Portfolio_Optimization_With_Unconstraint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Portfolio Optimization With Unconstraint¶\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A tutorial for a portfolio optimization problem for n assets:\n",
    "\n",
    "$$\n",
    "\\min_{w\\in\\{0,1\\}^n}\\ qw^T \\Sigma w - R^T w\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver, QAOA, SamplingVQE\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from qiskit.result import QuasiDistribution\n",
    "from qiskit_aer.primitives import Sampler\n",
    "from qiskit_finance.applications.optimization import PortfolioOptimization\n",
    "from qiskit_finance.data_providers import RandomDataProvider\n",
    "from qiskit_optimization.algorithms import MinimumEigenOptimizer\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define problem instance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "生成数据，定义问题"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "n \\to num\\_assets\n",
    "\\\\\n",
    "R \\to R\n",
    "\\\\\n",
    "\\Sigma \\to Sigma\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set number of assets (= number of qubits)\n",
    "num_assets = 4\n",
    "seed = 123\n",
    "\n",
    "# Generate expected return and covariance matrix from (random) time-series\n",
    "stocks = [(\"TICKER%s\" % i) for i in range(num_assets)]\n",
    "data = RandomDataProvider(\n",
    "    tickers=stocks,\n",
    "    start=datetime.datetime(2021, 11, 17),\n",
    "    end=datetime.datetime(2022, 11, 17),\n",
    "    seed=seed,\n",
    ")\n",
    "data.run()\n",
    "\n",
    "R = data.get_period_return_mean_vector()\n",
    "Sigma = data.get_period_return_covariance_matrix()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "公式到代码的替换：\n",
    "$$\n",
    "q \\to q\n",
    "\\\\\n",
    "B \\to budget\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<QuadraticProgram: minimize 3.827312812733226e-05*x_0^2 + 2.589054469082886e-0..., 4 variables, 0 constraints, 'Portfolio optimization'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = 0.5  # set risk factor\n",
    "budget = num_assets // 2  # set budget\n",
    "\n",
    "portfolio = PortfolioOptimization(\n",
    "    expected_returns=R, covariances=Sigma, risk_factor=q, budget=budget\n",
    ")\n",
    "\n",
    "unconstraint_quadratic_problem = portfolio.to_quadratic_program()\n",
    "unconstraint_quadratic_problem.remove_linear_constraint(0)\n",
    "unconstraint_quadratic_problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "定义一个方法用于打印结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_result(result):\n",
    "    selection = result.x\n",
    "    value = result.fval\n",
    "    print(\"Optimal: selection {}, value {:.4f}\".format(selection, value))\n",
    "\n",
    "    eigenstate = result.min_eigen_solver_result.eigenstate\n",
    "    probabilities = (\n",
    "        eigenstate.binary_probabilities()\n",
    "        if isinstance(eigenstate, QuasiDistribution)\n",
    "        else {k: np.abs(v) ** 2 for k, v in eigenstate.to_dict().items()}\n",
    "    )\n",
    "    print(\"\\n----------------- Full result ---------------------\")\n",
    "    print(\"selection\\tvalue\\t\\tprobability\")\n",
    "    print(\"---------------------------------------------------\")\n",
    "    probabilities = sorted(probabilities.items(), key=lambda x: x[1], reverse=True)\n",
    "\n",
    "    for k, v in probabilities:\n",
    "        x = np.array([int(i) for i in list(reversed(k))])\n",
    "        value = portfolio.to_quadratic_program().objective.evaluate(x)\n",
    "        print(\"%10s\\t%.4f\\t\\t%.4f\" % (x, value, v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPyMinimumEigensolver (as a classical reference)¶\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们在这里首先考虑经典的解决方案。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们使用经典的NumPyMinimumEigensolver算法，来求解上述二次约束问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal: selection [1. 0. 1. 0.], value -0.0022\n",
      "\n",
      "----------------- Full result ---------------------\n",
      "selection\tvalue\t\tprobability\n",
      "---------------------------------------------------\n",
      " [1 0 1 0]\t-0.0022\t\t1.0000\n"
     ]
    }
   ],
   "source": [
    "exact_mes = NumPyMinimumEigensolver()\n",
