diff --git a/00_aoi_caching_simulation/.gitignore b/.gitignore similarity index 76% rename from 00_aoi_caching_simulation/.gitignore rename to .gitignore index 87620ac..a8172fa 100644 --- a/00_aoi_caching_simulation/.gitignore +++ b/.gitignore @@ -1 +1,2 @@ .ipynb_checkpoints/ +*.csv diff --git a/01_nb_cncf_optimization/.ipynb_checkpoints/nb_cost_optimization-checkpoint.ipynb b/01_nb_cncf_optimization/00-hitrate_optimization.ipynb similarity index 100% rename from 01_nb_cncf_optimization/.ipynb_checkpoints/nb_cost_optimization-checkpoint.ipynb rename to 01_nb_cncf_optimization/00-hitrate_optimization.ipynb diff --git a/01_nb_cncf_optimization/01-objective_gridsearch.ipynb b/01_nb_cncf_optimization/01-objective_gridsearch.ipynb new file mode 100644 index 0000000..84a8fa7 --- /dev/null +++ b/01_nb_cncf_optimization/01-objective_gridsearch.ipynb @@ -0,0 +1,287 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "ab5cd7d1-1a57-46fc-8282-dae0a6cc2944", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import random\n", + "import pandas as pd\n", + "import itertools\n", + "from tqdm import tqdm" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3d1ad0b9-f6a8-4e98-84aa-6e02e4279954", + "metadata": {}, + "outputs": [], + "source": [ + "SEED = 42\n", + "np.random.seed(SEED)\n", + "random.seed(SEED)\n", + "\n", + "ZIPF_CONSTANT = 2" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "5a27d416-8f98-4814-af9e-6c6bef95f4ef", + "metadata": {}, + "outputs": [], + "source": [ + "def eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals):\n", + " num = (db_object_count * c_f - cache_sz * c_delta)\n", + " denom = np.sum(1.0/lambda_vals)\n", + " if denom == 0:\n", + " print(\"sum(1.0/lambda_vals) == 0\")\n", + " print(db_object_count, c_f, cache_sz, c_delta, lambda_vals)\n", + " return max(0, num/denom)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "6276a9ce-f839-4fe6-90f2-2195cf065fc8", + "metadata": {}, + "outputs": [], + "source": [ + "def h_i_star(c_f, eta, lambda_vals, c_delta):\n", + " optimized_hitrate = (c_f - (eta/lambda_vals)) / c_delta\n", + " return optimized_hitrate" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "dcd31a8c-6864-4b9a-8bb3-998f0c32baf6", + "metadata": {}, + "outputs": [], + "source": [ + "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n", + " lower_bound_violation = hitrates[(hitrates < 0)]\n", + " upper_bound_violation = hitrates[(hitrates > 1)]\n", + " smallest_delta = np.abs(np.min(lower_bound_violation))\n", + " biggest_delta = np.max(upper_bound_violation) - 1\n", + " if smallest_delta > biggest_delta:\n", + " print(smallest_delta)\n", + " index = np.where(hitrates == np.min(local_hitrates))[0][0]\n", + " return index\n", + " else:\n", + " \n", + " index = np.where(hitrates == np.max(local_hitrates))[0][0]\n", + " return index" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "9d774304-ae68-43b3-a76a-e970c06c5236", + "metadata": {}, + "outputs": [], + "source": [ + "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n", + " outside_bounds = (hitrates < 0) | (hitrates > 1)\n", + " distances = np.where(outside_bounds, np.maximum(np.abs(hitrates - 0), np.abs(hitrates - 1)), -np.inf)\n", + " index = np.argmax(distances)\n", + " return index" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c", + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "def optimize_hitrates(db_object_count, cache_size, c_f, c_delta, lambda_vals):\n", + " optimized_hitrates = np.zeros(db_object_count)\n", + " current_db_object_count = db_object_count\n", + " current_cache_size = cache_size\n", + " \n", + " differenc_set = np.arange(db_object_count)\n", + " fix_i = []\n", + " while True:\n", + " if current_db_object_count == 0:\n", + " if current_cache_size > 0:\n", + " # print(\"Re-optimize objects with optimal hitrate of 0.