feat(eta_calculation): Implementing "Joint Caching and Freshness Optimization" (in progress)
Signed-off-by: Tuan-Dat Tran <tuan-dat.tran@tudattr.dev>
This commit is contained in:
Tuan-Dat Tran
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "ab5cd7d1-1a57-46fc-8282-dae0a6cc2944",
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import random"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "3d1ad0b9-f6a8-4e98-84aa-6e02e4279954",
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"metadata": {},
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"outputs": [],
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"source": [
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"DATABASE_OBJECT_COUNT = 100\n",
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"CACHE_SIZE = DATABASE_OBJECT_COUNT/2\n",
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"ZIPF_CONSTANT = 2\n",
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"\n",
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"CACHE_MISS_COST = 2\n",
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"CACHE_REFRESH_COST = 1\n",
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"\n",
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"SEED = 42\n",
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"np.random.seed(SEED)\n",
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"random.seed(SEED)\n",
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"\n",
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"LAMBDA_VALUES = np.array([np.random.zipf(ZIPF_CONSTANT) for i in np.arange(1, DATABASE_OBJECT_COUNT + 1,1)])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "9cc83cf6-5c78-4f0d-b7cb-08cdb80c362e",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 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",
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"# DATABASE_OBJECT_COUNT = len(LAMBDA_VALUES)\n",
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"# CACHE_SIZE = 4.4\n",
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"# CACHE_MISS_COST = 7\n",
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"# CACHE_REFRESH_COST = 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "3dc07233-0b56-4fee-a93b-212836c18b42",
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"metadata": {},
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"outputs": [],
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"source": [
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"db_object_count = DATABASE_OBJECT_COUNT\n",
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"cache_sz = CACHE_SIZE\n",
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"\n",
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"lambda_vals = LAMBDA_VALUES\n",
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"c_f = CACHE_MISS_COST\n",
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"c_delta = CACHE_REFRESH_COST"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "5a27d416-8f98-4814-af9e-6c6bef95f4ef",
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"metadata": {},
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"outputs": [],
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"source": [
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"def eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals):\n",
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" num = (db_object_count * c_f - cache_sz * c_delta)\n",
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" denom = np.sum(1.0/lambda_vals)\n",
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" return max(0, num/denom)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "6276a9ce-f839-4fe6-90f2-2195cf065fc8",
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"metadata": {},
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"outputs": [],
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"source": [
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"def h_i_star(c_f, eta, lambda_vals, c_delta):\n",
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" optimized_hitrate = (c_f - (eta/lambda_vals)) / c_delta\n",
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" return optimized_hitrate"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "dcd31a8c-6864-4b9a-8bb3-998f0c32baf6",
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_index_of_furthest_hitrate_from_boundary(hitrates):\n",
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" local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
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" smallest_delta = np.abs(np.min(local_hitrates))\n",
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" biggest_delta = np.max(local_hitrates) - 1\n",
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" if smallest_delta > biggest_delta:\n",
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" index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
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" return index\n",
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" else:\n",
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" index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
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" return index"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "55b251f8-97ca-49a8-9ec6-be77dc1e49b2",
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"metadata": {
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"\"\"\"\n",
