whatsopt_segmoomoe.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "906c60b2-6e36-4973-8e37-26dee3b70628",
   "metadata": {},
   "source": [
    "# Tutorial SEGMOOMOE via web services"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e18b3fe-d4a9-4dee-a018-b84b9b886f98",
   "metadata": {},
   "source": [
    "This notebook describes the usage of segomoe using web services exposed by WhatsOpt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00e62f3f-9083-4ada-be9a-89424157c7cd",
   "metadata": {},
   "source": [
    "## Prerequisite"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b6b7499-f491-4670-b984-3ecaaec3920f",
   "metadata": {},
   "source": [
    "### wop (WhatsOpt command line interface)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "986d14c3-df47-469c-a87b-c8ed4dd9955b",
   "metadata": {},
   "source": [
    "You have to install the `wop` command:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "639e5e0e-5845-4064-a18e-146abcababfc",
   "metadata": {},
   "source": [
    "```bash\n",
    "pip install -U wop \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2e45518-3777-49ab-88a2-067064b762c8",
   "metadata": {},
   "source": [
    "You need to be logged in a WhatsOpt server either by using the <code>wop</code> command in a shell or the WhatsOpt API as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7ec06212-f547-4c08-8cc3-a255476da2f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32mSuccessfully logged in to remote WhatsOpt https://selene.onecert.fr/whatsopt\u001b[0m\n",
      "\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "from whatsopt.whatsopt_client import WhatsOpt\n",
    "wop = WhatsOpt(url=\"https://ether.onera.fr/whatsopt\")\n",
    "ok = wop.login(echo=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7521d79-6369-4dc9-888d-dd7b740ebd43",
   "metadata": {
    "tags": []
   },
   "source": [
    "To test if you are connected the following command should succeed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "95134148-d6aa-4c8b-a56b-ff4ff6c65828",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WhatsOpt 1.30.0 requires wop >= 1.20.0\u001b[0m\n",
      "You are using wop 2.5.5\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "wop.check_versions()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b412214f-55e1-42e7-a289-61ef84ef3208",
   "metadata": {},
   "source": [
    "### SMT (Surrogate Modeling Toolbox)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98a3aa47-5765-4d0b-b10c-2bfbc1611337",
   "metadata": {},
   "source": [
    "SMT is not required per se, but is used in this notebook to get optimized LHS sampling method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "229baf86-dfbe-4185-b6a1-287ec05fcb74",
   "metadata": {},
   "source": [
    "```bash\n",
    "pip install smt\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce3073a9-da6e-49a1-8f46-c2ee15b830fb",
   "metadata": {},
   "source": [
    "## Optimization with constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64941ab0-48d1-4b94-b58d-d522c6e33a20",
   "metadata": {},
   "source": [
    "### Objective function\n",
    "\n",
    "First we define the objective function we want to minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9881542b-ed47-416b-a50d-f2c2e6f7022f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def fun(x):  # function with 3 objectives\n",
    "    x = np.atleast_2d(x)\n",
    "    f1 = x[:, 0] - x[:, 1] * x[:, 2]\n",
    "    f2 = 4 * x[:, 0] ** 2 - 4 * x[:, 0] ** x[:, 2] + 1 + x[:, 1]\n",
    "    f3 = x[:, 0] ** 2\n",
    "    return np.hstack((np.atleast_2d(f1).T, np.atleast_2d(f2).T, np.atleast_2d(f3).T))\n",
    "\n",
    "\n",
    "def g1(x):  # constraint to force x < 0.8\n",
    "    x = np.atleast_2d(x)\n",
    "    return np.atleast_2d(x[:, 0] - 0.8).T\n",
    "\n",
    "\n",
    "def g2(x):  # constraint to force x > 0.2\n",
    "    x = np.atleast_2d(x)\n",
    "    return np.atleast_2d(0.2 - x[:, 0]).T\n",
    "\n",
    "\n",
    "def f_grouped(x):\n",
    "    resfun = fun(x)\n",
    "    resg1 = g1(x)\n",
    "    resg2 = g2(x)\n",
    "    res = np.hstack((resfun, resg1, resg2))\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0c69cac-3fb4-4a34-8c95-21048505f453",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84cda9f5-100f-4695-a9b8-01689a299312",
   "metadata": {},
   "source": [
    "First we create an optimization context to use the SEGMOOMOE optimizer with the design space <code>xlimits</code>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2c4aa810-694c-4a6c-8cc4-b558c9a94e9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from whatsopt.mooptimization import MOOptimization, FLOAT, INT\n",
    "\n",
    "xtypes = [{\"type\": FLOAT, \"limits\": [0., 1.]},\n",
    "          {\"type\": INT, \"limits\": [0, 3]},\n",
    "          {\"type\": INT, \"limits\": [0, 3]}]\n",
    "\n",
    "cstr_specs = 2*[{\"type\": '<', \"bound\": 0.0}]\n",
    "\n",
    "options={\"n_clusters\": 1, \"criterion\": \"PI\", \"pop_size\": 30, \"n_gen\": 30, \"verbose\": True, \"debug\": True}\n",
    "\n",
    "optim = MOOptimization(xtypes, n_obj=3, cstr_specs=cstr_specs, options=options)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cb8eea2-9dbe-428e-ac22-30f7671bde78",
   "metadata": {},
   "source": [
    "You can get the optimization identifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c77016f3-6d68-4e66-aef8-42b7d4316cae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optim._id"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c6cfc95-ea90-4d89-93b8-4e242cb703af",
   "metadata": {},
   "source": [
    "This id is be used to identify the optimization and visualize the results when using the WhatsOpt web application. It can also be used at a lower level to handle the optimization when using WhatsOpt REST API."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15dc798a-eb78-4acd-8c9c-3630685ed581",
