Starcraft 0 - Relaxação contínua .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cvxpy as cvx\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ao invés de contruirmos um trabalhador inteiro a cada N segundos(leia-se turnos), estaremos contínuamente construindo uma quantidade de trabalhador ϵ, capaz de ϵ-minerar e ϵ-construir.\n",
    "### As ϵ-construções são capazes de ϵ-treinar ϵ-unidades."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dessa forma, em cada turno, só precisamos gerir os Recursos, Unidades e Estruturas como se fossem grandezas contínuas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $F_{obj}$ = max |Exército|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Structures = cvx.Variable(1)\n",
    "Builders   = cvx.Variable(1)\n",
    "Gatherers  = cvx.Variable(1)\n",
    "Army       = cvx.Variable(1)\n",
    "Resources  = cvx.Variable(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_obj = cvx.Maximize(Army)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Restrito a: Tempo, Supply, Dinheiro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_s = 2 # produão de exercito por estrutura\n",
    "w_s = 5 # produção de builder por estrutura\n",
    "\n",
    "c_a = 5 # custo do exercito\n",
    "c_w = 2 # custo dos builders\n",
    "c_g = 2 # custo dos gatherers\n",
    "\n",
    "s_r = -9 # recursos por estruras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_r = 3  # produção de recursos por gatherer\n",
    "b_c = -10 # gasto dos builders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_b = 1 # produção de estrutura por builder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_lim = 20\n",
    "t = t_lim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, R, S):\n",
    "    return S*a_s - c_a*R\n",
    "\n",
    "def g(t, G, B, S):\n",
    "    return t*(p_r*G + s_r*S + b_c*B)\n",
    "\n",
    "def h(t, S, R):\n",
    "    return t*(w_s*S - c_w*R)\n",
    "\n",
    "def i(t, S, R):\n",
    "    return h(t, S, R)\n",
    "\n",
    "def j(t, B, R):\n",
    "    return t*(s_b*B - R*s_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraints = [Army == f(t, Resources, Structures), \n",
    "               Resources == g(t, Gatherers, Builders, Structures), \n",
    "               Gatherers == h(t, Structures, Resources),\n",
    "               Builders  == i(t, Structures, Resources),\n",
    "               Structures == j(t, Builders, Resources),\n",
    "              ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $State = [Recursos, Estruturas, Unidades]^T$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### State[i] = [Recursos_i, Estruturas_i, Unidades_i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problema iterativo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "S - Estruturas  \n",
    "R - Recursos  \n",
    "U - Unidades  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$U = U_1 + U_2 + U_3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Max_supply = cvx.Variable(1)\n",
    "Supply     = cvx.Variable(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### As equações:\n",
    "\n",
    "$ \\partial U_2 = C \\partial R $, $\\partial U_1 = D \\partial S $, $ \\partial R = E \\partial S$  \n",
    "$ \\partial S = F \\partial A$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Decomposição das variáveis:\n",
    "\n",
    "$U = U_1 + U_2$  # bulding e gthering  \n",
    "$S = S_1 + S_2$  # army trainer e worker trainer  \n",
    "$R = R_1 + R_2$  # dinheiros  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cvx.constraints = [Max_supply >= Supply, Supply == sum(Workers) + Army, Resources >= 0, Workers >= 0, Army >= 0, Structures >= 1, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cvx.constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problema bazuka"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cvx\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "Buildings  = cvx.Variable(3)\n",
    "Gatherers  = cvx.Variable(3)\n",
    "Builders   = cvx.Variable(3)\n",
    "Army       = cvx.Variable(3)\n",
    "Resources  = cvx.Variable(3)\n",
    "Max_supply = cvx.Variable(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 2 # buildings costs\n",
    "c2 = 1 # units costs\n",
    "k  = 3 # supply per structure\n",
    "\n",
    "o = 2 # pessoinhas por casinhas\n",
    "q = 2 # resources gathered per gatherer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Obj = cvx.Maximize(Army[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = cvx.Variable(2)\n",
    "G = cvx.Variable(2)\n",
    "Br = cvx.Variable(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0 = cvx.Parameter(1)\n",
    "g0 = cvx.Parameter(1)\n",
    "br0 = cvx.Parameter(1)\n",
    "a0 = cvx.Parameter(1)\n",
    "r0 = cvx.Parameter(1)\n",
    "ms0 = cvx.Parameter(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0.value = 2       # starting buildings\n",
    "g0.value = 2       # starting gatherers\n",
    "br0.value = 2      # starting builders\n",
    "a0.value = 4       # starting army\n",
    "r0.value = 2       # starting resources\n",