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"Perform theoretical optimization to compute optimal hit probabilities.\n",
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"\n",
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"Parameters:\n",
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"- lambda_vals (numpy array): Request rates for each item.\n",
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"- B (float): Total cache size.\n",
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"- c_f (float): Fetching linear cost (cache miss cost).\n",
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"- c_delta (float): Age linear cost.\n",
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"\n",
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"Returns:\n",
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"- h_opt (numpy array): Optimal hit probabilities for each item.\n",
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"\"\"\"\n",
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"optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n",
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"differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
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"fix_i = []\n",
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"current_db_objects = DATABASE_OBJECT_COUNT\n",
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"current_cache_size = CACHE_SIZE\n",
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"\n",
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"while True:\n",
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" if current_db_objects == 0:\n",
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" # Handle special case: no items left to optimize\n",
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" if current_cache_size > 0:\n",
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" # Redistribute unused cache size among items with zero hit probability\n",
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" differenc_set = np.where(optimized_hitrates == 0)[0]\n",
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" fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
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" current_db_objects = len(differenc_set)\n",
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" continue\n",
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" else:\n",
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" optimized_hitrates[differenc_set] = 0\n",
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" break\n",
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" # Compute Lagrangian multiplier and optimal hit probabilities\n",
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" mu = max(0, (current_db_objects * c_f - current_cache_size * c_delta) / np.sum(1.0 / lambda_vals[differenc_set]))\n",
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" eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
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" assert(mu == eta)\n",
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" optimized_hitrates[differenc_set] = (c_f - mu / lambda_vals[differenc_set]) / c_delta\n",
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" # print(optimized_hitrates)\n",
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" # Handle the case where mu < 0\n",
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" if mu < 0:\n",
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" current_cache_size = current_db_objects * c_f / c_delta # Adjust cache size for next iteration\n",
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" continue\n",
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" # Check for constraint violations\n",
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" larger_i = np.where(optimized_hitrates > 1)[0] # h > 1\n",
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" smaller_i = np.where(optimized_hitrates < 0)[0] # h < 0\n",
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" # If no violations, optimization is complete\n",
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" break_con = len(smaller_i) == 0 and len(larger_i) == 0\n",
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" break_con1 = len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0\n",
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" assert(break_con == break_con1)\n",
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" if break_con:\n",
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" break\n",
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" # Find the furthest violating item\n",
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" min_viol, min_viol_i = (0, -1)\n",
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" if len(smaller_i) > 0:\n",
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" min_viol_i = np.argmin(optimized_hitrates)\n",
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" min_viol = optimized_hitrates[min_viol_i]\n",
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" max_viol, max_viol_i = (0, -1)\n",
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" if len(larger_i) > 0:\n",
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" larger = optimized_hitrates - 1\n",
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" max_viol_i = np.argmax(larger)\n",