   "metadata": {},
   "source": [
    "We need to have an initial DOE (n_samples, nx) and the corresponding outputs y (n_samples, 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "211969ff-52cb-42e8-9cc6-78bfcd7450a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial DOE\n",
      "xdoe=[[0.36691555 0.         1.        ]\n",
      " [0.58432706 1.         1.        ]\n",
      " [0.09227899 1.         2.        ]\n",
      " [0.95274182 1.         2.        ]\n",
      " [0.72873502 1.         3.        ]\n",
      " [0.87115983 2.         1.        ]\n",
      " [0.24346361 2.         3.        ]\n",
      " [0.4221473  2.         0.        ]\n",
      " [0.10886813 2.         1.        ]\n",
      " [0.65557784 3.         2.        ]\n",
      " [0.39532629 2.         0.        ]]\n",
      "ydoe=[[ 0.36691555  0.07084588  0.13462702 -0.43308445 -0.16691555]\n",
      " [-0.41567294  1.02844421  0.34143811 -0.21567294 -0.38432706]\n",
      " [-1.90772101  2.          0.00851541 -0.70772101  0.10772101]\n",
      " [-1.04725818  2.          0.90771698  0.15274182 -0.75274182]\n",
      " [-2.27126498  2.5762262   0.53105473 -0.07126498 -0.52873502]\n",
      " [-1.12884017  2.55103848  0.75891945  0.07115983 -0.67115983]\n",
      " [-5.75653639  3.17937335  0.05927453 -0.55653639 -0.04346361]\n",
      " [ 0.4221473  -0.28716663  0.17820834 -0.3778527  -0.2221473 ]\n",
      " [-1.89113187  2.61193656  0.01185227 -0.69113187  0.09113187]\n",
      " [-5.34442216  4.          0.4297823  -0.14442216 -0.45557784]\n",
      " [ 0.39532629 -0.3748685   0.15628288 -0.40467371 -0.19532629]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "# from smt.sampling_methods import LHS\n",
    "# lhs = LHS(xlimits=np.array(xlimits), criterion='ese')\n",
    "# xdoe = lhs(5)\n",
    "\n",
    "xdoe = np.array(\n",
    "    [        \n",
    "     [0.36691555, 0.,        1.        ],\n",
    "     [0.58432706, 1.,       1.        ],\n",
    "     [0.09227899, 1.,         2.        ],\n",
    "     [0.95274182, 1.,         2.        ],\n",
    "     [0.72873502, 1.,         3.        ],\n",
    "     [0.87115983, 2.,         1.        ],\n",
    "     [0.24346361, 2.,         3.        ],\n",
    "     [0.4221473 , 2.,         0.        ],\n",
    "     [0.10886813, 2.,         1.        ],\n",
    "     [0.65557784, 3.,         2.        ],\n",
    "     [0.39532629, 2.,         0.        ]\n",
    "    ]\n",
    ")\n",
    "ydoe = f_grouped(xdoe)\n",
    "print(\"Initial DOE\")\n",
    "print(\"xdoe={}\".format(xdoe))\n",
    "print(\"ydoe={}\".format(ydoe))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d34f4b1-b2a6-4352-a42f-8cc357b2e554",
   "metadata": {},
   "source": [
    "We initialize the optimizer with the inital DOE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "598bb14c-16a2-48b8-96cb-7ddc1b6aabbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "optim.tell_doe(xdoe, ydoe)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a21afff9-d50d-4459-bf8c-83c149e9e5ef",
   "metadata": {},
   "source": [
    "We trigger the optimization using the \"ask and tell\" interface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6cd0c88f-49c9-408b-8c7e-bb9cafe1fb3c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 x suggested = [0.7370702549962509, 3.0, 3.0] with status: pending\n",
      "new y = [[-8.26292975  4.57137006  0.54327256 -0.06292975 -0.53707025]]\n",
      "1 x suggested = [0.20000054130064435, 2.0, 2.0] with status: pending\n",
      "new y = [[-3.79999946e+00  3.00000000e+00  4.00002165e-02 -5.99999459e-01\n",
      "  -5.41300644e-07]]\n",
      "Found approx pareto y_opt = [[0.027105600171699606, -0.9769517030888495, 0.312986916555557], [0.26890808642161046, -0.7147333354903309, -0.21207472228164226], [-2.435955088404744, 1.8686997180933123, -0.2146374673474123], [-8.20682127570078, 3.723265233215578, 0.9907868808012683], [-8.264820911134889, 4.540590761711645, 0.4270804028147521], [-5.761543606836482, 2.783497227716061, 0.1870968650452542], [-5.327682817300804, 4.3697497937100565, -0.214635882184961], [-8.152120695986888, 3.266006278243318, 0.41298855577838367], [-3.139971136335076, 2.4058868039800947, 0.5719412426536465], [-2.2907782534032703, 0.5463474142351912, 0.4128659417744393], [-1.5481165552769542, 0.019086939510204015, 0.3323388335455911], [-3.4124886244268584, 2.648085613259823, 0.41291300167983463], [-0.6969755254272205, -0.6201107728756692, -0.21460025770675684], [0.25391903320088494, -0.7462303531884342, -0.1284953582592161], [-3.169709770387309, 2.4507158313021193, 0.5230903182235281], [-2.1660331955906478, 1.3533227025545522, -0.20325560879512816], [-8.214166481239994, 3.797734189746472, 0.6323001271439541], [-8.200280092398327, 3.6600514111530362, 0.7402180263347365], [-1.4479814102713287, 0.19891958296697587, -0.21462844197661912], [-5.761536324928281, 2.799023097731918, 0.13504882424833356], [-0.7418735276722919, -0.7240230954160634, 0.9321222824060429], [-8.22122732492351, 3.8731832208179107, -0.017245924911056476], [-0.01819848712250538, -0.9687820346979832, 0.41275176699934246], [-8.240156621234034, 4.09882506565312, 0.1107926803461195], [-2.445951693601384, 1.8209428519154898, 0.0035065398116969626], [-8.203751945094321, 3.6932564629478604, 0.9267284136871717], [-2.532327594344238, 1.4678374120153839, 0.4081991919168638], [-8.21178096763074, 3.773121912389378, 0.8222872705262059], [-2.5050439498387753, 1.564352972946716, 0.05065085283330345], [-2.1652251755357352, 1.3589056700823938, -0.21423469846667675]] at x_opt = [[0.04237926945187015, 2.0, 0.0], [0.27124466984792245, 2.0, 0.0], [0.2743172091975529, 1.0, 3.0], [0.1856598553998187, 3.0, 3.0], [0.6531520227126679, 3.0, 3.0], [0.06285517258756945, 2.0, 3.0], [0.2743172091975529, 3.0, 2.0], [2.7828492116244163e-05, 3.0, 3.0], [0.8058649778034586, 3.0, 1.0], [0.00024499643447706276, 0.0, 2.0], [0.038184661382185, 3.0, 0.0], [0.00016139770836995707, 3.0, 1.0], [0.2740811167391944, 1.0, 0.0], [0.2567631665229144, 2.0, 0.0], [0.7239307123339024, 3.0, 1.0], [0.2677814822783512, 0.0, 3.0], [0.21638687032604814, 3.0, 3.0], [0.1598754419427478, 3.0, 3.0], [0.27429448521103567, 3.0, 0.0], [0.0701414380632166, 2.0, 3.0], [0.17394960244769192, 1.0, 0.0], [0.24807583632339364, 3.0, 3.0], [0.00044248892524598703, 2.0, 0.0], [0.3486491980412602, 3.0, 3.0], [0.2467557484138671, 1.0, 3.0], [0.1733919732313741, 3.0, 3.0], [0.006593973934057751, 1.0, 3.0], [0.20618017165600483, 3.0, 3.0], [0.08295846461042694, 1.0, 3.0], [0.27317241485107224, 0.0, 3.0]]\n"
