1_Regional_Optimal_Pools.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "gross-corps",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from pymoo.optimize import minimize\n",
    "from pymoo.factory import get_crossover, get_mutation, get_sampling\n",
    "from pymoo.algorithms.soo.nonconvex.ga import GA\n",
    "\n",
    "from pooling_functions import calc_pool_conc, MinConcProblem, MinNumCntrProblem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e7ba220",
   "metadata": {},
   "source": [
    "This notebook relies on pymoo \"0.5.0\". To install it, one needs to run:\n",
    "\n",
    "> pip install pymoo==0.5.0\n",
    "\n",
    "from the command line."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "naked-jacob",
   "metadata": {},
   "source": [
    "Load data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "blank-seven",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ASM</th>\n",
       "      <th>KHM</th>\n",
       "      <th>COK</th>\n",
       "      <th>FJI</th>\n",
       "      <th>PYF</th>\n",
       "      <th>IDN</th>\n",
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       "      <th>LAO</th>\n",
       "      <th>MYS</th>\n",
       "      <th>MHL</th>\n",
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       "      <th>ZWE</th>\n",
       "      <th>BWA</th>\n",
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       "      <th>SWZ</th>\n",
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       "      <td>81.644624</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.093447e+07</td>\n",
       "      <td>1.342145e+07</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.236010e+07</td>\n",
       "      <td>3.473528e+07</td>\n",
       "      <td>702363.195433</td>\n",
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       "    <tr>\n",
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       "<p>5 rows × 87 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            ASM           KHM            COK          FJI          PYF  \\\n",
       "0  0.000000e+00  1.174686e+05   61567.633482     0.000000  2066.621255   \n",
       "1  0.000000e+00  2.135547e+07       0.000000     0.000000  1817.411519   \n",
       "2  2.615973e+07  6.706448e+08    2374.730234     0.000000    42.486543   \n",
       "3  6.236010e+07  3.473528e+07  702363.195433  4825.253640     0.000000   \n",
       "4  0.000000e+00  2.488902e+07       0.000000   158.037936     0.000000   \n",
       "\n",
       "            IDN  KIR           LAO           MYS        MHL  ...  MWI  \\\n",
       "0  4.932370e+09  0.0  1.468178e+05  1.363927e+10   0.000000  ...  0.0   \n",
       "1  0.000000e+00  0.0  2.456694e+06  5.648761e+06  81.644624  ...  0.0   \n",
       "2  6.417800e+07  0.0  0.000000e+00  3.386322e+05   0.000000  ...  0.0   \n",
       "3  0.000000e+00  0.0  0.000000e+00  2.667397e+09   0.000000  ...  0.0   \n",
       "4  3.155947e+09  0.0  0.000000e+00  0.000000e+00   0.000000  ...  0.0   \n",
       "\n",
       "            MUS           MOZ           SOM           TZA  ZMB  ZWE  BWA  \\\n",
       "0  4.132596e+08  1.240871e+07  1.518563e+07  8.905124e+09  0.0  0.0  0.0   \n",
       "1  3.394774e+05  1.486315e+08  0.000000e+00  7.669974e+06  0.0  0.0  0.0   \n",
       "2  6.093447e+07  1.342145e+07  0.000000e+00  0.000000e+00  0.0  0.0  0.0   \n",
       "3  1.005025e+05  1.356082e+04  8.197128e+05  0.000000e+00  0.0  0.0  0.0   \n",
       "4  5.339540e+05  0.000000e+00  0.000000e+00  0.000000e+00  0.0  0.0  0.0   \n",
       "\n",
       "            ZAF  SWZ  \n",
       "0  1.297125e+06  0.0  \n",
       "1  0.000000e+00  0.0  \n",
       "2  0.000000e+00  0.0  \n",
       "3  0.000000e+00  0.0  \n",
       "4  0.000000e+00  0.0  \n",
       "\n",
       "[5 rows x 87 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datay = pd.read_csv('data/yearly_damages.csv', index_col=0)\n",
    "datay.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1160178c",
   "metadata": {},
   "source": [
    "Load damages by region:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1cf30b3d",
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_names = ['EAP', 'LAC', 'SA', 'SSA']\n",
    "\n",
    "df_reg = {}\n",
    "\n",
    "for reg_name in reg_names:\n",
    "    regs = np.loadtxt('data/{}.txt'.format(reg_name), dtype=str)\n",
    "\n",