\")\n", + " differenc_set = np.where(optimized_hitrates == 0)[0]\n", + " fix_i = np.setdiff1d(np.arange(db_object_count), differenc_set).tolist()\n", + " current_db_object_count = len(differenc_set)\n", + " continue\n", + " else:\n", + " # print(\"Stop optimization.\")\n", + " optimized_hitrates[differenc_set] = 0\n", + " break\n", + " \n", + " eta = eta_star(current_db_object_count, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n", + " optimized_hitrates[differenc_set] = h_i_star(c_f, eta, lambda_vals[differenc_set], c_delta)\n", + "\n", + " if eta < 0:\n", + " # print(\"eta was negative.\")\n", + " current_cache_size = current_db_object_count * c_f / c_delta # Adjust cache size for next iteration\n", + " continue\n", + " \n", + " if len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0:\n", + " # print(\"All values optimized.\")\n", + " break\n", + " \n", + " max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n", + " fix_i.append(max_outbound_index)\n", + " differenc_set = np.setdiff1d(np.arange(db_object_count), fix_i)\n", + " \n", + " old_hitrate = optimized_hitrates[max_outbound_index]\n", + " optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n", + " \n", + " current_db_object_count -= 1\n", + " current_cache_size -= optimized_hitrates[max_outbound_index]\n", + " return optimized_hitrates" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b6bf3329-3a63-4807-ab8b-8a54f824f47e", + "metadata": {}, + "outputs": [], + "source": [ + "def objective_function(optimized_hitrates, c_f, c_delta, lambda_vals):\n", + " return np.sum(lambda_vals*(1-optimized_hitrates)*c_f+0.5*np.power(optimized_hitrates,2)*c_delta)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "7a998837-72b8-4039-95a5-ca8d9c8e65ab", + "metadata": {}, + "outputs": [], + "source": [ + "# Perform grid search\n", + "def grid_search(db_object_counts, cache_sizes, c_f_values, c_delta_values):\n", + " best_objective = float('inf')\n", + " best_params = None\n", + "\n", + " # Iterate through all combinations of parameters\n", + " for db_object_count, cache_size, c_f, c_delta in tqdm(itertools.product(db_object_counts, cache_sizes, c_f_values, c_delta_values), total=len(db_object_counts) * len(cache_sizes) * len(c_f_values) * len(c_delta_values), desc=\"Grid Search Progress\"):\n", + " if db_object_count < cache_size:\n", + " continue\n", + " lambda_vals = np.array([np.random.zipf(ZIPF_CONSTANT) for i in np.arange(1, db_object_count + 1,1)])\n", + " # print(db_object_count, cache_size, c_f, c_delta)\n", + " # Call the optimization function\n", + " optimized_hitrates = optimize_hitrates(db_object_count, cache_size, c_f, c_delta, lambda_vals)\n", + "\n", + " # Compute the objective function\n", + " objective = objective_function(optimized_hitrates, c_f, c_delta, lambda_vals)\n", + " \n", + " # Track the best (minimum) objective and corresponding parameters\n", + " if objective < best_objective:\n", + " best_objective = objective\n", + " best_params = (db_object_count, cache_size, c_f, c_delta)\n", + "\n", + " return best_objective, best_params" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "a271b52d-1f24-4670-ae3f-af5dd9096a2f", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Grid Search Progress: 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 64152/64152 [12:27<00:00, 85.87it/s]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 12min 16s, sys: 11.5 s, total: 12min 28s\n", + "Wall time: 12min 27s\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "# Define the grid search space\n", + "test_ratios = np.array([0.1, 0.2, 0.5, 0.7, 1, 1.5, 2, 5, 10])\n", + "db_object_count_values = np.round(np.array([10, 15, 30, 100, 200, 500]))\n", + "cache_size_values = np.unique(np.round(np.array([db_object_count_values * i for i in test_ratios]).flatten()))\n", + "c_f_values = np.array([0.1, 0.2, 0.5, 0.7, 1, 1.5, 2, 5, 10])\n", + "c_delta_values = np.unique(np.array([c_f_values * i for i in test_ratios]).flatten())\n", + "\n", + "best_objective, best_params = grid_search(db_object_count_values, cache_size_values, c_f_values, c_delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b2f625d0-ebe0-4a5d-92ff-7de03942ef51", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.05000000000000002, (10, 10.0, 1.5, 0.010000000000000002))" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "best_objective, best_params " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "86a23d02-6f14-4d4d-ad8a-39084ea69151", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "graphs", + "language": "python", + "name": "graphs" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/01_nb_cncf_optimization/02-objective_multi-core_gridsearch.ipynb b/01_nb_cncf_optimization/02-objective_multi-core_gridsearch.ipynb new file mode 100644 index 0000000..4e5a32e --- /dev/null +++ b/01_nb_cncf_optimization/02-objective_multi-core_gridsearch.ipynb @@ -0,0 +1,270 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "ab5cd7d1-1a57-46fc-8282-dae0a6cc2944", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import random\n", + "import pandas as pd\n", + "import itertools\n", + "from joblib import Parallel, delayed\n", + "import os.path" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3d1ad0b9-f6a8-4e98-84aa-6e02e4279954", + "metadata": {}, + "outputs": [], + "source": [ + "SEED = 42\n", + "np.random.seed(SEED)\n", + "random.seed(SEED)\n", + "\n", + "ZIPF_CONSTANT = 2" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "5a27d416-8f98-4814-af9e-6c6bef95f4ef", + "metadata": {}, + "outputs": [], + "source": [ + "def eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals):\n", + " num = (db_object_count * c_f - cache_sz * c_delta)\n", + " denom = np.sum(1.0/lambda_vals)\n", + " if denom == 0:\n", + " print(\"sum(1.0/lambda_vals) == 0\")\n", + " print(db_object_count, c_f, cache_sz, c_delta, lambda_vals)\n", + " return max(0, num/denom)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "6276a9ce-f839-4fe6-90f2-2195cf065fc8", + "metadata": {}, + "outputs": [], + "source": [ + "def h_i_star(c_f, eta, lambda_vals, c_delta):\n", + " optimized_hitrate = (c_f - (eta/lambda_vals)) / c_delta\n", + " return optimized_hitrate" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "dcd31a8c-6864-4b9a-8bb3-998f0c32baf6", + "metadata": {}, + "outputs": [], + "source": [ + "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n", + " lower_bound_violation = hitrates[(hitrates < 0)]\n", + " upper_bound_violation = hitrates[(hitrates > 1)]\n", + " smallest_delta = np.abs(np.min(lower_bound_violation))\n", + " biggest_delta = np.max(upper_bound_violation) - 1\n", + " if smallest_delta > biggest_delta:\n", + " index = np.where(hitrates == np.min(local_hitrates))[0][0]\n", + " return index\n", + " else:\n", + " \n", + " index = np.where(hitrates == np.max(local_hitrates))[0][0]\n", + " return index" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "9d774304-ae68-43b3-a76a-e970c06c5236", + "metadata": {}, + "outputs": [], + "source": [ + "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n", + " outside_bounds = (hitrates < 0) | (hitrates > 1)\n", + " distances = np.where(outside_bounds, np.maximum(np.abs(hitrates - 0), np.abs(hitrates - 1)), -np.inf)\n", + " index = np.argmax(distances)\n", + " return index" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c", + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "def optimize_hitrates(db_object_count, cache_size, c_f, c_delta, lambda_vals):\n", + " optimized_hitrates = np.zeros(db_object_count)\n", + " current_db_object_count = db_object_count\n", + " current_cache_size = cache_size\n", + " \n", + " differenc_set = np.arange(db_object_count)\n", + " fix_i = []\n", + " while True:\n", + " if current_db_object_count == 0:\n", + " if current_cache_size > 0:\n", + " # print(\"Re-optimize objects with optimal hitrate of 0.