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created CMA class that works for continuous functions in project 1 #5

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225 changes: 209 additions & 16 deletions project_1.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -20,16 +20,16 @@
},
{
"cell_type": "code",
"execution_count": 55,
"execution_count": 112,
"id": "9d9c91f7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best solution: [0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1\n",
" 1 0 1 0 1 1 0 1 1 1 1 0 1]\n",
"Best solution: [1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0\n",
" 1 0 1 0 1 0 1 1 1 0 1 0 1]\n",
"Total value: 309.0\n"
]
}
Expand Down Expand Up @@ -130,19 +130,27 @@
"print(\"Total value:\", best_value)\n"
]
},
{
"cell_type": "markdown",
"id": "f3e72e7b",
"metadata": {},
"source": [
"#### Knapsack CMA"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 113,
"id": "9be946a4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best solution (binary vector): [1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0\n",
"Best solution (binary vector): [0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0\n",
" 0 0 1 1 0 0 1 0 0 0 1 1 0]\n",
"Best total value: 73.0\n"
"Best total value: 70.0\n"
]
}
],
Expand Down Expand Up @@ -301,7 +309,7 @@
},
{
"cell_type": "code",
"execution_count": 57,
"execution_count": 114,
"id": "8a6129d6",
"metadata": {},
"outputs": [],
Expand All @@ -315,7 +323,7 @@
},
{
"cell_type": "code",
"execution_count": 58,
"execution_count": 115,
"id": "e75e2f25",
"metadata": {},
"outputs": [],
Expand All @@ -331,7 +339,7 @@
},
{
"cell_type": "code",
"execution_count": 59,
"execution_count": 116,
"id": "33adaa91",
"metadata": {},
"outputs": [],
Expand Down Expand Up @@ -378,15 +386,15 @@
},
{
"cell_type": "code",
"execution_count": 60,
"execution_count": 117,
"id": "8b4668c0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0\n"
"6.684735230633176e-14\n"
]
}
],
Expand Down Expand Up @@ -419,7 +427,7 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 118,
"id": "b948ed30",
"metadata": {},
"outputs": [],
Expand All @@ -433,7 +441,7 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 119,
"id": "1aa84235",
"metadata": {},
"outputs": [],
Expand All @@ -451,7 +459,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 120,
"id": "b19497d6",
"metadata": {},
"outputs": [],
Expand Down Expand Up @@ -499,7 +507,7 @@
},
{
"cell_type": "code",
"execution_count": 4,
"execution_count": 121,
"id": "4a91facf",
"metadata": {},
"outputs": [
Expand Down Expand Up @@ -529,10 +537,195 @@
"print(population[sorted_ind[0]], np.average(fitness(population)))"
]
},
{
"cell_type": "markdown",
"id": "dcc99684",
"metadata": {},
"source": [
"#### CMA (for all non-binary problems)"
]
},
{
"cell_type": "code",
"execution_count": 125,
"id": "443c16e6",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"class CMAES:\n",
" def __init__(self, n_dim, problem='parabola', \n",
" pop_size=None, mu=None, sigma=None, max_iter=500):\n",
" \"\"\"\n",
" CMA for continuous minimization problems.\n",
" Supports: 'parabola', 'ellipsoid', 'rastrigin'\n",
" \"\"\"\n",
" self.n = int(n_dim)\n",
" self.problem = problem\n",
"\n",
" # CMA-ES parameters\n",
" self.lam = pop_size if pop_size else 4 + int(3 * np.log(self.n + 1))\n",
" self.mu = mu if mu else self.lam // 2\n",
" self.sigma = sigma if sigma else 0.2\n",
" self.max_iter = max_iter\n",
"\n",
" # recombination weights\n",
" w = np.log(self.mu + 0.5) - np.log(np.arange(1, self.mu + 1))\n",
" self.weights = w / np.sum(w)\n",
" self.mueff = np.sum(self.weights)**2 / np.sum(self.weights**2)\n",
"\n",
" # initialization\n",
" self.mean = np.zeros(self.n)\n",
" self.C = np.identity(self.n)\n",
" self.pc = np.zeros(self.n)\n",
" self.ps = np.zeros(self.n)\n",
"\n",
" # constants\n",
" self.cc = (4 + self.mueff/self.n) / (self.n + 4 + 2*self.mueff/self.n)\n",
" self.cs = (self.mueff + 2) / (self.n + self.mueff + 5)\n",
" self.c1 = 2 / ((self.n + 1.3)**2 + self.mueff)\n",
" self.cmu = min(1 - self.c1,\n",
" 2*(self.mueff - 2 + 1/self.mueff) /\n",
" ((self.n + 2)**2 + self.mueff))\n",
" self.damps = 1 + 2*max(0, np.sqrt((self.mueff-1)/(self.n+1)) - 1) + self.cs\n",
"\n",
" # eigen decomposition\n",
" self.B = np.identity(self.n)\n",
" self.D = np.ones(self.n)\n",
" self.inv_sqrt_C = np.identity(self.n)\n",
" self.chiN = np.sqrt(self.n) * (1 - 1/(4*self.n) + 1/(21*self.n**2))\n",
"\n",
" self.history = []\n",
"\n",
" # Objective functions\n",
" def fitness(self, x):\n",
" \"\"\"Return f(x) for the current problem (minimization).\"\"\"\n",
" if self.problem == 'parabola':\n",
" return 10 * np.sum(x**2)\n",
"\n",
" elif self.problem == 'ellipsoid':\n",
" # Rotated hyper-ellipsoid\n",
" x1, x2 = x[0], x[1]\n",
" term1 = (np.sqrt(3)/2*(x1 - 3) + 0.5*(x2 - 5))**2\n",
" term2 = 5*((np.sqrt(3)/2*(x2 - 5) - 0.5*(x1 - 3)))**2\n",
" return term1 + term2\n",
"\n",
" elif self.problem == 'rastrigin':\n",
" d = len(x)\n",
" return 10*d + np.sum((x - 2)**2 - 10*np.cos(2*np.pi*(x - 2)))\n",
"\n",
" else:\n",
" raise ValueError(f\"Unknown problem '{self.problem}'\")\n",
"\n",
" \n",
" # Core CMA logic\n",
" def ask(self):\n",
" \"\"\"Generate new candidate population.\"\"\"\n",
" arz = np.random.randn(self.n, self.lam)\n",
" ary = self.B @ (self.D.reshape(-1, 1) * arz)\n",
" arx = self.mean.reshape(-1, 1) + self.sigma * ary\n",
" return arx.T, arz.T\n",
"\n",
" def run(self):\n",
" best_val = np.inf\n",
" best_x = None\n",
"\n",
" for gen in range(self.max_iter):\n",
" arx, arz = self.ask()\n",
" fits = np.array([self.fitness(x) for x in arx])\n",
" idx = np.argsort(fits)\n",
" arx, arz, fits = arx[idx], arz[idx], fits[idx]\n",
"\n",
" if fits[0] < best_val:\n",
" best_val = fits[0]\n",
" best_x = arx[0]\n",
"\n",
" xold = self.mean\n",
" self.mean = np.dot(self.weights, arx[:self.mu])\n",
" y = np.dot(self.weights, arz[:self.mu])\n",
"\n",
" # evolution paths\n",
" self.ps = (1 - self.cs)*self.ps + np.sqrt(self.cs*(2-self.cs)*self.mueff)*(self.B @ y)\n",
" hsig = int(\n",
" (np.linalg.norm(self.ps)/np.sqrt(1-(1-self.cs)**(2*(gen+1)))/self.chiN)\n",
" < (1.4 + 2/(self.n+1))\n",
" )\n",
" self.pc = (1 - self.cc)*self.pc + hsig*np.sqrt(self.cc*(2-self.cc)*self.mueff)*(self.B @ (self.D*y))\n",
"\n",
" # covariance update\n",
" artmp = (1/self.sigma)*(arx[:self.mu] - xold)\n",
" self.C = (1 - self.c1 - self.cmu)*self.C \\\n",
" + self.c1*(np.outer(self.pc, self.pc) + (1-hsig)*self.cc*(2-self.cc)*self.C) \\\n",
" + self.cmu*np.sum([w*np.outer(ar, ar)\n",
" for w, ar in zip(self.weights, artmp)], axis=0)\n",
"\n",
" # step size\n",
" self.sigma *= np.exp((self.cs/self.damps)*(np.linalg.norm(self.ps)/self.chiN - 1))\n",
"\n",
" # decomposition update\n",
" if gen % (self.n//10 + 1) == 0:\n",
" self.D, self.B = np.linalg.eigh(self.C)\n",
" self.D = np.sqrt(np.maximum(self.D, 1e-20))\n",
" self.inv_sqrt_C = self.B @ np.diag(self.D**-1) @ self.B.T\n",
"\n",
" self.history.append(best_val)\n",
"\n",
" # stop once essentially converged\n",
" if best_val < 1e-40:\n",
" break\n",
"\n",
" return best_x, best_val, self.history\n"
]
},
{
"cell_type": "code",
"execution_count": 126,
"id": "1bdb6c52",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best x: [-1.57456597e-21]\n",
"Best f(x)=10x²: 2.479258000512089e-41\n"
]
}
],
"source": [
"cma_para = CMAES(n_dim=1, problem='parabola', sigma=0.05, max_iter=1000)\n",
"best_x, best_val, hist = cma_para.run()\n",
"print(\"Best x:\", best_x)\n",
"print(\"Best f(x)=10x²:\", best_val)\n"
]
},
{
"cell_type": "code",
"execution_count": 127,
"id": "f0d4eba1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best x: [3. 5.]\n",
"Best f(x): 0.0\n"
]
}
],
"source": [
"cma_ellip = CMAES(n_dim=2, problem='ellipsoid', sigma=0.3, max_iter=600)\n",
"best_x, best_val, hist = cma_ellip.run()\n",
"print(\"Best x:\", best_x)\n",
"print(\"Best f(x):\", best_val)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e954d523",
"id": "6fa924ed",
"metadata": {},
"outputs": [],
"source": []
Expand Down