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MIPLearn/docs/benchmarks/stab.ipynb

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"# Maximum Weight Stable Set\n",
"\n",
"## Problem definition\n",
"\n",
"Given a simple undirected graph $G=(V,E)$ and weights $w \\in \\mathbb{R}^V$, the problem is to find a stable set $S \\subseteq V$ that maximizes $\\sum_{v \\in V} w_v$. We recall that a subset $S \\subseteq V$ is a *stable set* if no two vertices of $S$ are adjacent. This is one of Karp's 21 NP-complete problems.\n",
"\n",
"## Random instance generator\n",
"\n",
"The class `MaxWeightStableSetGenerator` can be used to generate random instances of this problem, with user-specified probability distributions. When the constructor parameter `fix_graph=True` is provided, one random Erdős-Rényi graph $G_{n,p}$ is generated during the constructor, where $n$ and $p$ are sampled from user-provided probability distributions `n` and `p`. To generate each instance, the generator independently samples each $w_v$ from the user-provided probability distribution `w`. When `fix_graph=False`, a new random graph is generated for each instance, while the remaining parameters are sampled in the same way.\n",
"\n",
"## Challenge A\n",
"\n",
"* Fixed random Erdős-Rényi graph $G_{n,p}$ with $n=200$ and $p=5\\%$\n",
"* Random vertex weights $w_v \\sim U(100, 125)$\n",
"* 512 training instances, 64 test instances"
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"CPU times: user 43.6 s, sys: 1min 42s, total: 2min 25s\n",
"Wall time: 1min 56s\n"
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],
"text/plain": [
"<Figure size 576x576 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%time\n",
"%config InlineBackend.figure_formats = ['svg']\n",
"%matplotlib inline\n",
"\n",
"from miplearn.benchmark import run_benchmarks\n",
"from miplearn.problems.stab import MaxWeightStableSetGenerator\n",
"from scipy.stats import uniform, randint\n",
"\n",
"instances = MaxWeightStableSetGenerator(\n",
" w=uniform(loc=100.0, scale=25.0),\n",
" n=randint(low=150, high=151),\n",
" p=uniform(loc=0.05, scale=0.0),\n",
" fix_graph=True,\n",
").generate(576)\n",
"\n",
"run_benchmarks(\n",
" train_instances = instances[:512],\n",
" test_instances = instances[512:],\n",
" n_jobs=16,\n",
");"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6973a585",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "miplearn",
"language": "python",
"name": "miplearn"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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