     ]
    }
   ],
   "source": [
    "# We loop using the iteration budget\n",
    "n_iter = 2\n",
    "with_best=False\n",
    "for i in range(n_iter):\n",
    "    with_best = with_best or (i == n_iter - 1)\n",
    "    x_suggested, status, x_opt, y_opt = optim.ask(with_best)\n",
    "    print(\"{} x suggested = {} with status: {}\".format(i, x_suggested, MOOptimization.STATUSES[status]))\n",
    "\n",
    "    # compute objective function at the suggested point\n",
    "    new_y = f_grouped(x_suggested)\n",
    "    print(\"new y = {}\".format(new_y))\n",
    "\n",
    "    optim.tell(x_suggested, new_y)\n",
    "         \n",
    "print(\"Found approx pareto y_opt = {} at x_opt = {}\".format(y_opt, x_opt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "68041015-33b9-4cd1-877a-79ce5fb525d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_opt = np.array(x_opt)\n",
    "y_opt = np.array(y_opt)\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x_opt[:,0], x_opt[:,1], marker='x',label = 'approx BO')\n",
    "plt.xlabel('$x_0$')\n",
    "plt.ylabel('$x_1$')\n",
    "plt.legend()\n",
    "plt.title(\"design space\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x_opt[:,0], x_opt[:,2], marker='x',label = 'approx BO')\n",
    "plt.xlabel('$x_0$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.legend()\n",
    "plt.title(\"design space\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter( y_opt[:,0],  y_opt[:,1],marker='x', label = 'approx BO')\n",
    "plt.xlabel('f1')\n",
    "plt.ylabel('f2')\n",
    "plt.legend()\n",
    "plt.title(\"objective space\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7505d5f0-3ecc-44e8-a20b-7db24caba112",
   "metadata": {},
   "outputs": [],
   "source": [
    "optim.tell_doe(xdoe, ydoe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b3b2dff3-bafb-4886-a0d1-3d888630919b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 x suggested = [0.621506214371434, 1.0, 3.0] with status: pending\n",
      "new y = [[-2.37849379  2.58480314  0.38626997 -0.17849379 -0.42150621]]\n",
      "1 x suggested = [0.7808470632950001, 3.0, 3.0] with status: pending\n",
      "new y = [[-8.21915294  4.53448959  0.60972214 -0.01915294 -0.58084706]]\n",
      "2 x suggested = [0.25375592195918173, 2.0, 0.0] with status: pending\n",
      "new y = [[ 0.25375592 -0.74243173  0.06439207 -0.54624408 -0.05375592]]\n",
      "3 x suggested = [0.4919306079221343, 1.0, 1.0] with status: pending\n",
      "new y = [[-0.50806939  1.00026046  0.24199572 -0.30806939 -0.29193061]]\n",
      "4 x suggested = [0.24656812958046048, 0.0, 0.0] with status: pending\n",
      "x_best=[[0.20027477231028218, 2.0, 0.0], [2.220963272170362e-05, 0.0, 1.0], [0.20054804244293423, 3.0, 3.0], [0.38975362869629937, 0.0, 1.0], [0.19756238557465422, 3.0, 1.0], [0.20077780734771183, 2.0, 3.0], [0.7979380165269789, 1.0, 3.0], [0.20025455946310436, 2.0, 2.0], [0.199668805042126, 3.0, 2.0], [0.1876590775208521, 0.0, 1.0], [0.5259483857257506, 1.0, 2.0], [0.20001271768255985, 1.0, 1.0], [0.38912214085987457, 0.0, 1.0], [0.42169862387698254, 1.0, 1.0], [0.20026704323442807, 1.0, 3.0], [0.38975362869629937, 0.0, 2.0], [0.04546752146825593, 0.0, 1.0], [0.000921587977772309, 0.0, 1.0], [0.10714112612520699, 0.0, 1.0], [0.7318708470635393, 1.0, 3.0], [0.20001271768255985, 1.0, 2.0], [0.12708029981960467, 0.0, 1.0], [0.0820582235636601, 0.0, 1.0], [0.16095616230094056, 0.0, 1.0], [0.07300007567711406, 0.0, 1.0], [0.4848115773089361, 1.0, 2.0], [0.04959366868167747, 0.0, 1.0], [0.17804826541430346, 0.0, 1.0], [0.5554171376086197, 1.0, 3.0], [0.12600390341856593, 0.0, 1.0]]\n",
      "y_best=[[0.2002836522019682, -0.8350710343489858, 0.04007935097710075], [0.019320152420933212, 0.3631056860989532, 2.5097062899350084], [-8.768062500330768, 3.9485600316503873, -0.0559134097666521], [0.3885592003178915, 0.06984231466011837, -0.010098495956875397], [-2.7825396221627083, 2.9319406741216216, -0.058113609289030144], [-5.799143116868437, 3.144077913395787, 0.04045679216884335], [-2.20205493652669, 2.5700956837745297, 0.6367401217910543], [-3.800497266361461, 2.897910667806763, 0.04018518465899873], [-5.776259149579843, 3.7714813901054525, -0.056562272458354435], [0.1970618094708576, 0.15199647270979333, 1.2902051363840312], [-1.4741972163523211, 1.9425900491681467, 0.276712314706627], [-0.7998921081673556, 1.0623403224260468, 0.04023826740887987], [0.38796070013623174, 0.06984117556673786, -0.006107196989171171], [-0.578289723520033, 0.9942323992357768, 0.1779475228954627], [-2.7995441268143466, 2.5996654587529413, 0.04156163330266577], [0.21909650664119384, 2.066873831683674, -0.01022833792170047], [0.062363875987780704, 0.3016502580040612, 2.2155338237647557], [0.02017196760430684, 0.3618325546047714, 2.5038994152368965], [0.12078340551321554, 0.22832926935772369, 1.8145601720562414], [-2.2681300886455933, 2.575956412707472, 0.5356369652433799], [-1.8000517021305493, 1.9752057938032528, 0.040846700050220786], [0.13967178261504065, 0.20729945915187442, 1.6847015641798604], [0.09702324951502495, 0.2566771165549193, 1.977805554121929], [0.17176380502538602, 0.17474427144282978, 1.4640411256136971], [0.08844300571812314, 0.2674181509482616, 2.036710170145062], [-1.515333075225922, 1.943012681640039, 0.2352283108943503], [0.06627213326596237, 0.29637116755907233, 2.188758693573033], [0.1879565101616545, 0.15988193904524528, 1.3527526649417936], [-2.4445711411646114, 2.5893005966021283, 0.30860826720673357], [0.13865209798688127, 0.2083999487265238, 1.691712974866871]]\n",