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" max_viol = larger[max_viol_i]\n",
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" # Compare the furthest violations and adjust accordingly\n",
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" viol_i = min_viol_i\n",
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" min_viol_flag = True # True if furthest is from the left boundary\n",
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" if max_viol > abs(min_viol):\n",
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" viol_i = max_viol_i\n",
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" min_viol_flag = False \n",
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" index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
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" if viol_i != index:\n",
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" print(optimized_hitrates[viol_i])\n",
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" print(optimized_hitrates[index])\n",
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" assert(viol_i == index)\n",
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" if min_viol_flag:\n",
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" optimized_hitrates[viol_i] = 0\n",
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" else:\n",
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" optimized_hitrates[viol_i] = min(1, current_cache_size)\n",
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"\n",
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" # Update parameters for next iteration\n",
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" current_cache_size =- optimized_hitrates[viol_i]\n",
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" fix_i.append(viol_i)\n",
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" differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
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" current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "efa16eaf-a10b-4927-99cd-190e2ffe1d1e",
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"metadata": {},
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"outputs": [],
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"source": [
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"a = optimized_hitrates\n",
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"b = differenc_set"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"All values optimized.\n"
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]
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}
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],
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"source": [
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"\"\"\"\n",
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"Perform theoretical optimization to compute optimal hit probabilities.\n",
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"\n",
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"Parameters:\n",
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"- lambda_vals (numpy array): Request rates for each item.\n",
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"- B (float): Total cache size.\n",
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"- c_f (float): Fetching linear cost (cache miss cost).\n",
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"- c_delta (float): Age linear cost.\n",
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"\n",
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"Returns:\n",
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"- h_opt (numpy array): Optimal hit probabilities for each item.\n",
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"\"\"\"\n",
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"optimized_hitrates = np.zeros(DATABASE_OBJECT_COUNT)\n",
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"differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
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"fix_i = []\n",
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"current_db_objects = DATABASE_OBJECT_COUNT\n",
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"current_cache_size = CACHE_SIZE\n",
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"\n",
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"while True:\n",
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" if current_db_objects == 0:\n",
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" # Handle special case: no items left to optimize\n",
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" if current_cache_size > 0:\n",
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" # Redistribute unused cache size among items with zero hit probability\n",
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" differenc_set = np.where(optimized_hitrates == 0)[0]\n",
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" fix_i = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), differenc_set)\n",
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" current_db_objects = len(differenc_set)\n",
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" continue\n",
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" else:\n",
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" optimized_hitrates[differenc_set] = 0\n",
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" break\n",