\")\n", + " differenc_set = np.where(optimized_hitrates == 0)[0]\n", + " fix_i = np.setdiff1d(np.arange(db_object_count), differenc_set).tolist()\n", + " current_db_object_count = len(differenc_set)\n", + " continue\n", + " else:\n", + " # print(\"Stop optimization.\")\n", + " optimized_hitrates[differenc_set] = 0\n", + " break\n", + " \n", + " eta = eta_star(current_db_object_count, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n", + " optimized_hitrates[differenc_set] = h_i_star(c_f, eta, lambda_vals[differenc_set], c_delta)\n", + "\n", + " if eta < 0:\n", + " # print(\"eta was negative.\")\n", + " current_cache_size = current_db_object_count * c_f / c_delta # Adjust cache size for next iteration\n", + " continue\n", + " \n", + " if len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0:\n", + " # print(\"All values optimized.\")\n", + " break\n", + " \n", + " max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n", + " fix_i.append(max_outbound_index)\n", + " differenc_set = np.setdiff1d(np.arange(db_object_count), fix_i)\n", + " \n", + " old_hitrate = optimized_hitrates[max_outbound_index]\n", + " optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n", + " \n", + " current_db_object_count -= 1\n", + " current_cache_size -= optimized_hitrates[max_outbound_index]\n", + " return optimized_hitrates" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b6bf3329-3a63-4807-ab8b-8a54f824f47e", + "metadata": {}, + "outputs": [], + "source": [ + "def objective_function(optimized_hitrates, c_f, c_delta, lambda_vals):\n", + " return np.sum(lambda_vals*(1-optimized_hitrates)*c_f+0.5*np.power(optimized_hitrates,2)*c_delta)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "bd4536e9-273b-4f49-b06c-2f00605e0f7d", + "metadata": {}, + "outputs": [], + "source": [ + "# Define the task to be parallelized\n", + "def grid_search_task(db_object_count, cache_size, c_f, c_delta, db_object_counts, cache_sizes, c_f_values, c_delta_values):\n", + " if db_object_count < cache_size:\n", + " return None # Skip this combination if db_object_count < cache_size\n", + " \n", + " # Generate lambda_vals\n", + " lambda_vals = np.array([np.random.zipf(ZIPF_CONSTANT) for _ in np.arange(1, db_object_count + 1, 1)])\n", + " \n", + " # Call the optimization function\n", + " optimized_hitrates = optimize_hitrates(db_object_count, cache_size, c_f, c_delta, lambda_vals)\n", + "\n", + " # Compute the objective function\n", + " objective = objective_function(optimized_hitrates, c_f, c_delta, lambda_vals)\n", + "\n", + " return (objective, db_object_count, cache_size, c_f, c_delta)\n", + "\n", + "# Perform grid search with parallelization and tqdm progress bar\n", + "def grid_search(db_object_counts, cache_sizes, c_f_values, c_delta_values):\n", + " results = [] # List to collect the results (objective, parameters)\n", + " total_combinations = len(db_object_counts) * len(cache_sizes) * len(c_f_values) * len(c_delta_values)\n", + " \n", + " # Use Parallel from joblib to parallelize the grid search\n", + " task_results = Parallel(n_jobs=-1, verbose=1)(\n", + " delayed(grid_search_task)(db_object_count, cache_size, c_f, c_delta, db_object_counts, cache_sizes, c_f_values, c_delta_values)\n", + " for db_object_count, cache_size, c_f, c_delta in itertools.product(db_object_counts, cache_sizes, c_f_values, c_delta_values)\n", + " )\n", + "\n", + " # Collect valid results\n", + " for result in task_results:\n", + " if result is not None:\n", + " results.append(result)\n", + " \n", + " # Convert the results into a pandas DataFrame\n", + " df = pd.DataFrame(results, columns=[\"Objective\", \"db_object_count\", \"cache_size\", \"c_f (Miss Cost)\", \"c_delta (Refresh Cost)\"])\n", + " \n", + " return