      "new y = [[ 0.24656813 -2.75681663  0.06079584 -0.55343187 -0.04656813]]\n",
      "Found optimum y_opt = [[ 2.00283652e-01 -8.35071034e-01  4.00793510e-02]\n",
      " [ 1.93201524e-02  3.63105686e-01  2.50970629e+00]\n",
      " [-8.76806250e+00  3.94856003e+00 -5.59134098e-02]\n",
      " [ 3.88559200e-01  6.98423147e-02 -1.00984960e-02]\n",
      " [-2.78253962e+00  2.93194067e+00 -5.81136093e-02]\n",
      " [-5.79914312e+00  3.14407791e+00  4.04567922e-02]\n",
      " [-2.20205494e+00  2.57009568e+00  6.36740122e-01]\n",
      " [-3.80049727e+00  2.89791067e+00  4.01851847e-02]\n",
      " [-5.77625915e+00  3.77148139e+00 -5.65622725e-02]\n",
      " [ 1.97061809e-01  1.51996473e-01  1.29020514e+00]\n",
      " [-1.47419722e+00  1.94259005e+00  2.76712315e-01]\n",
      " [-7.99892108e-01  1.06234032e+00  4.02382674e-02]\n",
      " [ 3.87960700e-01  6.98411756e-02 -6.10719699e-03]\n",
      " [-5.78289724e-01  9.94232399e-01  1.77947523e-01]\n",
      " [-2.79954413e+00  2.59966546e+00  4.15616333e-02]\n",
      " [ 2.19096507e-01  2.06687383e+00 -1.02283379e-02]\n",
      " [ 6.23638760e-02  3.01650258e-01  2.21553382e+00]\n",
      " [ 2.01719676e-02  3.61832555e-01  2.50389942e+00]\n",
      " [ 1.20783406e-01  2.28329269e-01  1.81456017e+00]\n",
      " [-2.26813009e+00  2.57595641e+00  5.35636965e-01]\n",
      " [-1.80005170e+00  1.97520579e+00  4.08467001e-02]\n",
      " [ 1.39671783e-01  2.07299459e-01  1.68470156e+00]\n",
      " [ 9.70232495e-02  2.56677117e-01  1.97780555e+00]\n",
      " [ 1.71763805e-01  1.74744271e-01  1.46404113e+00]\n",
      " [ 8.84430057e-02  2.67418151e-01  2.03671017e+00]\n",
      " [-1.51533308e+00  1.94301268e+00  2.35228311e-01]\n",
      " [ 6.62721333e-02  2.96371168e-01  2.18875869e+00]\n",
      " [ 1.87956510e-01  1.59881939e-01  1.35275266e+00]\n",
      " [-2.44457114e+00  2.58930060e+00  3.08608267e-01]\n",
      " [ 1.38652098e-01  2.08399949e-01  1.69171297e+00]] at x_opt = [[2.00274772e-01 2.00000000e+00 0.00000000e+00]\n",
      " [2.22096327e-05 0.00000000e+00 1.00000000e+00]\n",
      " [2.00548042e-01 3.00000000e+00 3.00000000e+00]\n",
      " [3.89753629e-01 0.00000000e+00 1.00000000e+00]\n",
      " [1.97562386e-01 3.00000000e+00 1.00000000e+00]\n",
      " [2.00777807e-01 2.00000000e+00 3.00000000e+00]\n",
      " [7.97938017e-01 1.00000000e+00 3.00000000e+00]\n",
      " [2.00254559e-01 2.00000000e+00 2.00000000e+00]\n",
      " [1.99668805e-01 3.00000000e+00 2.00000000e+00]\n",
      " [1.87659078e-01 0.00000000e+00 1.00000000e+00]\n",
      " [5.25948386e-01 1.00000000e+00 2.00000000e+00]\n",
      " [2.00012718e-01 1.00000000e+00 1.00000000e+00]\n",
      " [3.89122141e-01 0.00000000e+00 1.00000000e+00]\n",
      " [4.21698624e-01 1.00000000e+00 1.00000000e+00]\n",
      " [2.00267043e-01 1.00000000e+00 3.00000000e+00]\n",
      " [3.89753629e-01 0.00000000e+00 2.00000000e+00]\n",
      " [4.54675215e-02 0.00000000e+00 1.00000000e+00]\n",
      " [9.21587978e-04 0.00000000e+00 1.00000000e+00]\n",
      " [1.07141126e-01 0.00000000e+00 1.00000000e+00]\n",
      " [7.31870847e-01 1.00000000e+00 3.00000000e+00]\n",
      " [2.00012718e-01 1.00000000e+00 2.00000000e+00]\n",
      " [1.27080300e-01 0.00000000e+00 1.00000000e+00]\n",
      " [8.20582236e-02 0.00000000e+00 1.00000000e+00]\n",
      " [1.60956162e-01 0.00000000e+00 1.00000000e+00]\n",
      " [7.30000757e-02 0.00000000e+00 1.00000000e+00]\n",
      " [4.84811577e-01 1.00000000e+00 2.00000000e+00]\n",
      " [4.95936687e-02 0.00000000e+00 1.00000000e+00]\n",
      " [1.78048265e-01 0.00000000e+00 1.00000000e+00]\n",
      " [5.55417138e-01 1.00000000e+00 3.00000000e+00]\n",
      " [1.26003903e-01 0.00000000e+00 1.00000000e+00]]\n"
     ]
    }
   ],
   "source": [
    "x_opt, y_opt = optim.run(f_grouped, n_iter=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e67fc3f5-b0c6-4c9c-9776-b31b9d49a676",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x_opt[:,0], x_opt[:,1], marker='x',label = 'approx BO')\n",
    "plt.xlabel('$x_0$')\n",
    "plt.ylabel('$x_1$')\n",
    "plt.legend()\n",
    "plt.title(\"design space\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x_opt[:,0], x_opt[:,2], marker='x',label = 'approx BO')\n",
    "plt.xlabel('$x_0$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.legend()\n",
    "plt.title(\"design space\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter( y_opt[:,0],  y_opt[:,1],marker='x', label = 'approx BO')\n",
    "plt.xlabel('f1')\n",
    "plt.ylabel('f2')\n",
    "plt.legend()\n",
    "plt.title(\"objective space\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "52651aa1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34\n"
     ]
    }
   ],
   "source": [
    "print(optim._id)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88b3388f-6bac-4f54-a664-8115d2a1463e",
   "metadata": {},
   "source": [
    "## Options"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09c4cc1d",
   "metadata": {},
   "source": [
    "### Options for the optimization solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0b298afb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_clusters': 1, 'verbose': True, 'debug': True}\n",
      "0 x suggested = [0.621506214371434, 1.0, 3.0] with status: pending\n",
