Experiment with the ability to modify a constraint of an existing optimization problem modeled with JuMP

JuMP modify constraint.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Modification of optimization constraints\n",
    "\n",
    "Experiment with the ability to modify a constraint of an existing optimization problem modeled with JuMP.\n",
    "\n",
    "discussion on forum: https://discourse.julialang.org/t/modify-equality-constraints-in-jump/\n",
    "\n",
    "JuMP 0.18 doc: http://www.juliaopt.org/JuMP.jl/0.18/probmod.html#modifying-constraints\n",
    "\n",
    "The doc says only the RHS of *inequalities* can be change, but @odow on the forum suggests that it may work also for equalities. Here is a test.\n",
    "\n",
    "→ seems to work indeed!\n",
    "\n",
    "PH, May 2018"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "v\"0.6.2\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VERSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using JuMP\n",
    "using Clp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "v\"0.18.0\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pkg.installed(\"JuMP\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create model, with 2 variables in the [0,1]² box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":Optimal"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Model(solver = ClpSolver())\n",
    "\n",
    "# two variables\n",
    "@variable(m, 0 <= x <= 1)\n",
    "@variable(m, 0 <= y <= 1)\n",
    "\n",
    "# equality constraint\n",
    "@constraint(m, mycon, x + y == 1.5)\n",
    "\n",
    "@objective(m, Max, y)\n",
    "\n",
    "solve(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5, 1.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getvalue(x), getvalue(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ x + y = 1.5 $$"
      ],
      "text/plain": [
       "x + y = 1.5"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mycon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modify the equality constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ x + y = 0.5 $$"
      ],
      "text/plain": [
       "x + y = 0.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JuMP.setRHS(mycon, 0.5)\n",
    "mycon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[33mWARNING: \u001b[39m\u001b[22m\u001b[33mSolver does not appear to support providing initial feasible solutions.\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       ":Optimal"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.5)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getvalue(x), getvalue(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TODO: performance analysis, comparing the two options:\n",
    "\n",
    "* generate the model from scratch, and then solve\n",
    "* modify the preexisting model, and then solve\n",
    "\n",
    "(probably the result would depend on the solver's abilities for warm starts)"
   ]
  }
 ],
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