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" # Compute Lagrangian multiplier and optimal hit probabilities\n",
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" eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
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" optimized_hitrates[differenc_set] = (c_f - eta / lambda_vals[differenc_set]) / c_delta\n",
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"\n",
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" if mu < 0:\n",
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" current_cache_size = current_db_objects * c_f / c_delta # Adjust cache size for next iteration\n",
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" continue\n",
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" \n",
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" if len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0:\n",
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" print(\"All values optimized.\")\n",
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" break\n",
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" max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
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" optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
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"\n",
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" current_cache_size =- optimized_hitrates[max_outbound_index]\n",
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" fix_i.append(max_outbound_index)\n",
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" differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
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" current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "4f64253f-b389-4be9-b403-08027d480121",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
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" 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
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" 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.])"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"optimized_hitrates"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"id": "17d818db-ec88-4c26-92af-6d74862525d9",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([ 0. , 0. , 0. , 0. , 0. ,\n",
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" 0. , 0. , 0. , -0. , 0. ,\n",
|
||||||
|
" 0.04878049, 0.04878049, 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0.43902439, 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" -0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" -0. , 0. , 1. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , -0. , 0. ,\n",
|
||||||
|
" 0. , 0.43902439, 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0.04878049, 0. ])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 12,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"a"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 13,
|
||||||
|
"id": "791b3f96-527a-489e-970e-c92ec950177f",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([ 6, 27, 31, 33, 40, 41, 50, 81, 98])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 13,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"b"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 14,
|
||||||
|
"id": "c22fa973-432a-4c05-89bf-2a6ea82ae3d2",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([ 6, 27, 50, 81])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 14,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"differenc_set"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 15,
|
||||||
|
"id": "898e1266-5aaa-46f4-ac0f-c7807ac2b6bb",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"db_object_count = DATABASE_OBJECT_COUNT\n",
|
||||||
|
"cache_sz = CACHE_SIZE\n",
|
||||||
|
"loop_lambda = lambda_vals\n",
|
||||||
|
"\n",
|
||||||
|
"non_optimized_values = np.arange(db_object_count)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 16,
|
||||||
|
"id": "8cc9b8a9-f7ae-48fc-adfb-ac4b7a4998f1",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"db_object_count = DATABASE_OBJECT_COUNT\n",
|
||||||
|
"cache_sz = CACHE_SIZE\n",
|
||||||
|
"loop_lambda = lambda_vals\n",
|
||||||
|
"\n",
|
||||||
|
"optimized_hitrate = np.zeros(db_object_count)\n",
|
||||||
|
"non_optimized_values = np.arange(db_object_count)\n",
|
||||||
|
"optimized_value = {}\n",
|
||||||
|
"\n",
|
||||||
|
"eta = eta_star(db_object_count, c_f, cache_sz, c_delta, loop_lambda[non_optimized_values])\n",
|
||||||
|
"optimized_hitrate[non_optimized_values] = h_i_star(c_f, eta, loop_lambda[non_optimized_values], c_delta)\n",
|
||||||
|
"\n",
|
||||||
|
"max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrate)\n",
|
||||||
|
"optimized_value[max_outbound_index] = (1 if optimized_hitrate[max_outbound_index] > 1 else 0)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 17,
|
||||||
|
"id": "cbcf3592-fcf2-4f54-a3cd-761097c12972",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"{67: 1}"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 17,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"optimized_value"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "db732331-1d09-45b7-915c-73daa270b5e2",
|
||||||
|
"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
|
||||||
|
}
|
||||||
@@ -1,6 +1,251 @@
|
|||||||
{
|
{
|
||||||
"cells": [],
|
"cells": [
|
||||||
"metadata": {},
|
{
|
||||||
|
"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"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"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 = 1\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",
|
||||||
|
" local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
|
||||||
|
" smallest_delta = np.abs(np.min(local_hitrates))\n",
|
||||||
|
" biggest_delta = np.max(local_hitrates) - 1\n",
|
||||||
|
" if smallest_delta > biggest_delta:\n",
|
||||||
|
" index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
|
||||||
|
" return index\n",
|
||||||
|
" else:\n",
|
||||||
|
" index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
|
||||||
|
" return index"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 14,
|
||||||
|
"id": "ccd4b95d-1cdd-4c99-a22e-4b31338993cf",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([0.30256805, 0.76752268, 0.30256805, 0.30256805, 0.65128403,\n",
|
||||||
|
" 0.30256805, 0.86051361, 0.30256805, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.65128403, 0.30256805, 0.30256805, 0.30256805, 0.65128403,\n",
|
||||||
|
" 0.65128403, 0.30256805, 0.30256805, 0.76752268, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.30256805, 0.30256805, 0.65128403, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.30256805, 0.86051361, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.82564201, 0.30256805, 0.82564201, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.30256805, 0.76752268, 0.91282101, 0.30256805,\n",
|
||||||
|
" 0.82564201, 0.82564201, 0.65128403, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.93025681, 0.30256805, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.86051361, 0.92250756, 0.30256805, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.30256805, 0.95897459, 0.65128403, 0.30256805,\n",
|
||||||
|
" 0.97317569, 0.30256805, 0.30256805, 0.65128403, 0.30256805,\n",
|
||||||
|
" 0.93025681, 0.30256805, 0.98989229, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.65128403, 0.30256805, 0.30256805, 0.30256805, 0.76752268,\n",
|
||||||
|
" 0.65128403, 0.65128403, 0.76752268, 0.95350454, 0.30256805,\n",
|
||||||
|
" 0.30256805, 0.86051361, 0.65128403, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.65128403, 0.30256805, 0.65128403, 0.30256805, 0.30256805,\n",
|
||||||
|
" 0.65128403, 0.65128403, 0.76752268, 0.30256805, 0.65128403,\n",
|
||||||
|
" 0.30256805, 0.30256805, 0.98115049, 0.82564201, 0.65128403])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 14,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"eta = eta_star(db_object_count, c_f, cache_sz, c_delta, lambda_vals)\n",
|
||||||
|
"optimized_hitrates = (c_f - eta / lambda_vals) / c_delta\n",
|
||||||
|
"optimized_hitrates"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 8,
|
||||||
|
"id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
|
||||||
|
"metadata": {
|
||||||
|
"scrolled": true
|
||||||
|
},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"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",
|
||||||
|
" # 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)\n",
|
||||||
|
" current_db_object_count = len(differenc_set)\n",
|
||||||
|
" continue\n",
|
||||||
|
" else:\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",
|
||||||
|
"\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",
|
||||||
|
" optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
|
||||||
|
"\n",
|
||||||
|
" current_cache_size =- optimized_hitrates[max_outbound_index]\n",
|
||||||
|
" fix_i.append(max_outbound_index)\n",
|
||||||
|
" differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
|
||||||
|
" current_db_object_count -= 1"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "11682b36-e705-4bd9-9d75-79012791d1ee",
|
||||||
|
"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": 4,
|
||||||
"nbformat_minor": 5
|
"nbformat_minor": 5
|
||||||
}
|
}
|
||||||
|
|||||||
473
01_nb_cncf_optimization/gen_nb_cost_optimization.ipynb
Normal file
473
01_nb_cncf_optimization/gen_nb_cost_optimization.ipynb
Normal file
@@ -0,0 +1,473 @@
|
|||||||
|
{
|
||||||
|
"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"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"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",
|
||||||
|
" local_hitrates = hitrates[(hitrates < 0) | (hitrates > 1)]\n",
|
||||||
|
" smallest_delta = np.abs(np.min(local_hitrates))\n",
|
||||||
|
" biggest_delta = np.max(local_hitrates) - 1\n",
|
||||||
|
" if smallest_delta > biggest_delta:\n",
|
||||||
|
" index = np.where(hitrates == np.min(local_hitrates))[0][0]\n",
|
||||||
|
" return index\n",
|
||||||
|
" else:\n",
|
||||||
|
" index = np.where(hitrates == np.max(local_hitrates))[0][0]\n",
|
||||||
|
" return index"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 18,
|
||||||
|
"id": "55b251f8-97ca-49a8-9ec6-be77dc1e49b2",
|
||||||
|
"metadata": {
|
||||||
|
"scrolled": true
|
||||||
|
},
|
||||||
|
"outputs": [],
|
||||||
|
"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",
|
||||||
|
"differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
|
||||||
|
"fix_i = []\n",
|
||||||
|
"current_db_objects = DATABASE_OBJECT_COUNT\n",
|
||||||
|
"current_cache_size = CACHE_SIZE\n",
|
||||||
|
"\n",
|
||||||
|
"while True:\n",
|
||||||
|
" if current_db_objects == 0:\n",
|
||||||
|
" # Handle special case: no items left to optimize\n",
|
||||||
|
" if current_cache_size > 0:\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)\n",
|
||||||
|
" current_db_objects = len(differenc_set)\n",
|
||||||
|
" continue\n",
|
||||||
|
" else:\n",
|
||||||
|
" optimized_hitrates[differenc_set] = 0\n",
|
||||||
|
" break\n",
|
||||||
|
" # Compute Lagrangian multiplier and optimal hit probabilities\n",
|
||||||
|
" mu = max(0, (current_db_objects * c_f - current_cache_size * c_delta) / np.sum(1.0 / lambda_vals[differenc_set]))\n",
|
||||||
|
" eta = eta_star(current_db_objects, c_f, current_cache_size, c_delta, lambda_vals[differenc_set])\n",
|
||||||
|
" assert(mu == eta)\n",
|
||||||
|
" optimized_hitrates[differenc_set] = (c_f - mu / lambda_vals[differenc_set]) / c_delta\n",
|
||||||
|
" # print(optimized_hitrates)\n",
|
||||||
|
" # Handle the case where mu < 0\n",
|
||||||
|
" if mu < 0:\n",
|
||||||
|
" current_cache_size = current_db_objects * c_f / c_delta # Adjust cache size for next iteration\n",
|
||||||
|
" continue\n",
|
||||||
|
" # Check for constraint violations\n",
|
||||||
|
" larger_i = np.where(optimized_hitrates > 1)[0] # h > 1\n",
|
||||||
|
" smaller_i = np.where(optimized_hitrates < 0)[0] # h < 0\n",
|
||||||
|
" # If no violations, optimization is complete\n",
|
||||||
|
" break_con = len(smaller_i) == 0 and len(larger_i) == 0\n",
|
||||||
|
" break_con1 = len((optimized_hitrates[differenc_set])[((optimized_hitrates[differenc_set]) < 0) | ((optimized_hitrates[differenc_set])> 1)]) == 0\n",
|
||||||
|
" assert(break_con == break_con1)\n",
|
||||||
|
" if break_con:\n",
|
||||||
|
" break\n",
|
||||||
|
" # Find the furthest violating item\n",
|
||||||
|
" min_viol, min_viol_i = (0, -1)\n",
|
||||||
|
" if len(smaller_i) > 0:\n",
|
||||||
|
" min_viol_i = np.argmin(optimized_hitrates)\n",
|
||||||
|
" min_viol = optimized_hitrates[min_viol_i]\n",
|
||||||
|
" max_viol, max_viol_i = (0, -1)\n",
|
||||||
|
" if len(larger_i) > 0:\n",
|
||||||
|
" larger = optimized_hitrates - 1\n",
|
||||||
|
" max_viol_i = np.argmax(larger)\n",
|
||||||
|
" max_viol = larger[max_viol_i]\n",
|
||||||
|
" # Compare the furthest violations and adjust accordingly\n",
|
||||||
|
" viol_i = min_viol_i\n",
|
||||||
|
" min_viol_flag = True # True if furthest is from the left boundary\n",
|
||||||
|
" if max_viol > abs(min_viol):\n",
|
||||||
|
" viol_i = max_viol_i\n",
|
||||||
|
" min_viol_flag = False \n",
|
||||||
|
" index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
|
||||||
|
" if viol_i != index:\n",
|
||||||
|
" print(optimized_hitrates[viol_i])\n",
|
||||||
|
" print(optimized_hitrates[index])\n",
|
||||||
|
" assert(viol_i == index)\n",
|
||||||
|
" if min_viol_flag:\n",
|
||||||
|
" optimized_hitrates[viol_i] = 0\n",
|
||||||
|
" else:\n",
|
||||||
|
" optimized_hitrates[viol_i] = min(1, current_cache_size)\n",
|
||||||
|
"\n",
|
||||||
|
" # Update parameters for next iteration\n",
|
||||||
|
" current_cache_size =- optimized_hitrates[viol_i]\n",
|
||||||
|
" fix_i.append(viol_i)\n",
|
||||||
|
" differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
|
||||||
|
" current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 9,
|
||||||
|
"id": "efa16eaf-a10b-4927-99cd-190e2ffe1d1e",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"a = optimized_hitrates\n",
|
||||||
|
"b = differenc_set"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 10,
|
||||||
|
"id": "0e21c26f-058a-4e56-a5ad-1c47bf28656c",
|
||||||
|
"metadata": {
|
||||||
|
"scrolled": true
|
||||||
|
},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"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",
|
||||||
|
"differenc_set = np.arange(DATABASE_OBJECT_COUNT)\n",
|
||||||
|
"fix_i = []\n",
|
||||||
|
"current_db_objects = DATABASE_OBJECT_COUNT\n",
|
||||||
|
"current_cache_size = CACHE_SIZE\n",
|
||||||
|
"\n",
|
||||||
|
"while True:\n",
|
||||||
|
" if current_db_objects == 0:\n",
|
||||||
|
" # Handle special case: no items left to optimize\n",
|
||||||
|
" if current_cache_size > 0:\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)\n",
|
||||||
|
" current_db_objects = len(differenc_set)\n",
|
||||||
|
" continue\n",
|
||||||
|
" else:\n",
|
||||||
|
" optimized_hitrates[differenc_set] = 0\n",
|
||||||
|
" break\n",
|
||||||
|
" # Compute Lagrangian multiplier and optimal hit probabilities\n",
|
||||||
|
" eta = eta_star(current_db_objects, 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",
|
||||||
|
"\n",
|
||||||
|
" if mu < 0:\n",
|
||||||
|
" current_cache_size = current_db_objects * 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",
|
||||||
|
" max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrates)\n",
|
||||||
|
" optimized_hitrates[max_outbound_index] = (1 if optimized_hitrates[max_outbound_index] > 1 else 0)\n",
|
||||||
|
"\n",
|
||||||
|
" current_cache_size =- optimized_hitrates[max_outbound_index]\n",
|
||||||
|
" fix_i.append(max_outbound_index)\n",
|
||||||
|
" differenc_set = np.setdiff1d(np.arange(DATABASE_OBJECT_COUNT), fix_i)\n",
|
||||||
|
" current_db_objects = DATABASE_OBJECT_COUNT - len(fix_i)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 11,
|
||||||
|
"id": "4f64253f-b389-4be9-b403-08027d480121",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([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.,\n",
|
||||||
|
" 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.,\n",
|
||||||
|
" 1., 0., 0., 0., 0., 0., 1., 0., 0., 1., 0., 0., 0., 0., 1., 0., 1.,\n",
|
||||||
|
" 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.,\n",
|
||||||
|
" 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 11,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"optimized_hitrates"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 12,
|
||||||
|
"id": "17d818db-ec88-4c26-92af-6d74862525d9",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([ 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0.43902439, 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0.43902439, 0. , 0. ,\n",
|
||||||
|
" 0. , 0.04878049, 0. , 0.04878049, 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , -0. , 0. ,\n",
|
||||||
|
" 0.04878049, 0.04878049, 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0.43902439, 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" -0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" -0. , 0. , 1. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , -0. , 0. ,\n",
|
||||||
|
" 0. , 0.43902439, 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0. , 0. ,\n",
|
||||||
|
" 0. , 0. , 0. , 0.04878049, 0. ])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 12,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"a"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 13,
|
||||||
|
"id": "791b3f96-527a-489e-970e-c92ec950177f",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([ 6, 27, 31, 33, 40, 41, 50, 81, 98])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 13,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"b"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 14,
|
||||||
|
"id": "c22fa973-432a-4c05-89bf-2a6ea82ae3d2",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"array([ 6, 27, 50, 81])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 14,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"differenc_set"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 15,
|
||||||
|
"id": "898e1266-5aaa-46f4-ac0f-c7807ac2b6bb",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"db_object_count = DATABASE_OBJECT_COUNT\n",
|
||||||
|
"cache_sz = CACHE_SIZE\n",
|
||||||
|
"loop_lambda = lambda_vals\n",
|
||||||
|
"\n",
|
||||||
|
"non_optimized_values = np.arange(db_object_count)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 16,
|
||||||
|
"id": "8cc9b8a9-f7ae-48fc-adfb-ac4b7a4998f1",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"db_object_count = DATABASE_OBJECT_COUNT\n",
|
||||||
|
"cache_sz = CACHE_SIZE\n",
|
||||||
|
"loop_lambda = lambda_vals\n",
|
||||||
|
"\n",
|
||||||
|
"optimized_hitrate = np.zeros(db_object_count)\n",
|
||||||
|
"non_optimized_values = np.arange(db_object_count)\n",
|
||||||
|
"optimized_value = {}\n",
|
||||||
|
"\n",
|
||||||
|
"eta = eta_star(db_object_count, c_f, cache_sz, c_delta, loop_lambda[non_optimized_values])\n",
|
||||||
|
"optimized_hitrate[non_optimized_values] = h_i_star(c_f, eta, loop_lambda[non_optimized_values], c_delta)\n",
|
||||||
|
"\n",
|
||||||
|
"max_outbound_index = get_index_of_furthest_hitrate_from_boundary(optimized_hitrate)\n",
|
||||||
|
"optimized_value[max_outbound_index] = (1 if optimized_hitrate[max_outbound_index] > 1 else 0)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 17,
|
||||||
|
"id": "cbcf3592-fcf2-4f54-a3cd-761097c12972",
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"{67: 1}"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 17,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"optimized_value"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": null,
|
||||||
|
"id": "db732331-1d09-45b7-915c-73daa270b5e2",
|
||||||
|
"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
|
||||||
|
}
|
||||||
@@ -1,25 +1,25 @@
|
|||||||
function [h_optt] = Theoritical_opt(lambda,B,c_f,c_delta)
|
function [h_optt] = Theoritical_opt(lambda,B,c_f,c_delta)
|
||||||
%% Theoritical optimization
|
%% Theoritical optimization
|
||||||
|
|
||||||
|
|
||||||
%% Iterative identification of active constraints
|
%% Iterative identification of active constraints
|
||||||
N=length(lambda)
|
N=length(lambda)
|
||||||
flag=1;
|
flag=1;
|
||||||
h_optt=zeros(N,1); %optimal hit prob
|
h_optt=zeros(N,1); %optimal hit prob
|
||||||
differenc_set=1:N; % the set of variables to optimize
|
differenc_set=1:N; % the set of variables to optimize
|
||||||
fix_i=[]; % set of variables that reached optimality and are excluded from the optimization
|
fix_i=[]; % set of variables that reached optimality and are excluded from the optimization
|
||||||
n=N;
|
n=N;
|
||||||
b=B;
|
b=B;
|
||||||
|
|
||||||
%%
|
%%
|
||||||
while flag
|
while flag
|
||||||
if(n==0)
|
if(n==0)
|
||||||
if(b>0) % if there is left over cache size and mu is not zero (the loop would break), redistribute it among the zero hit probability
|
if(b>0) % if there is left over cache size and mu is not zero (the loop would break), redistribute it among the zero hit probability
|
||||||
differenc_set=find(h_optt==0)';
|
differenc_set=find(h_optt==0)';
|
||||||
fix_i=setdiff(1:N,differenc_set)';
|
fix_i=setdiff(1:N,differenc_set)';
|
||||||
n=length(differenc_set);
|
n=length(differenc_set);
|
||||||
continue;
|
continue;
|
||||||
else
|
else
|
||||||
h_optt(differenc_set)=0;
|
h_optt(differenc_set)=0;
|
||||||
break;
|
break;
|
||||||
end
|
end
|
||||||
@@ -27,23 +27,23 @@ while flag
|
|||||||
% Optimal Lagrangian mult. and hit prob. calculated theoritically for the set of variables in differenc_set
|
% Optimal Lagrangian mult. and hit prob. calculated theoritically for the set of variables in differenc_set
|
||||||
mu=max(0,(n*c_f-b*c_delta)/ sum(1./lambda(differenc_set))); %optimal lagrangian mult.