      "new y = [[-2.37849379  2.58480314  0.38626997 -0.17849379 -0.42150621]]\n",
      "1 x suggested = [0.3440809843650637, 1.0, 3.0] with status: pending\n",
      "new y = [[-2.65591902  2.31062153  0.11839172 -0.45591902 -0.14408098]]\n",
      "2 x suggested = [0.46660988832957523, 1.0, 1.0] with status: pending\n",
      "new y = [[-0.53339011  1.0044596   0.21772479 -0.33339011 -0.26660989]]\n",
      "3 x suggested = [0.3123393370680104, 0.0, 1.0] with status: pending\n",
      "new y = [[ 0.31233934  0.1408661   0.09755586 -0.48766066 -0.11233934]]\n",
      "4 x suggested = [0.280725219341119, 1.0, 3.0] with status: pending\n",
      "x_best=[[0.25989553426173656, 2.0, 3.0], [0.3669907999008217, 1.0, 3.0], [0.3990470420335775, 2.0, 0.0], [0.4863439654609255, 3.0, 0.0], [0.17822117693336426, 2.0, 3.0], [0.20639588074284632, 2.0, 3.0], [0.333433868765621, 1.0, 0.0], [0.40208392822291983, 3.0, 0.0], [0.38320967956545626, 1.0, 2.0], [0.37148280692971486, 2.0, 0.0], [0.21771115308077477, 2.0, 3.0], [0.3666223818749943, 1.0, 1.0], [0.3953118242283261, 1.0, 3.0], [0.464433221957551, 3.0, 0.0], [0.33490464987885504, 1.0, 0.0], [0.37736587865789467, 2.0, 0.0], [0.38320967956545626, 1.0, 3.0], [0.4387078053140637, 3.0, 0.0], [0.37711060476006397, 1.0, 3.0], [0.38664060194068134, 1.0, 0.0], [0.3374038996608417, 1.0, 0.0], [0.39866907281917974, 2.0, 0.0], [0.3416867243299102, 1.0, 0.0], [0.3487499886885491, 1.0, 0.0], [0.4190813927593477, 1.0, 3.0], [0.37557668685237583, 1.0, 3.0], [0.4027598788273047, 1.0, 3.0], [0.3710190044949552, 1.0, 0.0], [0.3999656837236617, 1.0, 3.0], [0.3661644246557159, 1.0, 1.0]]\n",
      "y_best=[[-5.65018071723501, 3.307594138657718, 0.09594656266232651], [-3.4171016079138905, 1.6942398991326697, 0.02613059706504467], [0.4168893985987392, -0.37759865504338874, 0.15604855854822167], [-1.751981921386338, 0.8079125733626078, 0.3432037700186363], [-4.371749033683876, 2.206431108400573, 0.16672939663820802], [-5.243909053116261, 2.6226536453228406, 0.11404609650077843], [-1.7417530673895734, 0.12477716806242989, 0.23161077819765769], [-1.7519787180125364, 0.0831977931735377, 0.32933969497530385], [-1.8411242633234892, 1.0218704453263638, 0.058063780632245154], [0.13877485179014193, -0.24592346892376238, 0.18187872535065014], [-5.500339097592422, 2.8094410003985737, 0.083029843543025], [-1.3944187245982154, -0.015553768610925722, 0.026388085967137764], [-3.691426877768652, 1.2760844736766612, 0.10317174983707483], [-1.7519801347627209, 0.527095207094588, 0.33974199149567474], [-1.7413433609164481, 0.10665526321733876, 0.21359153714174073], [0.2190001265796666, -0.2946964757350883, 0.1721933782094646], [-3.662001821813409, 1.4034320800992015, 0.05804090736537182], [-1.7519791519646448, 0.2403336148411539, 0.33413213487689486], [-3.5989031649929695, 1.4966841108354028, 0.04005537331660991], [-1.7193045358210275, -0.2440946162551927, 0.07058564243517806], [-1.740619997888506, 0.07658608527265676, 0.18467077645309496], [0.41495243288323436, -0.3775446093071655, 0.15602150913288781], [-1.7392995279309913, 0.02734542565901399, 0.1404534034047344], [-1.736893912257533, -0.04679254089676976, 0.083393470773657], [-3.4585016047882546, 1.2234745661453879, 0.17895614622497913], [-3.5776076229337006, 1.5232297965076795, 0.0364684490567419], [-3.653720543365619, 1.2338759669847168, 0.1311705918742838], [-1.7274484006793616, -0.2088850048094324, 0.02935740435058032], [-3.672329124723369, 1.2466629312545034, 0.12093290308313431], [-1.397779329257235, -0.01679785383198973, 0.026436410368584573]]\n",
      "new y = [[-2.71927478  2.22673454  0.07880665 -0.51927478 -0.08072522]]\n",
      "Found optimum y_opt = [[-5.65018072  3.30759414  0.09594656]\n",
      " [-3.41710161  1.6942399   0.0261306 ]\n",
      " [ 0.4168894  -0.37759866  0.15604856]\n",
      " [-1.75198192  0.80791257  0.34320377]\n",
      " [-4.37174903  2.20643111  0.1667294 ]\n",
      " [-5.24390905  2.62265365  0.1140461 ]\n",
      " [-1.74175307  0.12477717  0.23161078]\n",
      " [-1.75197872  0.08319779  0.32933969]\n",
      " [-1.84112426  1.02187045  0.05806378]\n",
      " [ 0.13877485 -0.24592347  0.18187873]\n",
      " [-5.5003391   2.809441    0.08302984]\n",
      " [-1.39441872 -0.01555377  0.02638809]\n",
      " [-3.69142688  1.27608447  0.10317175]\n",
      " [-1.75198013  0.52709521  0.33974199]\n",
      " [-1.74134336  0.10665526  0.21359154]\n",
      " [ 0.21900013 -0.29469648  0.17219338]\n",
      " [-3.66200182  1.40343208  0.05804091]\n",
      " [-1.75197915  0.24033361  0.33413213]\n",
      " [-3.59890316  1.49668411  0.04005537]\n",
      " [-1.71930454 -0.24409462  0.07058564]\n",
      " [-1.74062     0.07658609  0.18467078]\n",
      " [ 0.41495243 -0.37754461  0.15602151]\n",
      " [-1.73929953  0.02734543  0.1404534 ]\n",
      " [-1.73689391 -0.04679254  0.08339347]\n",
      " [-3.4585016   1.22347457  0.17895615]\n",
      " [-3.57760762  1.5232298   0.03646845]\n",
      " [-3.65372054  1.23387597  0.13117059]\n",
      " [-1.7274484  -0.208885    0.0293574 ]\n",
      " [-3.67232912  1.24666293  0.1209329 ]\n",
      " [-1.39777933 -0.01679785  0.02643641]] at x_opt = [[0.25989553 2.         3.        ]\n",
      " [0.3669908  1.         3.        ]\n",
      " [0.39904704 2.         0.        ]\n",
      " [0.48634397 3.         0.        ]\n",
      " [0.17822118 2.         3.        ]\n",
      " [0.20639588 2.         3.        ]\n",
      " [0.33343387 1.         0.        ]\n",
      " [0.40208393 3.         0.        ]\n",
      " [0.38320968 1.         2.        ]\n",
      " [0.37148281 2.         0.        ]\n",
      " [0.21771115 2.         3.        ]\n",
      " [0.36662238 1.         1.        ]\n",
      " [0.39531182 1.         3.        ]\n",
      " [0.46443322 3.         0.        ]\n",
      " [0.33490465 1.         0.        ]\n",
      " [0.37736588 2.         0.        ]\n",
      " [0.38320968 1.         3.        ]\n",
      " [0.43870781 3.         0.        ]\n",
      " [0.3771106  1.         3.        ]\n",
      " [0.3866406  1.         0.        ]\n",
      " [0.3374039  1.         0.        ]\n",
      " [0.39866907 2.         0.        ]\n",
      " [0.34168672 1.         0.        ]\n",
      " [0.34874999 1.         0.        ]\n",
      " [0.41908139 1.         3.        ]\n",
      " [0.37557669 1.         3.        ]\n",
      " [0.40275988 1.         3.        ]\n",
      " [0.371019   1.         0.        ]\n",
      " [0.39996568 1.         3.        ]\n",
      " [0.36616442 1.         1.        ]]\n"
     ]
    }
   ],
   "source": [
    "# criterion=\"WB2S\", \"EHVI\", \"MPI\", PI\"\n",
    "# If WB2S is chosen two other options: 'subcrit' has to be given\n",
    "# subcrit= \"EHVI\", \"MPI\", \"PI\", by default: \"EHVI\" is set\n",
    "# transfo=lambda x: np.sum(x): by default\n",
    "\n",
    "# options={\"n_clusters\": 1, \"n_start\": 10, \"criterion\": \"WB2S\", \"subcrit\": \"MPI\" , \"pop_size\": 30, \"n_gen\": 30, \"verbose\": True, \"debug\": True}\n",
    "options={\"n_clusters\": 1, \"verbose\": True, \"debug\": True}\n",
    "\n",
    "optim_options = MOOptimization(xtypes, n_obj=3, cstr_specs=cstr_specs, options=options)\n",
    "print(options)\n",
    "optim_options.tell_doe(xdoe, ydoe)\n",
    "x_opt, y_opt = optim_options.run(f_grouped, n_iter=5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "33be1394",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35\n"
     ]
    }
   ],
   "source": [
    "print(optim_options._id)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "303b5fe9",
   "metadata": {},
   "source": [
    "### Optimization with mixed variables: float, integer and categorical variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fd123e65",
   "metadata": {},
   "outputs": [],
   "source": [
    "from smt.applications.mixed_integer import MixedIntegerSamplingMethod\n",
    "from smt.sampling_methods import LHS\n",
    "import numpy as np\n",
    "from whatsopt.mooptimization import MOOptimization, FLOAT, INT, ENUM\n",
    "import time\n",
    "from smt.utils.design_space import (\n",
    "    CategoricalVariable,\n",
    "    DesignSpace,\n",
    "    FloatVariable,\n",
    "    IntegerVariable,\n",
    ")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "270057f0",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{array}{cl}\n",
    "    \\underset{x\\in \\mathbb{R}^3}{\\min} (f_1(x),f_2(x),f_3(x)) & \\\\\n",
    "    \\mbox{with} & f_1=x_0-x_1x_2 \\\\\n",
    "    & f_2= 4x_0^2 - 4x_0^{x_2} +1 + x_1\\\\\n",
    "    & f_3= x_0^2\\\\\n",
    "    \\mbox{s.t.} & g_1(x)=x_0-0.8 \\ge 0  \\\\\n",
    "    &  g_2(x) = 0.2-x_0 \\ge 0\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "Here \n",
    "- $x_0\\in [0,1] \\subset \\mathbb{R}$\n",
    "- $x_1$ is a integer $\\in \\{0,1,2,3\\}$  4 possibilities\n",
    "- $x_2$ is a categorical variable $\\in \\{\"blue\",\"red\",\"green\"\\}$ : 3 levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e1cf2459",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fun_mixed_color(x):#function with 3 objectives\n",
    "    if x[2]==\"blue\":\n",
    "        x2=0\n",
    "    elif x[2]==\"red\":\n",
    "        x2=1\n",
    "    elif x[2]==\"green\":\n",
    "        x2=2\n",
    "    f1 = x[0] -float(x[1])*x2\n",
    "    f2 = 4*x[0]**2 - 4*x[0]**x2 +1 + float(x[1])\n",
    "    f3= x[0]**2\n",
    "    return [f1,f2,f3]\n",
    "\n",
    "def g1(x):#constraint to force x < 0.8\n",
    "    return (x[0]-0.8, False)\n",
    "def g2(x):#constraint to force x > 0.2\n",
    "    return (0.2 - x[0], False)\n",
    "\n",
    "# To group functions relative to objective &  constraint \n",
    "def f_grouped(x):\n",
    "    #print('ds fgrouped',x)\n",
    "    resfun = fun_mixed_color(x)\n",
    "    resg1 = g1(x)[0]\n",
    "    resg2 = g2(x)[0]\n",
    "    #print(resfun, resg1,resg2)\n",
    "    res = np.hstack((resfun, resg1, resg2))\n",
    "    return res,False\n",
    "\n",
    "# Specifications for constraints \n",
    "cstr_specs = 2*[{\"type\": '<', \"bound\": 0.0}]\n",
    "\n",
    "# Definition of design variables \n",
    "xtypes_whatsopt = [{\"type\": FLOAT, \"limits\": [0.0, 1.0]},\n",
    "                   {\"type\": INT,  \"limits\": [0, 3]},\n",
    "                   {\"type\": ENUM,  \"limits\": [\"blue\",\"red\",\"green\"]}]\n",
    "\n",
    "design_space = DesignSpace(\n",
    "            [\n",
    "                FloatVariable(0.0, 1.0),\n",
    "                IntegerVariable(0, 3),\n",
    "                CategoricalVariable([\"blue\", \"red\", \"green\"]),\n",
    "            ]\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "66cb8af7",
   "metadata": {},
   "outputs": [],
   "source": [
    "options={\"n_clusters\": 1, \"criterion\": \"MPI\", \"pop_size\": 30, \"n_gen\": 30, \"verbose\": True, \"debug\": True}\n",
    "# options[\"mod_obj__type\"]       =\"MIXED\"\n",
    "# options[\"mod_obj__name\"]       =\"KPLS\"\n",
    "# options[\"mod_obj__n_comp\"]     = 2 # PLS components to reduce the initial dimension\n",
    "# options[\"mod_obj__eval_noise\"] = False\n",
    "# options[\"mod_obj__corr\"]       = \"squar_exp\" # correlation kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "267ff0d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "optim = MOOptimization(xtypes_whatsopt, cstr_specs=cstr_specs, n_obj=3,  options=options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "34980119",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial DOE\n",
      "xdoe=[[ 0.37454012  2.          0.        ]\n",
      " [ 0.95071431 -0.          1.        ]\n",
      " [ 0.73199394  1.          0.        ]\n",
      " [ 0.59865848  1.          2.        ]\n",
      " [ 0.15601864  1.          0.        ]\n",
      " [ 0.15599452  3.          1.        ]\n",
      " [ 0.05808361 -0.          0.        ]\n",
      " [ 0.86617615  2.          1.        ]\n",
      " [ 0.60111501  2.          1.        ]\n",
      " [ 0.70807258 -0.          0.        ]\n",
      " [ 0.02058449  2.          2.        ]\n",
      " [ 0.96990985 -0.          2.        ]\n",
      " [ 0.83244264 -0.          2.        ]\n",
      " [ 0.21233911  3.          2.        ]\n",
      " [ 0.18182497  3.          1.        ]\n",
      " [ 0.18340451  3.          2.        ]\n",
      " [ 0.30424224  1.          0.        ]\n",
      " [ 0.52475643 -0.          0.        ]\n",
      " [ 0.43194502  2.          0.        ]\n",
      " [ 0.29122914  1.          0.        ]]\n"
     ]
    }
   ],
   "source": [
    "sampling = MixedIntegerSamplingMethod(LHS, design_space=design_space, criterion=\"ese\")\n",
    "\n",
    "num = 20\n",
    "xdoe = sampling(num)\n",
    "print(\"Initial DOE\")\n",
    "print(\"xdoe={}\".format(xdoe))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c5448367",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.37454012 2.         0.        ]\n",
      " [0.95071431 0.         1.        ]\n",
      " [0.73199394 1.         0.        ]\n",
      " [0.59865848 1.         2.        ]\n",
      " [0.15601864 1.         0.        ]\n",
      " [0.15599452 3.         1.        ]\n",
      " [0.05808361 0.         0.        ]\n",
      " [0.86617615 2.         1.        ]\n",
      " [0.60111501 2.         1.        ]\n",
      " [0.70807258 0.         0.        ]\n",
      " [0.02058449 2.         2.        ]\n",
      " [0.96990985 0.         2.        ]\n",
      " [0.83244264 0.         2.        ]\n",
      " [0.21233911 3.         2.        ]\n",
      " [0.18182497 3.         1.        ]\n",
      " [0.18340451 3.         2.        ]\n",
      " [0.30424224 1.         0.        ]\n",
      " [0.52475643 0.         0.        ]\n",
      " [0.43194502 2.         0.        ]\n",
      " [0.29122914 1.         0.        ]]\n",
      "\n",
      "DOE with original  values - first elements - objectives \n",
      " [[0.3745401188473625, 2.0, 'blue'], [0.9507143064099162, 0.0, 'red'], [0.7319939418114051, 1.0, 'blue'], [0.5986584841970366, 1.0, 'green'], [0.15601864044243652, 1.0, 'blue']] \n",
      " [[ 0.37454012 -0.4388788   0.1402803  -0.42545988 -0.17454012]\n",
      " [ 0.95071431  0.81257354  0.90385769  0.15071431 -0.75071431]\n",
      " [ 0.73199394  0.14326052  0.53581513 -0.06800606 -0.53199394]\n",
      " [-1.40134152  2.          0.35839198 -0.20134152 -0.39865848]\n",
      " [ 0.15601864 -1.90263274  0.02434182 -0.64398136  0.04398136]]\n",
      "DOE to give to the WhatsOpt optimizer - first elements - obj & constraints \n",
      " [[0.37454012 2.         0.        ]\n",
      " [0.95071431 0.         1.        ]\n",
      " [0.73199394 1.         0.        ]\n",
      " [0.59865848 1.         2.        ]\n",
      " [0.15601864 1.         0.        ]] \n",
      " [[ 0.37454012 -0.4388788   0.1402803  -0.42545988 -0.17454012]\n",
      " [ 0.95071431  0.81257354  0.90385769  0.15071431 -0.75071431]\n",
      " [ 0.73199394  0.14326052  0.53581513 -0.06800606 -0.53199394]\n",
      " [-1.40134152  2.          0.35839198 -0.20134152 -0.39865848]\n",
      " [ 0.15601864 -1.90263274  0.02434182 -0.64398136  0.04398136]]\n"
     ]
    }
   ],
   "source": [
    "# To have the DOE with the original values (float, integer and categorical)\n",
    "\n",
    "xdoe_cat=design_space.correct_get_acting(xdoe)[0]\n",
    "print(xdoe_cat)\n",
    "print()\n",
    "ydoe= np.array([f_grouped(design_space.decode_values(xdoe_cat[i]))[0] for i in range(len(xdoe))])\n",
    "print('DOE with original  values - first elements - objectives \\n', design_space.decode_values(xdoe_cat[:5]),'\\n', ydoe[:5])\n",
    "print('DOE to give to the WhatsOpt optimizer - first elements - obj & constraints \\n', xdoe[:5],'\\n', ydoe[:5])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5aa80d2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "optim.tell_doe(xdoe, ydoe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "47788d3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 x suggested = [0.20000107614401472, 2.0, 1.0] with status: pending\n",
      "--- 19.20342516899109 seconds ---\n",
      "new y = [-1.79999892e+00  2.35999742e+00  4.00004305e-02 -5.99998924e-01\n",
      " -1.07614401e-06]\n",
      "1 x suggested = [0.5036664306421086, 1.0, 1.0] with status: pending\n",
      "--- 20.30583381652832 seconds ---\n",
      "new y = [-0.49633357  1.00005377  0.25367987 -0.29633357 -0.30366643]\n",
      "2 x suggested = [0.20000307247630156, 1.0, 2.0] with status: pending\n",
      "--- 20.318299531936646 seconds ---\n",
      "new y = [-1.79999693e+00  2.00000000e+00  4.00012290e-02 -5.99996928e-01\n",
      " -3.07247630e-06]\n",
      "3 x suggested = [0.20000077972656544, 1.0, 1.0] with status: pending\n",
      "--- 20.553574562072754 seconds ---\n",
      "new y = [-7.99999220e-01  1.35999813e+00  4.00003119e-02 -5.99999220e-01\n",
      " -7.79726565e-07]\n",
      "4 x suggested = [0.20059743999866006, 1.0, 1.0] with status: pending\n",
      "--- 25.09089684486389 seconds ---\n",
      "new y = [-7.99402560e-01  1.35856757e+00  4.02393329e-02 -5.99402560e-01\n",
      " -5.97439999e-04]\n",
      "5 x suggested = [0.20110865817082463, 1.0, 1.0] with status: pending\n",
      "--- 25.19495987892151 seconds ---\n",
      "new y = [-7.98891342e-01  1.35734414e+00  4.04446924e-02 -5.98891342e-01\n",
      " -1.10865817e-03]\n",
      "6 x suggested = [0.2010097775697046, 1.0, 1.0] with status: pending\n",
      "--- 25.28503441810608 seconds ---\n",
      "new y = [-7.98990222e-01  1.35758061e+00  4.04049307e-02 -5.98990222e-01\n",
      " -1.00977757e-03]\n",
      "7 x suggested = [0.20088727895647318, 1.0, 1.0] with status: pending\n",
      "--- 26.19409680366516 seconds ---\n",
      "new y = [-7.99112721e-01  1.35787368e+00  4.03556988e-02 -5.99112721e-01\n",
      " -8.87278956e-04]\n",
      "8 x suggested = [0.20093597825558004, 1.0, 1.0] with status: pending\n",
      "--- 25.364500045776367 seconds ---\n",
      "new y = [-7.99064022e-01  1.35775716e+00  4.03752674e-02 -5.99064022e-01\n",
      " -9.35978256e-04]\n",
      "9 x suggested = [0.20119202023570132, 1.0, 1.0] with status: pending\n",
      "--- 38.345492124557495 seconds ---\n",
      "new y = [-7.98807980e-01  1.35714484e+00  4.04782290e-02 -5.98807980e-01\n",
      " -1.19202024e-03]\n",
      "Found approx pareto y_opt = [[-5.785493231646436, 3.995174615018329, 0.04154490910110828], [-0.3585547668926772, 1.2503134527769595, 0.36560874609352023], [0.21120255224157558, -2.7327187772145924, 0.05605523016047001], [-2.794267306191608, 3.2940416007501527, 0.03670813541465437], [0.19695861926321945, -1.897326249575915, 0.04154490910110828], [-3.7913426146765508, 2.861427613222981, 0.04638168278756219], [-5.757005365689723, 3.9653391676026617, 0.05605523016047001], [-3.5634396870228495, 2.757003547268146, 0.19148489338117947], [-1.5265572711178956, 1.6978451640119654, 0.2108319881269951], [-0.3870426328493899, 1.265231176484793, 0.3124042355425272], [-2.8085112391699645, 3.3089593244579865, 0.03670813541465437], [-2.794267306191608, 3.2940416007501527, 0.03670813541465437], [-0.5579698285896657, 1.7127628877197991, 0.16730102494890992], [-0.4155304988061025, 1.2801489001926267, 0.28822036711025767], [-1.7971919977066657, 1.966364190752969, 0.05605523016047001], [-0.42977443178445884, 1.3099843476082937, 0.2591997249915342], [-3.6346593519146313, 2.786838994683813, 0.13344360914373254], [-1.7971919977066657, 1.966364190752969, 0.05605523016047001], [-1.6689966009014587, 1.7873515062589667, 0.10925974071146302], [-0.5437258956113094, 1.7276806114276324, 0.162464251262456], [-1.6405087349447462, 1.7575160588432994, 0.12860683545727863], [-0.45826229774117144, 1.4144084135631285, 0.22050553549990293], [-0.5009940966762405, 1.488997032102296, 0.19632166706763338], [-0.44401836476281514, 1.3696552424396278, 0.23501585655926466], [-0.45826229774117144, 1.3547375187317943, 0.2446894039321725], [-1.6974844668581714, 1.8022692299668002, 0.09474941965210129], [-3.720122949784769, 2.8017567183916467, 0.07540232490628565], [-0.5152380296545968, 1.5785033743492973, 0.18181134600827165], [-1.7259723328148842, 1.8321046773824672, 0.08023909859273956], [-1.6974844668581714, 1.8171869536746337, 0.08991264596564738]] at x_opt = [[0.20546292828247506, 3.0, 2.0], [0.5731336910217916, 1.0, 1.0], [0.18917603629988552, 0.0, 0.0], [0.21650515148250749, 3.0, 1.0], [0.21152232715077912, 1.0, 0.0], [0.2175262586864716, 2.0, 2.0], [0.2258649620343819, 3.0, 2.0], [0.4171590869418578, 2.0, 2.0], [0.4531018693409412, 1.0, 2.0], [0.5188029151655353, 1.0, 1.0], [0.21140641742568633, 3.0, 1.0], [0.21624955599056794, 3.0, 1.0], [0.20359732630737748, 1.0, 1.0], [0.4918390467047006, 1.0, 1.0], [0.19737501411731623, 1.0, 2.0], [0.45185783640905935, 1.0, 1.0], [0.3517863056335082, 2.0, 2.0], [0.19512412857110867, 1.0, 2.0], [0.3199143158980486, 1.0, 2.0], [0.1984548415483698, 1.0, 1.0], [0.35313600344821483, 1.0, 2.0], [0.37128096747346057, 1.0, 1.0], [0.31569537597878294, 1.0, 1.0], [0.4020004517295052, 1.0, 1.0], [0.42038910097193705, 1.0, 1.0], [0.29818215944427323, 1.0, 2.0], [0.27236707577487407, 2.0, 2.0], [0.27236707577487407, 1.0, 1.0], [0.2702649686296919, 1.0, 2.0], [0.28831121973982626, 1.0, 2.0]]\n"
     ]
    }
   ],
   "source": [
    "# We loop using the iteration budget\n",
    "n_iter = 10\n",
    "with_best=False\n",
    "for i in range(n_iter):\n",
    "    with_best = with_best or (i == n_iter - 1)\n",
    "    start_time = time.time()\n",
    "    x_suggested, status, x_opt, y_opt = optim.ask(with_best)\n",
    "    print(\"{} x suggested = {} with status: {}\".format(i, x_suggested, MOOptimization.STATUSES[status]))\n",
    "    print(\"--- %s seconds ---\" % (time.time() - start_time))\n",
    "    # compute objective functions & constraints  at the suggested point\n",
    "    new_y = f_grouped(design_space.decode_values(np.array(x_suggested)))[0]\n",
    "    print(\"new y = {}\".format(new_y))\n",
    "    \n",
    "    optim.tell(x_suggested, new_y)\n",
    "         \n",
    "print(\"Found approx pareto y_opt = {} at x_opt = {}\".format(y_opt, x_opt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "41aadbe1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_opt = np.array(x_opt)\n",
    "y_opt = np.array(y_opt)\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x_opt[:,0], x_opt[:,1], marker='x',label = 'approx BO')\n",
    "plt.xlabel('$x_0$')\n",
    "plt.ylabel('$x_1$')\n",
    "plt.legend()\n",
    "plt.title(\"design space\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x_opt[:,0], x_opt[:,2], marker='x',label = 'approx BO')\n",
    "plt.xlabel('$x_0$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.legend()\n",
    "plt.title(\"design space\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter( y_opt[:,0],  y_opt[:,1],marker='x', label = 'approx BO')\n",
    "plt.xlabel('f1')\n",
    "plt.ylabel('f2')\n",
    "plt.legend()\n",
    "plt.title(\"objective space\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01843728-6940-4d0f-81ec-a0b6f66ccf03",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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