    "    df_reg.update({reg_name: datay[regs]})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a0093b",
   "metadata": {},
   "source": [
    "Define alpha:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4112230d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.995"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RT = 200\n",
    "\n",
    "alpha = 1-1/RT\n",
    "alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e1c8d16",
   "metadata": {},
   "source": [
    "Find optimal pool for each region:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "tough-medication",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FIND OPTIMAL POOL FOR REGION EAP\n",
      "\n",
      "Step 1 - Find the pool with the minimum concentration\n",
      "Pool has 19 countries and a concentration of 0.34 (i.e., and diversification of 0.66)\n",
      "\n",
      "Step 2 - Find the smallest sub-pool which maintains the same concentration\n",
      "Sub-pool has 7.0 countries\n",
      "\n",
      "FIND OPTIMAL POOL FOR REGION LAC\n",
      "\n",
      "Step 1 - Find the pool with the minimum concentration\n",
      "Pool has 25 countries and a concentration of 0.25 (i.e., and diversification of 0.75)\n",
      "\n",
      "Step 2 - Find the smallest sub-pool which maintains the same concentration\n",
      "Sub-pool has 18.0 countries\n",
      "\n",
      "FIND OPTIMAL POOL FOR REGION SA\n",
      "\n",
      "Step 1 - Find the pool with the minimum concentration\n",
      "Pool has 5 countries and a concentration of 0.66 (i.e., and diversification of 0.34)\n",
      "\n",
      "Step 2 - Find the smallest sub-pool which maintains the same concentration\n",
      "Sub-pool has 4.0 countries\n",
      "\n",
      "FIND OPTIMAL POOL FOR REGION SSA\n",
      "\n",
      "Step 1 - Find the pool with the minimum concentration\n",
      "Pool has 7 countries and a concentration of 0.5 (i.e., and diversification of 0.5)\n",
      "\n",
      "Step 2 - Find the smallest sub-pool which maintains the same concentration\n",
      "Sub-pool has 6.0 countries\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for reg in df_reg.keys():\n",
    "\n",
    "    bools = df_reg[reg] >= np.quantile(df_reg[reg], alpha, axis=0)\n",
    "    problem = MinConcProblem(df_reg[reg], bools.values, alpha, calc_pool_conc)\n",
    "\n",
    "    print(\"FIND OPTIMAL POOL FOR REGION {}\\n\".format(reg))\n",
    "    print(\"Step 1 - Find the pool with the minimum concentration\")\n",
    "\n",
    "    algorithm = GA(pop_size=df_reg[reg].shape[1],\n",
    "    sampling=get_sampling(\"bin_random\"),\n",
    "    crossover=get_crossover(\"bin_hux\"),\n",
    "    mutation=get_mutation(\"bin_bitflip\"),\n",
    "    eliminate_duplicates=True)\n",
    "\n",
    "    res_reg = minimize(problem,\n",
    "                         algorithm,\n",
    "                         ('n_gen', 750),\n",
    "                         verbose=False,\n",
    "                         save_history=True,\n",
    "                         pf=np.array(0.0))\n",
    "\n",
    "    print(f\"Pool has {np.sum(res_reg.X)} countries and a concentration of {res_reg.F[0]} (i.e., and diversification of {np.round(1-res_reg.F[0],2)})\\n\")\n",
    "    print(\"Step 2 - Find the smallest sub-pool which maintains the same concentration\")\n",
    "\n",
    "    cntries = res_reg.X.astype(int)\n",
    "\n",
    "    reg_datay_opt = df_reg[reg][df_reg[reg].columns[cntries > 0]]\n",
    "    bools_opt = reg_datay_opt >= np.quantile(reg_datay_opt, alpha, axis=0)\n",
    "\n",
    "    problem = MinNumCntrProblem(reg_datay_opt, bools_opt.values, alpha, calc_pool_conc, res_reg.F[0])\n",
    "\n",
    "    algorithm = GA(pop_size=reg_datay_opt.shape[1],\n",
    "    sampling=get_sampling(\"bin_random\"),\n",
    "    crossover=get_crossover(\"bin_hux\"),\n",
    "    mutation=get_mutation(\"bin_bitflip\"),\n",
    "    eliminate_duplicates=True)\n",
    "\n",
    "    res_reg2 = minimize(problem,\n",
    "                         algorithm,\n",
    "                         ('n_gen', 750),\n",
    "                         verbose=False,\n",
    "                         save_history=True,\n",
    "                         pf=np.array(0.0))\n",
    "\n",
    "    print(f\"Sub-pool has {np.sum(res_reg2.F[0])} countries\\n\")"
   ]
  }
 ],
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