    "ms0.value = 2      # starting maximum supply"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Na mão para 2 estágios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "Constraints1 = [B[0] == Buildings[1] - Buildings[0],\n",
    "              B[0] >= 0,\n",
    "              G[0] == Gatherers[1] - Gatherers[0],\n",
    "              G[0] >= 0,\n",
    "              Br[0] == Builders[1] - Builders[0],\n",
    "              Br[0]>= 0,\n",
    "              \n",
    "             \n",
    "               \n",
    "              Army[1]       == Builders[1] + Gatherers[1],\n",
    "              Army[1] - Army[0] <= o*Buildings[0], \n",
    "              Max_supply[1] == Buildings[1]*k,\n",
    "              Army[1] <= Max_supply[1],\n",
    "              Resources[1] == Resources[0] + q*Gatherers[0] - c1*B[0] - c2*G[0] - c2*Br[0],\n",
    "              Resources[1] >= 0,\n",
    "               \n",
    "              B[0+1] == Buildings[1+1] - Buildings[0+1],\n",
    "              B[0+1] >= 0,\n",
    "              G[0+1] == Gatherers[1+1] - Gatherers[0+1],\n",
    "              G[0+1] >= 0,\n",
    "              Br[0+1] == Builders[1+1] - Builders[0+1],\n",
    "              Br[0+1]>= 0,\n",
    "              \n",
    "             \n",
    "               \n",
    "              Army[1+1]       == Builders[1+1] + Gatherers[1+1],\n",
    "              Army[1+1] - Army[0+1] <= o*Buildings[0+1], \n",
    "              Max_supply[1+1] == Buildings[1+1]*k,\n",
    "              Army[1+1] <= Max_supply[1+1],\n",
    "              Resources[1+1] == Resources[0+1] + q*Gatherers[1] - c1*B[0+1] - c2*G[0+1] - c2*Br[0+1],\n",
    "              Resources[2] >= 0,\n",
    "               \n",
    "             # Stage 0\n",
    "              Buildings[0] == b0,\n",
    "              Gatherers[0] == g0,\n",
    "              Builders[0]  == br0,\n",
    "              Army[0]      == a0,\n",
    "              Resources[0] == r0,\n",
    "              Max_supply[0]== ms0,\n",
    "              ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Com um for"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "Constraints2 = [Buildings[0] == b0,\n",
    "              Gatherers[0] == g0,\n",
    "              Builders[0]  == br0,\n",
    "              Army[0]      == a0,\n",
    "              Resources[0] == r0,\n",
    "              Max_supply[0]== ms0,\n",
    "              B >= 0,\n",
    "              G >= 0,\n",
    "              Br>= 0]\n",
    "\n",
    "for i in range(T-1):\n",
    "    Constraints.append(B[i]  == Buildings[i+1] - Buildings[i])\n",
    "    Constraints.append(Buildings[i+1] == Buildings[i] + c*Builders[i])\n",
    "    Constraints.append(G[i]  == Gatherers[i+1] - Gatherers[i])\n",
    "    Constraints.append(Br[i] == Builders[i+1]  - Builders[i])\n",
    "#    Constraints.append(c1*B[i] + c2*G[i] + c2*Br[i] <= Resources[i])\n",
    "    Constraints.append(Army[i+1] == Builders[i+1] + Gatherers[i+1])\n",
    "    Constraints.append(Army[i+1] - Army[i] <= o*Buildings[i])\n",
    "    Constraints.append(Army[i+1] <= Max_supply[i+1])\n",
    "    Constraints.append(Max_supply[i+1] == Buildings[i+1]*k)\n",
    "    Constraints.append(Resources[i+1] == Resources[i] + q*Gatherers[i] - c1*B[i] - c2*G[i] - c2*Br[i])\n",
    "    Constraints.append(Resources[i+1] >= 0)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forma Vetorizada"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "Constraints = [B == Buildings[1:] - Buildings[:-1],\n",
    "              B >= 0,\n",
    "              G == Gatherers[1:] - Gatherers[:-1],\n",
    "              G >= 0,\n",
    "              Br == Builders[1:] - Builders[:-1],\n",
    "              Br>= 0,\n",
    "#              c1*B + c2*G + c2*Br <= Resources[:-1],\n",
    "               \n",
    "              Army       == Builders + Gatherers,\n",
    "              Army[1:] - Army[:-1] <= o*Buildings[:-1], \n",
    "              Max_supply == Buildings*k,\n",
    "               \n",
    "              Resources[1:] == Resources[:-1] + q*Gatherers[1:] - c1*B[:-1] - c2*G[:-1] - c2*Br[:-1],\n",
    "               \n",
    "               \n",
    "             # Stage 0\n",
    "              Buildings[0] == b0,\n",
    "              Gatherers[0] == g0,\n",
    "              Builders[0]  == br0,\n",
    "              Army[0]      == a0,\n",
    "              Resources[0] == r0,\n",
    "              Max_supply[0]== ms0,\n",
    "              ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem = cvx.Problem(F_Obj, Constraints1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.999999992420967"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2.        ],\n",
       "        [3.09909281],\n",
       "        [4.79537313]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Buildings.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2.        ],\n",
       "        [5.0885311 ],\n",
       "        [8.18760585]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gatherers.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2.        ],\n",