    "exact_eigensolver = MinimumEigenOptimizer(exact_mes)\n",
    "\n",
    "result = exact_eigensolver.solve(unconstraint_quadratic_problem)\n",
    "\n",
    "print_result(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution using SamplingVQE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用VQE方法进行求解问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们现在可以使用采样变分量子特征求解器（SamplingVQE）来解决该问题。我们将指定要使用的优化器和变分形式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal: selection [1. 0. 1. 0.], value -0.0022\n",
      "\n",
      "----------------- Full result ---------------------\n",
      "selection\tvalue\t\tprobability\n",
      "---------------------------------------------------\n",
      " [1 0 1 0]\t-0.0022\t\t0.6602\n",
      " [1 0 1 1]\t-0.0018\t\t0.1660\n",
      " [0 0 1 1]\t-0.0013\t\t0.0967\n",
      " [1 1 0 0]\t0.0021\t\t0.0312\n",
      " [0 0 1 0]\t-0.0017\t\t0.0146\n",
      " [1 1 1 1]\t0.0008\t\t0.0117\n",
      " [0 1 1 0]\t0.0009\t\t0.0049\n",
      " [0 0 0 1]\t0.0004\t\t0.0049\n",
      " [0 0 0 0]\t0.0000\t\t0.0049\n",
      " [1 1 1 0]\t0.0004\t\t0.0029\n",
      " [1 0 0 0]\t-0.0005\t\t0.0010\n",
      " [1 1 0 1]\t0.0025\t\t0.0010\n"
     ]
    }
   ],
   "source": [
    "from qiskit.utils import algorithm_globals\n",
    "\n",
    "algorithm_globals.random_seed = 1234\n",
    "\n",
    "## 选择优化器，封装在qiskit.algorithms.optimizers中。\n",
    "cobyla = COBYLA()\n",
    "cobyla.set_options(maxiter=500)\n",
    "\n",
    "ry = TwoLocal(num_assets, \"ry\", \"cz\", reps=3, entanglement=\"full\")\n",
    "\n",
    "vqe_mes = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=cobyla)\n",
    "vqe = MinimumEigenOptimizer(vqe_mes)\n",
    "result = vqe.solve(unconstraint_quadratic_problem)\n",
    "\n",
    "print_result(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 2252.61x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ry.decompose().draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution using QAOA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们还在这里展示了使用量子近似优化算法（QAOA）的结果。这是另一种变分算法，它使用根据问题创建的内部变分形式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal: selection [1. 0. 1. 0.], value -0.0022\n",
      "\n",
      "----------------- Full result ---------------------\n",
      "selection\tvalue\t\tprobability\n",
      "---------------------------------------------------\n",
      " [0 0 0 1]\t0.0004\t\t0.0762\n",
      " [1 1 1 1]\t0.0008\t\t0.0742\n",
      " [0 1 0 0]\t0.0025\t\t0.0713\n",
      " [0 0 1 1]\t-0.0013\t\t0.0674\n",
      " [0 0 1 0]\t-0.0017\t\t0.0674\n",
      " [1 1 0 1]\t0.0025\t\t0.0625\n",
      " [1 0 0 1]\t-0.0001\t\t0.0615\n",
      " [1 1 0 0]\t0.0021\t\t0.0615\n",
      " [0 1 1 0]\t0.0009\t\t0.0605\n",
      " [0 1 0 1]\t0.0030\t\t0.0596\n",
      " [1 0 0 0]\t-0.0005\t\t0.0576\n",
      " [1 1 1 0]\t0.0004\t\t0.0576\n",
      " [1 0 1 1]\t-0.0018\t\t0.0576\n",
      " [0 0 0 0]\t0.0000\t\t0.0557\n",
      " [1 0 1 0]\t-0.0022\t\t0.0547\n",
      " [0 1 1 1]\t0.0013\t\t0.0547\n"
     ]
    }
   ],
   "source": [
    "algorithm_globals.random_seed = 1234\n",
    "\n",
    "## 选择优化器\n",
    "cobyla = COBYLA()\n",
    "cobyla.set_options(maxiter=250)\n",
    "\n",
    "## 构建QAOA电路，其中p为3.\n",
    "qaoa_mes = QAOA(sampler=Sampler(), optimizer=cobyla, reps=3)\n",
    "qaoa = MinimumEigenOptimizer(qaoa_mes)\n",
    "result = qaoa.solve(unconstraint_quadratic_problem)\n",
    "\n",
    "print_result(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2252.61x1956.5 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoa_mes.ansatz.decompose().draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### QAOA with GradientDescent Optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal: selection [1. 0. 1. 0.], value -0.0022\n",
      "\n",
      "----------------- Full result ---------------------\n",
      "selection\tvalue\t\tprobability\n",
      "---------------------------------------------------\n",
      " [0 1 1 0]\t0.0009\t\t0.1836\n",
      " [1 1 0 0]\t0.0021\t\t0.1729\n",
      " [0 1 0 1]\t0.0030\t\t0.1670\n",
      " [0 0 1 1]\t-0.0013\t\t0.1592\n",
      " [1 0 1 0]\t-0.0022\t\t0.1582\n",
      " [1 0 0 1]\t-0.0001\t\t0.1494\n",
      " [1 1 0 1]\t0.0025\t\t0.0039\n",
      " [0 0 0 1]\t0.0004\t\t0.0029\n",
      " [1 0 1 1]\t-0.0018\t\t0.0010\n",
      " [0 1 0 0]\t0.0025\t\t0.0010\n",
      " [0 0 0 0]\t0.0000\t\t0.0010\n"
     ]
    }
   ],
   "source": [
    "from qiskit.algorithms.optimizers import  GradientDescent\n",
    "\n",
    "result_g = MinimumEigenOptimizer(QAOA(Sampler(), GradientDescent(),reps=3)).solve(\n",
    "    qp\n",
    ")\n",
    "print_result(result_g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPyMinimumEigensolver aver running time 0.03235528469085693 s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "s = time.time()\n",
    "for i in range(10):\n",
    "    result = exact_eigensolver.solve(unconstraint_quadratic_problem)\n",
    "e = time.time()\n",
    "aver_time = (e-s)/10\n",
    "print(\"NumPyMinimumEigensolver aver running time\", aver_time ,\"s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vqe with COBYLA aver running time 1.4146004676818849 s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "s = time.time()\n",
    "for i in range(10):\n",
    "    result = vqe.solve(unconstraint_quadratic_problem)\n",
    "e = time.time()\n",
    "aver_time = (e-s)/10\n",
    "print(\"vqe with COBYLA aver running time\", aver_time ,\"s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qaoa with COBYLA aver running time 1.4639244318008422 s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "s = time.time()\n",
    "for i in range(10):\n",
    "    result = qaoa.solve(unconstraint_quadratic_problem)\n",
    "e = time.time()\n",
    "aver_time = (e-s)/10\n",
    "print(\"qaoa with COBYLA aver running time\", aver_time ,\"s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qaoa with GradientDescent aver running time 11.414355969429016 s\n"
     ]
    }
   ],
   "source": [
    "qaoa_g = MinimumEigenOptimizer(QAOA(Sampler(), GradientDescent(),reps=3))\n",
    "import time\n",
    "s = time.time()\n",
    "for i in range(10):\n",
    "    result = qaoa_g.solve(unconstraint_quadratic_problem)\n",
    "e = time.time()\n",
    "aver_time = (e-s)/10\n",
    "print(\"qaoa with GradientDescent aver running time\", aver_time ,\"s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TwoLocal+PSO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[TwoLocal](https://qiskit.org/documentation/stubs/qiskit.circuit.library.TwoLocal.html#qiskit.circuit.library.TwoLocal)是一个参数化电路模板。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import BasicAer, execute\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from sko.PSO import PSO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "生成量子电路"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1792.5x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameterized_qc = TwoLocal(4, \"ry\", \"cx\")\n",
    "parameterized_qc.decompose().draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "exact_qc = parameterized_qc.bind_parameters(\n",
    "    list(range(parameterized_qc.num_parameters))\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "构建目标函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x1, x2, x3, x4):\n",
    "    return qp.objective.evaluate([x1,x2,x3,x4])\n",
    "\n",
    "\n",
    "def obj_func(params):\n",
    "    exact_qc = parameterized_qc.bind_parameters(params)\n",
    "    exact_qc.measure_all()\n",
    "    counts = (\n",
    "        execute(exact_qc, BasicAer.get_backend(\"qasm_simulator\"), shots=1000)\n",
    "        .result()\n",
    "        .get_counts()\n",
    "    )\n",
    "    counts = sorted(counts.items(), key=lambda x: x[1], reverse=True)\n",
    "    # print(\"input [x1,x2,x3,x4] is: \",list(map(int, list(counts[0][0]))))\n",
    "    return f(*list(map(int, list(counts[0][0]))))\n",
    "\n",
    "def get_x(params):\n",
    "    exact_qc = parameterized_qc.bind_parameters(params)\n",
    "    exact_qc.measure_all()\n",
    "    counts = (\n",
    "        execute(exact_qc, BasicAer.get_backend(\"qasm_simulator\"), shots=1000)\n",
    "        .result()\n",
    "        .get_counts()\n",
    "    )\n",
    "    counts = sorted(counts.items(), key=lambda x: x[1], reverse=True)\n",
    "    return list(map(int, list(counts[0][0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run pso to get iter\tgbest\n",
      "best x is:  1\t[1, 0, 0, 1]\n",
      "min object function value is: 1\t[-0.00011729]\n",
      "best x is:  2\t[1, 0, 0, 1]\n",
      "min object function value is: 2\t[-0.00011729]\n",