|
mu=max(0,(n*c_f-b*c_delta)/ sum(1./lambda(differenc_set))); %optimal lagrangian mult.
|
||||||
h_optt(differenc_set)=(c_f-mu./lambda(differenc_set))/c_delta %optimal hit prob
|
h_optt(differenc_set)=(c_f-mu./lambda(differenc_set))/c_delta %optimal hit prob
|
||||||
|
|
||||||
% mu has to be >=0
|
% mu has to be >=0
|
||||||
if(mu<0)
|
if(mu<0)
|
||||||
b=(n*c_f/c_delta); % this sets mu to zero in the next iteration
|
b=(n*c_f/c_delta); % this sets mu to zero in the next iteration
|
||||||
continue;
|
continue;
|
||||||
end
|
end
|
||||||
|
|
||||||
% check the violation of the hit_prob const
|
% check the violation of the hit_prob const
|
||||||
larger_i=find(h_optt>1); % h>1
|
larger_i=find(h_optt>1); % h>1
|
||||||
smaller_i=find(h_optt<0); % h<0
|
smaller_i=find(h_optt<0); % h<0
|
||||||
|
|
||||||
if(length(smaller_i)==0 && length(larger_i)==0)
|
if(length(smaller_i)==0 && length(larger_i)==0)
|
||||||
|
|
||||||
|
|
||||||
break;
|
break;
|
||||||
end
|
end
|
||||||
|
|
||||||
% find the furthest object from the 0 boundary
|
% find the furthest object from the 0 boundary
|
||||||
min_viol=0;
|
min_viol=0;
|
||||||
min_viol_i=-1;
|
min_viol_i=-1;
|
||||||
@@ -51,14 +51,14 @@ while flag
|
|||||||
[min_viol, min_viol_i]=min(h_optt);
|
[min_viol, min_viol_i]=min(h_optt);
|
||||||
end
|
end
|
||||||
% find the furthest object from the 1 boundary
|
% find the furthest object from the 1 boundary
|
||||||
max_viol=0;
|
max_viol=0;
|
||||||
max_viol_i=-1;
|
max_viol_i=-1;
|
||||||
if(length(larger_i)>0)
|
if(length(larger_i)>0)
|
||||||
larger=h_optt-1;
|
larger=h_optt-1;
|
||||||
[max_viol ,max_viol_i]=max(h_optt-1);
|
[max_viol ,max_viol_i]=max(h_optt-1);
|
||||||
|
|
||||||
end
|
end
|
||||||
|
|
||||||
% compare both furthest objects from both boundaries
|
% compare both furthest objects from both boundaries
|
||||||
viol_i=min_viol_i;
|
viol_i=min_viol_i;
|
||||||
min_viol_flag=1; % True if the furthest one is from the left
|
min_viol_flag=1; % True if the furthest one is from the left
|
||||||
@@ -73,18 +73,15 @@ while flag
|
|||||||
else
|
else
|
||||||
h_optt(viol_i)=min(1,b);
|
h_optt(viol_i)=min(1,b);
|
||||||
end
|
end
|
||||||
|
|
||||||
%calculate the new parameters after removing the furthest object from
|
%calculate the new parameters after removing the furthest object from
|
||||||
%the decision variables
|
%the decision variables
|
||||||
B_new=b-(h_optt(viol_i));
|
B_new=b-(h_optt(viol_i));
|
||||||
b=B_new;
|
b=B_new;
|
||||||
fix_i=[fix_i' viol_i']';
|
fix_i=[fix_i' viol_i']';
|
||||||
differenc_set=setdiff(1:N,fix_i) ;
|
differenc_set=setdiff(1:N,fix_i) ;
|
||||||
n=N-length(fix_i);
|
n=N-length(fix_i);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
end
|
end
|
||||||
|
|
||||||
end
|
end
|
||||||
|
|
||||||
|
|||||||
File diff suppressed because one or more lines are too long
45757
01_nb_cncf_optimization/notes_code.excalidraw
Normal file
45757
01_nb_cncf_optimization/notes_code.excalidraw
Normal file
File diff suppressed because one or more lines are too long
Reference in New Issue
Block a user