df\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "a92c6772-6609-41a8-a3d1-4d640b69a864", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 7.96 ms, sys: 21.6 ms, total: 29.6 ms\n", + "Wall time: 27 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "# Define the grid search space\n", + "test_ratios = np.array([0.1, 0.2, 0.5, 0.7, 1, 1.5, 2, 5, 10])\n", + "db_object_count_values = np.round(np.array([10, 15, 30, 100, 200, 500]))\n", + "cache_size_values = np.unique(np.round(np.array([db_object_count_values * i for i in test_ratios]).flatten()))\n", + "c_f_values = np.array([0.1, 0.2, 0.5, 0.7, 1, 1.5, 2, 5, 10])\n", + "c_delta_values = np.unique(np.array([c_f_values * i for i in test_ratios]).flatten())\n", + "\n", + "objective_result_file = \"./objective_grid-search_multi-core.csv\"\n", + "\n", + "results_df = None\n", + "if not os.path.isfile(objective_result_file):\n", + " # Call the grid search function\n", + " results_df = grid_search(db_object_count_values, cache_size_values, c_f_values, c_delta_values)\n", + " results_df.to_csv(objective_result_file,index=False)\n", + "else:\n", + " results_df = pd.read_csv(objective_result_file)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "45d7f86f-edee-4fc5-835f-1e311ab2e411", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "graphs", + "language": "python", + "name": "graphs" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/01_nb_cncf_optimization/nb_cost_optimization.ipynb b/01_nb_cncf_optimization/nb_cost_optimization.ipynb deleted file mode 100644 index 88de62d..0000000 --- a/01_nb_cncf_optimization/nb_cost_optimization.ipynb +++ /dev/null @@ -1,566 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "ab5cd7d1-1a57-46fc-8282-dae0a6cc2944", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import random\n", - "import pandas as pd" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "3d1ad0b9-f6a8-4e98-84aa-6e02e4279954", - "metadata": {}, - "outputs": [], - "source": [ - "DATABASE_OBJECT_COUNT = 100\n", - "CACHE_SIZE = DATABASE_OBJECT_COUNT/2\n", - "ZIPF_CONSTANT = 2\n", - "\n", - "CACHE_MISS_COST = 2\n", - "CACHE_REFRESH_COST = 1\n", - "\n", - "SEED = 42\n", - "np.random.seed(SEED)\n", - "random.seed(SEED)\n", - "\n", - "LAMBDA_VALUES = np.array([np.random.zipf(ZIPF_CONSTANT) for i in np.arange(1, DATABASE_OBJECT_COUNT + 1,1)])" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "9cc83cf6-5c78-4f0d-b7cb-08cdb80c362e", - "metadata": {}, - "outputs": [], - "source": [ - "# LAMBDA_VALUES = np.array([0.03, 0.04,0.05,0.06,0.07,1,1.1,1.2,1.3,1.4,1.5])\n", - "# DATABASE_OBJECT_COUNT = len(LAMBDA_VALUES)\n", - "# CACHE_SIZE = 4.4\n", - "# CACHE_MISS_COST = 7\n", - "# CACHE_REFRESH_COST = 1" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "3dc07233-0b56-4fee-a93b-212836c18b42", - "metadata": {}, - "outputs": [], - "source": [ - "db_object_count = DATABASE_OBJECT_COUNT\n", - "cache_sz = CACHE_SIZE\n", - "\n", - "lambda_vals = LAMBDA_VALUES\n", - "c_f = CACHE_MISS_COST\n", - "c_delta = CACHE_REFRESH_COST" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "5a27d416-8f98-4814-af9e-6c6bef95f4ef", - "metadata": {}, - "outputs": [], - "source": [ - "def eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals):\n", - " num = (db_object_count * c_f - cache_sz * c_delta)\n", - " denom = np.sum(1.0/lambda_vals)\n", - " return max(0, num/denom)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "6276a9ce-f839-4fe6-90f2-2195cf065fc8", - "metadata": {}, - "outputs": [], - "source": [ - "def h_i_star(c_f, eta, lambda_vals, c_delta):\n", - " optimized_hitrate = (c_f - (eta/lambda_vals)) / c_delta\n", - " return optimized_hitrate" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "dcd31a8c-6864-4b9a-8bb3-998f0c32baf6", - "metadata": {}, - "outputs": [], - "source": [ - "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n", - " lower_bound_violation = hitrates[(hitrates < 