       "        [2.71328327],\n",
       "        [5.81239414]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Builders.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 4.        ],\n",
       "        [ 7.80181437],\n",
       "        [13.99999999]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Army.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2.00000000e+00],\n",
       "        [5.86803774e-09],\n",
       "        [5.86315957e-01]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Resources.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 2.        ],\n",
       "        [ 9.29727843],\n",
       "        [14.38611938]])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Max_supply.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "var1631[0, 0] == param1640\n",
      "var1632[0, 0] == param1641\n"
     ]
    }
   ],
   "source": [
    "for i in problem.constraints:\n",
    "    if i.dual_value > 1:\n",
    "        print(i)\n",
    "    #print(i.dual_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Um problema de T estágios"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cvx\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [],
   "source": [
    "Buildings  = cvx.Variable(T)\n",
    "Gatherers  = cvx.Variable(T)\n",
    "Builders   = cvx.Variable(T)\n",
    "Army       = cvx.Variable(T)\n",
    "Resources  = cvx.Variable(T)\n",
    "Max_supply = cvx.Variable(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [],
   "source": [
    "custo_building      = 2 # buildings costs                         recurso/casinha\n",
    "custo_units         = 1 # units costs                             recurso/pessoinha\n",
    "supply_building     = 3 # supply per structure                    caminha/casinha\n",
    "army_building       = 2 # army trained per house                   pessoinhas/casinha\n",
    "building_builder    = 1 # buildings constructed per builder       casinhas/pessoinha1\n",
    "production_gatherer = 2 # resources gathered per gatherer          recursos/pessoinha2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 495,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Obj = cvx.Maximize(Army[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = cvx.Variable(T-1)\n",
    "G = cvx.Variable(T-1)\n",
    "Br = cvx.Variable(T-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0 = cvx.Parameter(1)\n",
    "g0 = cvx.Parameter(1)\n",
    "br0 = cvx.Parameter(1)\n",
    "r0 = cvx.Parameter(1)\n",
    "ms0 = cvx.Parameter(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0.value  = 1       # starting buildings\n",
    "g0.value  = 1       # starting gatherers\n",
    "br0.value = 0       # starting builders\n",
    "r0.value  = 0       # starting resources\n",
    "ms0.value = 2       # starting maximum supply"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {},
   "outputs": [],
   "source": [
    "Constraints = [Buildings[0] == b0,\n",
    "              Gatherers[0] == g0,\n",
    "              Builders[0]  == br0,\n",
    "              Army[0]      == g0 + br0,\n",
    "              Resources[0] == r0,\n",
    "              B >= 0,\n",
    "              G >= 0,\n",
    "              Br>= 0]\n",
    "\n",
    "for i in range(T-1):\n",
    "    \n",
    "    Constraints.append(B[i]  == Buildings[i+1] - Buildings[i])\n",
    "    Constraints.append(Br[i] == Builders[i+1]  - Builders[i])\n",
    "    Constraints.append(G[i]  == Gatherers[i+1] - Gatherers[i])\n",
    "    \n",
    "    Constraints.append(B[i] <= building_builder*Builders[i])\n",
    "    Constraints.append(Br[i] + G[i] <= army_building*Buildings[i])\n",
    "    \n",
    "    Constraints.append(Army[i+1]           == Builders[i+1] + Gatherers[i+1])\n",
    "    Constraints.append(Army[i+1]           <= Buildings[i+1]*supply_building)\n",
    "    \n",
    "    Constraints.append(Resources[i+1] == Resources[i]\n",
    "                       + production_gatherer*Gatherers[i]\n",
    "                       - custo_building*B[i] - custo_units*(G[i] + Br[i]))    \n",
    "    Constraints.append(Resources[i+1] >= 0)\n",
    "    Constraints.append(Resources[i]   >= custo_building*B[i] + custo_units*(G[i] + Br[i]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem = cvx.Problem(F_Obj, Constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 62.8 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.4000000010758267"
      ]
     },
     "execution_count": 501,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time problem.solve(solver='ECOS') #SCS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Buildings.value,'--*', label='buildings')\n",
    "\n",
    "plt.plot(Gatherers.value,'o--', label='gath')\n",
    "plt.plot(Builders.value, label='builders')\n",
    "#plt.plot(Army.value, label='')\n",
    "plt.plot(Resources.value, label='resources')\n",
    "#plt.plot(Max_supply.value, label='')\n",
    "#plt.plot(B.value, label='')\n",
    "#plt.plot(G.value, label='')\n",
    "\n",
    "plt.yscale('symlog')\n",
    "plt.grid()\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}