \n",
+ " optimize!(m)\n",
+ " \n",
+ " if !( \n",
+ " ( termination_status(m) == MOI.OPTIMAL ) || \n",
+ " ( termination_status(m) == MOI.TIME_LIMIT \n",
+ " && has_values(m) ) \n",
+ " )\n",
+ " error(\"Couldn't connect vertex 1 (PLNE failed).\")\n",
+ " end\n",
+ " \n",
+ " z = objective_value(m)\n",
+ " D = [sum(value.(X)[u,:]) for u ∈ 1:n]\n",
+ " # For the degree, we suppose a null diagonal, to be checked later on\n",
+ " \n",
+ " if z!=n # If not a tour, update\n",
+ " λ .= λ .+ 2.*(2.-D) # Experimenter d'autres règles\n",
+ " end\n",
+ " \n",
+ " end\n",
+ " \n",
+ " \n",
+ "end"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Julia 1.4.2",
+ "language": "julia",
+ "name": "julia-1.4"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.4.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/heldAndKarp.ipynb b/heldAndKarp.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..3907e9630960c50fca0d7e2550b8f5282778031c
--- /dev/null
+++ b/heldAndKarp.ipynb
@@ -0,0 +1,119 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Held \\& Karp algorithm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "┌ Info: Precompiling Graphs [86223c79-3864-5bf0-83f7-82e725a168b6]\n",
+ "â”” @ Base loading.jl:1260\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Modules loaded\n"
+ ]
+ }
+ ],
+ "source": [
+ "using LinearAlgebra\n",
+ "using JuMP\n",
+ "using Cbc\n",
+ "using Graphs\n",
+ "\n",
+ "println(\"Modules loaded\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "function hk(W)\n",
+ " \n",
+ " # Initialization\n",
+ " n = size(W, 1)\n",
+ " \n",
+ " if size(W, 2)!=n\n",
+ " error(\"Weight matrice must be square\")\n",
+ " end\n",
+ " # \n",
+ " \n",
+ " λ = zeros(n)\n",
+ "\n",
+ " g = simple_graph(n-1, is_directed = false)\n",
+ " W_reduced = W[2:n,2:n]\n",
+ " z = 0\n",
+ " while z!=n # While not a tour\n",
+ " \n",
+ " # Minimum spanning tree (span_tree : st)\n",
+ " st = kruskal_minimum_spantree(g, W_reduced)[1]\n",
+ " \n",
+ " # Connect vertex 1\n",
+ " m = Model(Cbc.Optimizer()) # PL(NE) Model\n",
+ " \n",
+ " @variable(m, X[1:n, 1:n], Bin)\n",
+ " \n",
+ " @objective(m, Min, \n",
+ " 2*sum(λ[2:n]) + \n",
+ " sum((W[u,v] - λ[u] - λ[v])*X[u,v] for u ∈ 1:n for v ∈ 1:u)\n",
+ " )\n",
+ " \n",
+ " @constraint(m, degreeRoot, sum(X[1,:]) == 2)\n",
+ " @constraint(m, spanningTree[u ∈ 2:n, v ∈ 2:n], X[u,v] == st[u,v])\n",
+ " \n",
+ " optimize!(m)\n",
+ " \n",
+ " if !( \n",
+ " ( termination_status(m) == MOI.OPTIMAL ) || \n",
+ " ( termination_status(m) == MOI.TIME_LIMIT \n",
+ " && has_values(m) ) \n",
+ " )\n",
+ " error(\"Couldn't connect vertex 1 (PLNE failed).\")\n",
+ " end\n",
+ " \n",
+ " z = objective_value(m)\n",
+ " D = [sum(value.(X)[u,:]) for u ∈ 1:n]\n",
+ " # For the degree, we suppose a null diagonal, to be checked later on\n",
+ " \n",
+ " if z!=n # If not a tour, update\n",
+ " λ .= λ .+ 2.*(2.-D) # Experimenter d'autres règles\n",
+ " end\n",
+ " \n",
+ " end\n",
+ " \n",
+ " \n",
+ "end"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Julia 1.4.2",
+ "language": "julia",
+ "name": "julia-1.4"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.4.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}