0)]\n", - " upper_bound_violation = hitrates[(hitrates > 1)]\n", - " smallest_delta = np.abs(np.min(lower_bound_violation))\n", - " biggest_delta = np.max(upper_bound_violation) - 1\n", - " if smallest_delta > biggest_delta:\n", - " print(smallest_delta)\n", - " index = np.where(hitrates == np.min(local_hitrates))[0][0]\n", - " return index\n", - " else:\n", - " \n", - " index = np.where(hitrates == np.max(local_hitrates))[0][0]\n", - " return index" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "9d774304-ae68-43b3-a76a-e970c06c5236", - "metadata": {}, - "outputs": [], - "source": [ - "def get_index_of_furthest_hitrate_from_boundary(hitrates):\n", - " outside_bounds = (hitrates < 0) | (hitrates > 1)\n", - " distances = np.where(outside_bounds, np.maximum(np.abs(hitrates - 0), np.abs(hitrates - 1)), -np.inf)\n", - " index = np.argmax(distances)\n", - " return index" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "19678083-15e1-439b-be8c-42033d501644", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 1, 3, 1, 1, 2, 1, 5, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1,\n", - " 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 4, 1, 4,\n", - " 1, 1, 1, 3, 8, 1, 4, 4, 2, 1, 1, 1, 10, 1, 1, 1, 5,\n", - " 9, 1, 1, 1, 1, 1, 17, 2, 1, 26, 1, 1, 2, 1, 10, 1, 69,\n", - " 1, 1, 2, 1, 1, 1, 3, 2, 2, 3, 15, 1, 1, 5, 2, 1, 1,\n", - " 2, 1, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 37, 4, 2])" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lambda_vals" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "ccd4b95d-1cdd-4c99-a22e-4b31338993cf", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "2.1159070575516945\n" - ] - }, - { - "data": { - "text/plain": [ - "array([-0.11590706, 1.29469765, -0.11590706, -0.11590706, 0.94204647,\n", - " -0.11590706, -0.11590706, -0.11590706, -0.11590706, 0.94204647,\n", - " -0.11590706, -0.11590706, -0.11590706, 0.94204647, 0.94204647,\n", - " -0.11590706, -0.11590706, 1.29469765, -0.11590706, -0.11590706,\n", - " -0.11590706, -0.11590706, 0.94204647, -0.11590706, -0.11590706,\n", - " -0.11590706, -0.11590706, -0.11590706, -0.11590706, 1.47102324,\n", - " -0.11590706, 1.47102324, -0.11590706, -0.11590706, -0.11590706,\n", - " 1.29469765, 1.73551162, -0.11590706, 1.47102324, 1.47102324,\n", - " 0.94204647, -0.11590706, -0.11590706, -0.11590706, 1.78840929,\n", - " -0.11590706, -0.11590706, -0.11590706, 1.76489922, -0.11590706,\n", - " -0.11590706, -0.11590706, -0.11590706, -0.11590706, 1.87553488,\n", - " 0.94204647, -0.11590706, 1.91861896, -0.11590706, -0.11590706,\n", - " 0.94204647, -0.11590706, 1.78840929, -0.11590706, 1.96933468,\n", - " -0.11590706, -0.11590706, 0.94204647, -0.11590706, -0.11590706,\n", - " -0.11590706, 1.29469765, 0.94204647, 0.94204647, 1.29469765,\n", - " 1.85893953, -0.11590706, -0.11590706, 0.94204647, -0.11590706,\n", - " -0.11590706, 0.94204647, -0.11590706, 0.94204647, -0.11590706,\n", - " -0.11590706, 0.94204647, 0.94204647, 1.29469765, -0.11590706,\n", - " 0.94204647, -0.11590706, -0.11590706, 1.94281332, 1.47102324,\n", - " 0.94204647])" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "eta = eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals[lambda_vals != lambda_vals[6]])\n", - "print(eta)\n", - "optimized_hitrates = (c_f - eta / lambda_vals[lambda_vals != lambda_vals[6]]) / c_delta\n", - "optimized_hitrates" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "05b17074-719f-4bca-8434-2aaee26094d0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
0
count96.000000
mean0.437500
std0.726101
min-0.115907
25%-0.115907
50%-0.115907
75%0.942046
max1.969335
\n", - "