      "best x is:  3\t[0, 0, 1, 0]\n",
      "min object function value is: 3\t[-0.00171637]\n",
      "best x is:  4\t[1, 0, 1, 0]\n",
      "min object function value is: 4\t[-0.00219702]\n",
      "best x is:  5\t[1, 0, 1, 0]\n",
      "min object function value is: 5\t[-0.00219702]\n",
      "best x is:  6\t[1, 0, 1, 0]\n",
      "min object function value is: 6\t[-0.00219702]\n",
      "best x is:  7\t[1, 0, 1, 0]\n",
      "min object function value is: 7\t[-0.00219702]\n",
      "best x is:  8\t[1, 0, 1, 0]\n",
      "min object function value is: 8\t[-0.00219702]\n",
      "best x is:  9\t[1, 0, 1, 0]\n",
      "min object function value is: 9\t[-0.00219702]\n",
      "best x is:  10\t[1, 0, 1, 0]\n",
      "min object function value is: 10\t[-0.00219702]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def run_pso(pso, iter, is_print):\n",
    "    print(\"run pso to get iter\\tgbest\")\n",
    "    for i in range(iter):\n",
    "        pso.run(1)\n",
    "        if is_print:\n",
    "            print(\"best x is: \",f\"{i+1}\\t{get_x(pso.gbest_x)}\")\n",
    "            print(\"min object function value is: \"f\"{i+1}\\t{pso.gbest_y}\")\n",
    "\n",
    "lb = [-np.pi]*parameterized_qc.num_parameters\n",
    "ub = [np.pi]*parameterized_qc.num_parameters\n",
    "\n",
    "pso = PSO(obj_func, parameterized_qc.num_parameters, pop=4, lb=lb, ub=ub)\n",
    "\n",
    "\n",
    "run_pso(pso,10,is_print=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "get time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "run pso to get iter\tgbest\n",
      "pso aver running time 1.3228692531585693 s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "s = time.time()\n",
    "for i in range(10):\n",
    "    result = run_pso(pso,10,is_print=False)\n",
    "e = time.time()\n",
    "aver_time = (e-s)/10\n",
    "print(\"pso aver running time\", aver_time ,\"s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TwoLocal+DE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run de to get iter\tgbest\n",
      "best x is:  1\t[1, 0, 1, 1]\n",
      "min object function value is: 1\t[-0.00183219]\n",
      "best x is:  2\t[1, 0, 1, 1]\n",
      "min object function value is: 2\t[0.00208871]\n",
      "best x is:  3\t[1, 0, 1, 0]\n",
      "min object function value is: 3\t[-0.00219702]\n",
      "best x is:  4\t[0, 0, 1, 0]\n",
      "min object function value is: 4\t[-0.00219702]\n",
      "best x is:  5\t[1, 0, 1, 0]\n",
      "min object function value is: 5\t[-0.00219702]\n",
      "best x is:  6\t[1, 0, 1, 0]\n",
      "min object function value is: 6\t[-0.00219702]\n",
      "best x is:  7\t[1, 0, 1, 0]\n",
      "min object function value is: 7\t[-0.00219702]\n",
      "best x is:  8\t[1, 0, 1, 0]\n",
      "min object function value is: 8\t[-0.00171637]\n",
      "best x is:  9\t[1, 0, 1, 0]\n",
      "min object function value is: 9\t[-0.00219702]\n",
      "best x is:  10\t[1, 0, 1, 0]\n",
      "min object function value is: 10\t[-0.00219702]\n"
     ]
    }
   ],
   "source": [
    "lb = [-np.pi]*parameterized_qc.num_parameters\n",
    "ub = [np.pi]*parameterized_qc.num_parameters\n",
    "\n",
    "\n",
    "\n",
    "#pso = PSO(obj_func, parameterized_qc.num_parameters, pop=4, lb=lb, ub=ub)\n",
    "from sko.DE import DE\n",
    "\n",
    "de = DE(obj_func, parameterized_qc.num_parameters, size_pop=4, lb=lb, ub=ub)\n",
    "\n",
    "\n",
    "def run_de(de, iter, is_print):\n",
    "    print(\"run de to get iter\\tgbest\")\n",
    "    for i in range(iter):\n",
    "        best_x, best_y = de.run(1)\n",
    "        if is_print:\n",
    "            print(\"best x is: \",f\"{i+1}\\t{get_x(best_x)}\")\n",
    "            print(\"min object function value is: \"f\"{i+1}\\t{best_y}\")\n",
    "run_de(de, 10, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "get time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "run de to get iter\tgbest\n",
      "de aver running time 3.1078768968582153 s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "s = time.time()\n",
    "for i in range(10):\n",
    "    result = run_de(de,10,is_print=False)\n",
    "e = time.time()\n",
    "aver_time = (e-s)/10\n",
    "print(\"de aver running time\", aver_time ,\"s\")"
   ]
  }
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