" - ], - "text/plain": [ - " 0\n", - "count 96.000000\n", - "mean 0.437500\n", - "std 0.726101\n", - "min -0.115907\n", - "25% -0.115907\n", - "50% -0.115907\n", - "75% 0.942046\n", - "max 1.969335" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "pd.DataFrame(optimized_hitrates).describe()" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimized: 67 1.97 // [ 1.79077042 -0.09229584 1. -0.09229584 -0.09229584]\n", - "Optimized: 97 1.94 // [-0.07876743 -0.07876743 1. 1.48030814 0.96061628]\n", - "Optimized: 60 1.92 // [ 0.96720258 -0.06559484 1. -0.06559484 -0.06559484]\n", - "Optimized: 57 1.88 // [-0.05274002 -0.05274002 1. 0.97362999 -0.05274002]\n", - "Optimized: 78 1.86 // [ 0.97977406 1.31984937 1. -0.04045188 -0.04045188]\n", - "Optimized: 46 1.80 // [-0.02836604 -0.02836604 1. -0.02836604 -0.02836604]\n", - "Optimized: 65 1.80 // [ 0.99140044 -0.01719911 1. -0.01719911 1. ]\n", - "Optimized: 51 1.78 // [-0.00600086 1.59879983 1. -0.00600086 -0.00600086]\n", - "Optimized: 38 1.75 // [0.00491746 1.33497249 1. 0.00491746 1.50122936]\n", - "Optimized: 6 1.60 // [1.00774103 0.01548205 1. 0.01548205 0.01548205]\n", - "Optimized: 27 1.60 // [0.02399435 0.02399435 1. 0.02399435 0.02399435]\n", - "Optimized: 50 1.61 // [0.03255485 0.03255485 1. 1. 0.03255485]\n", - "Optimized: 81 1.61 // [0.04116395 0.04116395 1. 1.02058197 0.04116395]\n", - "Optimized: 31 1.51 // [0.04982206 0.04982206 1. 0.04982206 1.51245552]\n", - "Optimized: 33 1.51 // [1. 0.05714286 1. 0.05714286 0.05714286]\n", - "Optimized: 40 1.52 // [1. 0.06451613 1. 1.51612903 1.03225806]\n", - "Optimized: 41 1.52 // [0.07194245 1. 1. 1.03597122 0.07194245]\n", - "Optimized: 98 1.52 // [0.07942238 1. 1. 1.03971119]\n", - "Optimized: 1 1.36 // []\n", - "Optimized: 18 1.36 // [0.09223301 0.09223301 1. 0.09223301 0.09223301]\n", - "Optimized: 37 1.37 // [0.09756098 0.09756098 1. 1. 0.09756098]\n", - "Optimized: 74 1.37 // [0.10294118 0.10294118 1. 1.05147059 1.05147059]\n", - "Optimized: 77 1.37 // [1.05418719 1.05418719 1. 1. 0.10837438]\n", - "Optimized: 92 1.37 // [1.05693069 1.05693069 1. 0.11386139 1.05693069]\n", - "Optimized: 4 1.06 // [0.11940299 0.11940299 1. 0.11940299 1. ]\n", - "Optimized: 10 1.06 // [0.12030075 0.12030075 1. 0.12030075 0.12030075]\n", - "Optimized: 14 1.06 // [0.12121212 0.12121212 1. 1.06060606 0.12121212]\n", - "Optimized: 15 1.06 // [0.1221374 1. 1. 0.1221374 0.1221374]\n", - "Optimized: 23 1.06 // [0.12307692 0.12307692 1. 0.12307692 0.12307692]\n", - "Optimized: 42 1.06 // [1. 1. 1. 0.12403101 0.12403101]\n", - "Optimized: 58 1.06 // [0.125 1. 1. 0.125 1. ]\n", - "Optimized: 63 1.06 // [0.12598425 0.12598425 1. 0.12598425 1. ]\n", - "Optimized: 70 1.06 // [0.12698413 0.12698413 1. 0.12698413 0.12698413]\n", - "Optimized: 75 1.06 // [0.128 1. 1. 1.064 1. ]\n", - "Optimized: 76 1.06 // [1. 1. 1. 1. 1.]\n", - "Optimized: 82 1.07 // [0.1300813 1. 1. 0.1300813 0.1300813]\n", - "Optimized: 85 1.07 // [0.13114754 0.13114754 1. 0.13114754 1.06557377]\n", - "Optimized: 87 1.07 // [1. 0.1322314 1. 0.1322314 0.1322314]\n", - "Optimized: 90 1.07 // [0.13333333 0.13333333 1. 1.06666667 1. ]\n", - "Optimized: 91 1.07 // [0.13445378 1. 1. 1. 0.13445378]\n", - "Optimized: 94 1.07 // [1. 0.13559322 1. 0.13559322 0.13559322]\n", - "Optimized: 99 1.07 // [1. 1. 1.]\n", - "All values optimized.\n" - ] - } - ], - "source": [ - "\"\"\"\n", - "Perform theoretical optimization to compute optimal hit probabilities.\n", - "\n", - "Parameters:\n", - "- lambda_vals (numpy array): Request rates for each item.\n", - "- B (float): Total cache size.\n", - "- c_f (float): Fetching linear cost (cache miss cost).\n", - "- c_delta (float): Age linear cost.\n", - "\n", - "Returns:\n", - "- h_opt (numpy array): Optimal hit probabilities for each item.\n", - "\"\"\"\n", - "optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n", - "current_db_object_count = DATABASE_OBJECT_COUNT\n", - "current_cache_size = CACHE_SIZE\n", - "\n", - "differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n", - "fix_i = []\n", - "\n", - "while True:\n", - " if current_db_object_count == 0:\n", - " print(\"No objects left to optimize.\")\n", - " if current_cache_size > 0:\n", - " print(\"Add obj with optimized hitrate 0 and add them to optimization pool for re-optimization.\")\n", - " # Redistribute unused cache size among items with zero hit probability\n", - " differenc_set = np.where(optimized_hitrates == 0)[0]\n", - " fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set).tolist()\n", - " current_db_object_count = len(differenc_set)\n", - " continue\n", - " else:\n", - " \"Reset\"\n", - " optimized_hitrates[differenc_set] = 0\n", - " break\n", - " # Compute Lagrangian multiplier and optimal hit probabilities\n", - " eta = eta_star(current_db_object_count, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n", - " optimized_hitrates[differenc_set] = (c_f - eta / lambda_vals[differenc_set]) / c_delta\n", - " if eta < 0:\n", - " print(\"eta was negative.\")\n", - " current_cache_size = current_db_object_count * c_f / c_delta # Adjust cache size for next iteration\n", - " continue\n", - " \n", - " if len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0:\n", - " print(\"All values optimized.\")\n", - " break\n", - " \n", - " max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n", - " fix_i.append(max_outbound_index)\n", - " differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n", - "\n", - " old_hitrate = optimized_hitrates[max_outbound_index]\n", - " optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n", - " \n", - " print(f\"Optimized: {max_outbound_index} {old_hitrate:.2f} // {optimized_hitrates[max_outbound_index-2:max_outbound_index+3]}\")\n", - " \n", - " current_db_object_count -= 1\n", - " current_cache_size -= optimized_hitrates[max_outbound_index]" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "f559ee7a-be2f-4076-b01c-f08950ad5a88", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([0.13793103, 1. , 0.13793103, 0.13793103, 1. ,\n", - " 0.13793103, 1. , 0.13793103, 0.13793103, 0.13793103,\n", - " 1. , 0.13793103, 0.13793103, 0.13793103, 1. ,\n", - " 1. , 0.13793103, 0.13793103, 1. , 0.13793103,\n", - " 0.13793103, 0.13793103, 0.13793103, 1. , 0.13793103,\n", - " 0.13793103, 0.13793103, 1. , 0.13793103, 0.13793103,\n", - " 0.13793103, 1. , 0.13793103, 1. , 0.13793103,\n", - " 0.13793103, 0.13793103, 1. , 1. , 0.13793103,\n", - " 1. , 1. , 1. , 0.13793103, 0.13793103,\n", - " 0.13793103, 1. , 0.13793103, 0.13793103, 0.13793103,\n", - " 1. , 1. , 0.13793103, 0.13793103, 0.13793103,\n", - " 0.13793103, 0.13793103, 1. , 1. , 0.13793103,\n", - " 1. , 0.13793103, 0.13793103, 1. , 0.13793103,\n", - " 1. , 0.13793103, 1. , 0.13793103, 0.13793103,\n", - " 1. , 0.13793103, 0.13793103, 0.13793103, 1. ,\n", - " 1. , 1. , 1. , 1. , 0.13793103,\n", - " 0.13793103, 1. , 1. , 0.13793103, 0.13793103,\n", - " 1. , 0.13793103, 1. , 0.13793103, 0.13793103,\n", - " 1. , 1. , 1. , 0.13793103, 1. ,\n", - " 0.13793103, 0.13793103, 1. , 1. , 1. ])" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "optimized_hitrates" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "8b2d3cea-1cc0-476e-92bf-2ac4344a9b1b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
0
count100.000000
mean0.500000
std0.427625
min0.137931
25%0.137931
50%0.137931
75%1.000000
max1.000000
\n", - "
" - ], - "text/plain": [ - " 0\n", - "count 100.000000\n", - "mean 0.500000\n", - "std 0.427625\n", - "min 0.137931\n", - "25% 0.137931\n", - "50% 0.137931\n", - "75% 1.000000\n", - "max 1.000000" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "pd.DataFrame(optimized_hitrates).describe()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7a998837-72b8-4039-95a5-ca8d9c8e65ab", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "graphs", - "language": "python", - "name": "graphs" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.12.7" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -}