{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "f6f9557f", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:49.973796Z", "iopub.status.busy": "2026-10-02T14:41:49.973502Z", "iopub.status.idle": "2026-10-02T14:41:49.978433Z", "shell.execute_reply": "2026-10-02T14:41:49.977675Z" }, "papermill": { "duration": 0.008409, "end_time": "2026-10-02T14:41:49.979398+00:00", "exception": false, "start_time": "2026-10-02T14:41:49.970989+00:00", "status": "completed" }, "tags": [ "remove-input", "active-ipynb", "remove-output" ] }, "outputs": [], "source": [ "try:\n", " from openmdao.utils.notebook_utils import notebook_mode # noqa: F401\n", "except ImportError:\n", " !python -m pip install openmdao[notebooks]" ] }, { "cell_type": "markdown", "id": "66ec00db", "metadata": { "papermill": { "duration": 0.001276, "end_time": "2026-10-02T14:41:49.982143+00:00", "exception": false, "start_time": "2026-10-02T14:41:49.980867+00:00", "status": "completed" }, "tags": [] }, "source": [ "# DifferentialEvolutionDriver\n", "\n", "```{note}\n", "DifferentialEvolutionDriver is based on SimpleGADriver and supports most of the same options and capabilities.\n", "```\n", "\n", "This [differential evolution](https://en.wikipedia.org/wiki/Differential_evolution) variant of a genetic algorithm optimizer supports only continuous variables. The DifferentialEvolutionDriver supports both constrained and unconstrained optimization.\n", "\n", "The DifferentialEvolutionDriver has advantages and disadvantages when compared to the SimpleGADriver:\n", "\n", " - Pros\n", " - DifferentialEvolutionDriver is typically about 3 times faster than SimpleGADriver\n", " - DifferentialEvolutionDriver is usually more accurate than SimpleGADriver because it does not limit the number of bits available to represent inputs\n", " - DifferentialEvolutionDriver does not require the user to manually specify a number of representation bits\n", "\n", " - Cons\n", " - DifferentialEvolutionDriver only supports continuous input variables; SimpleGADriver also supports discrete\n", " - DifferentialEvolutionDriver does not support SimpleGADriver’s “compute_pareto” option for multi-objective optimization\n", "\n", "Genetic algorithms do not use gradient information to find optimal solutions. This makes them ideal for problems that do not have gradients or problems with many local minima where gradient information is not helpful in finding the global minimum. A well known example of this is finding the global minimum of of the Rastrigin function: ![2D Rastrigin Example](rastrigin2d.png)\n", "\n", "The example below shows an OpenMDAO solution of a higher order [Rastrigin function](https://en.wikipedia.org/wiki/Rastrigin_function)." ] }, { "cell_type": "code", "execution_count": 2, "id": "a3109f11", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:49.985593Z", "iopub.status.busy": "2026-10-02T14:41:49.985411Z", "iopub.status.idle": "2026-10-02T14:42:04.122333Z", "shell.execute_reply": "2026-10-02T14:42:04.121322Z" }, "papermill": { "duration": 14.13951, "end_time": "2026-10-02T14:42:04.123009+00:00", "exception": false, "start_time": "2026-10-02T14:41:49.983499+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952112.547304] [runnervm8df0l:6879 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x5588ab0b2000 failed to create UD QP TX wr:256 sge:6 inl:64 resp:0 RX wr:4096 sge:1 resp:0 failed: Operation not supported\n", "[1790952112.547549] [runnervm8df0l:6879 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:06879] pml_ucx.c:313 Error: Failed to create UCP worker\n", "/home/runner/work/OpenMDAO/OpenMDAO/.pixi/envs/dev/lib/python3.13/site-packages/openmdao/drivers/differential_evolution_driver.py:100: OMDeprecationWarning:The `DifferentialEvolutionDriver` is deprecated. Please use `pymooDriver` for population based optimizations.\n", "/home/runner/work/OpenMDAO/OpenMDAO/.pixi/envs/dev/lib/python3.13/site-packages/openmdao/core/group.py:1197: DerivativesWarning:Constraints or objectives [rastrigin.y] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[0.]\n", "[0. 0. 0. 0. 0. 0.]\n" ] } ], "source": [ "import openmdao.api as om\n", "import numpy as np\n", "\n", "ORDER = 6 # dimension of problem\n", "span = 5 # upper and lower limits\n", "\n", "class RastriginComp(om.ExplicitComponent):\n", " def setup(self):\n", " self.add_input('x', np.zeros(ORDER))\n", " self.add_output('y', 0.0)\n", "\n", " def compute(self, inputs, outputs):\n", " x = inputs['x']\n", "\n", " # nth dimensional Rastrigin function, array input and scalar output\n", " # global minimum at f(0,0,0...) = 0\n", " n = len(x)\n", " s = 10 * n\n", " for i in range(n):\n", " if np.abs(x[i]) < 1e-200: # avoid underflow runtime warnings from squaring tiny numbers\n", " x[i] = 0.0\n", " s += x[i] * x[i] - 10 * np.cos(2 * np.pi * x[i])\n", "\n", " outputs['y'] = s\n", "\n", "prob = om.Problem()\n", "\n", "prob.model.add_subsystem('rastrigin', RastriginComp(), promotes_inputs=['x'])\n", "prob.model.add_design_var('x',\n", " lower=-span * np.ones(ORDER),\n", " upper=span * np.ones(ORDER))\n", "prob.model.add_objective('rastrigin.y')\n", "\n", "prob.driver = om.DifferentialEvolutionDriver()\n", "prob.driver.options['max_gen'] = 400\n", "prob.driver.options['Pc'] = 0.5\n", "prob.driver.options['F'] = 0.5\n", "\n", "prob.setup()\n", "prob.run_driver()\n", "\n", "print(prob['rastrigin.y'])\n", "print(prob['x'])" ] }, { "cell_type": "code", "execution_count": 3, "id": "d5b9017d", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:04.127152Z", "iopub.status.busy": "2026-10-02T14:42:04.126794Z", "iopub.status.idle": "2026-10-02T14:42:04.133516Z", "shell.execute_reply": "2026-10-02T14:42:04.132758Z" }, "papermill": { "duration": 0.009648, "end_time": "2026-10-02T14:42:04.134054+00:00", "exception": false, "start_time": "2026-10-02T14:42:04.124406+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.0)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from openmdao.utils.assert_utils import assert_near_equal\n", "assert_near_equal(prob['rastrigin.y'], 0.0, 1e-6)\n", "assert_near_equal(prob['x'], np.zeros(ORDER), 1e-6)" ] }, { "cell_type": "markdown", "id": "6c0d9c22", "metadata": { "papermill": { "duration": 0.002079, "end_time": "2026-10-02T14:42:04.137438+00:00", "exception": false, "start_time": "2026-10-02T14:42:04.135359+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DifferentialEvolutionDriver Options" ] }, { "cell_type": "code", "execution_count": 4, "id": "adfbdc60", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:04.140756Z", "iopub.status.busy": "2026-10-02T14:42:04.140575Z", "iopub.status.idle": "2026-10-02T14:42:04.145927Z", "shell.execute_reply": "2026-10-02T14:42:04.144927Z" }, "papermill": { "duration": 0.008034, "end_time": "2026-10-02T14:42:04.146567+00:00", "exception": false, "start_time": "2026-10-02T14:42:04.138533+00:00", "status": "completed" }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", "\n", "\n", "

\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
OptionDefaultAcceptable ValuesAcceptable TypesDescription
F0.9N/AN/ADifferential rate.
Pc0.9N/AN/ACrossover probability.
debug_print[]['desvars', 'nl_cons', 'ln_cons', 'objs', 'totals']['list']List of what type of Driver variables to print at each iteration.
invalid_desvar_behaviorwarn['warn', 'raise', 'ignore']N/ABehavior of driver if the initial value of a design variable exceeds its bounds. The default value may beset using the `OPENMDAO_INVALID_DESVAR_BEHAVIOR` environment variable to one of the valid options.
max_gen100N/AN/ANumber of generations before termination.
multi_obj_exponent1.0N/AN/AMulti-objective weighting exponent.
multi_obj_weights{}N/A['dict']Weights of objectives for multi-objective optimization.Weights are specified as a dictionary with the absolute namesof the objectives. The same weights for all objectives are assumed, if not given.
penalty_exponent1.0N/AN/APenalty function exponent.
penalty_parameter10.0N/AN/APenalty function parameter.
pop_size0N/AN/ANumber of points in the GA. Set to 0 and it will be computed as 20 times the total number of inputs.
procs_per_model1N/AN/ANumber of processors to give each model under MPI.
run_parallelFalse[True, False]['bool']Set to True to execute the points in a generation in parallel.
\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "om.show_options_table(\"openmdao.drivers.differential_evolution_driver.DifferentialEvolutionDriver\")" ] }, { "cell_type": "markdown", "id": "06b7da15", "metadata": { "papermill": { "duration": 0.001893, "end_time": "2026-10-02T14:42:04.149971+00:00", "exception": false, "start_time": "2026-10-02T14:42:04.148078+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DifferentialEvolutionDriver Constructor\n", "\n", "The call signature for the DifferentialEvolutionDriver constructor is:\n", "\n", "```{eval-rst}\n", " .. automethod:: openmdao.drivers.differential_evolution_driver.DifferentialEvolutionDriver.__init__\n", " :noindex:\n", "``` \n", "\n", "## Using DifferentialEvolutionDriver\n", "\n", "You can change the number of generations to run the genetic algorithm by setting the “max_gen” option." ] }, { "cell_type": "code", "execution_count": 5, "id": "a3420135", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:04.153810Z", "iopub.status.busy": "2026-10-02T14:42:04.153630Z", "iopub.status.idle": "2026-10-02T14:42:05.100905Z", "shell.execute_reply": "2026-10-02T14:42:05.100161Z" }, "papermill": { "duration": 0.950466, "end_time": "2026-10-02T14:42:05.101956+00:00", "exception": false, "start_time": "2026-10-02T14:42:04.151490+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "application/papermill.record/text/html": "
class Branin(om.ExplicitComponent):\n    """\n    The Branin test problem. This version is the standard version and\n    contains two continuous parameters.\n    """\n\n    def setup(self):\n        """\n        Define the independent variables, output variables, and partials.\n        """\n        # Inputs\n        self.add_input('x0', 0.0)\n        self.add_input('x1', 0.0)\n\n        # Outputs\n        self.add_output('f', val=0.0)\n\n    def setup_partials(self):\n        self.declare_partials(of='f', wrt=['x0', 'x1'])\n\n    def compute(self, inputs, outputs):\n        """\n        Define the function f(xI, xC).\n\n        When Branin is used in a mixed integer problem, x0 is integer and x1 is continuous.\n        """\n        x0 = inputs['x0']\n        x1 = inputs['x1']\n\n        a = 1.0\n        b = 5.1/(4.0*np.pi**2)\n        c = 5.0/np.pi\n        d = 6.0\n        e = 10.0\n        f = 1.0/(8.0*np.pi)\n\n        outputs['f'] = a*(x1 - b*x0**2 + c*x0 - d)**2 + e*(1-f)*np.cos(x0) + e\n\n    def compute_partials(self, inputs, partials):\n        """\n        Provide the Jacobian.\n        """\n        x0 = inputs['x0']\n        x1 = inputs['x1']\n\n        a = 1.0\n        b = 5.1/(4.0*np.pi**2)\n        c = 5.0/np.pi\n        d = 6.0\n        e = 10.0\n        f = 1.0/(8.0*np.pi)\n\n        partials['f', 'x1'] = 2.0*a*(x1 - b*x0**2 + c*x0 - d)\n        partials['f', 'x0'] = 2.0*a*(x1 - b*x0**2 + c*x0 - d)*(-2.*b*x0 + c) - e*(1.-f)*np.sin(x0)\n
\n", "application/papermill.record/text/latex": "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n\\PY{k}{class}\\PY{+w}{ }\\PY{n+nc}{Branin}\\PY{p}{(}\\PY{n}{om}\\PY{o}{.}\\PY{n}{ExplicitComponent}\\PY{p}{)}\\PY{p}{:}\n\\PY{+w}{ }\\PY{l+s+sd}{\\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\\PY{l+s+sd}{ The Branin test problem. This version is the standard version and}\n\\PY{l+s+sd}{ contains two continuous parameters.}\n\\PY{l+s+sd}{ \\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{setup}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{)}\\PY{p}{:}\n\\PY{+w}{ }\\PY{l+s+sd}{\\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\\PY{l+s+sd}{ Define the independent variables, output variables, and partials.}\n\\PY{l+s+sd}{ \\PYZdq{}\\PYZdq{}\\PYZdq{}}\n \\PY{c+c1}{\\PYZsh{} Inputs}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{add\\PYZus{}input}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x0}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+m+mf}{0.0}\\PY{p}{)}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{add\\PYZus{}input}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x1}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+m+mf}{0.0}\\PY{p}{)}\n\n \\PY{c+c1}{\\PYZsh{} Outputs}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{add\\PYZus{}output}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{n}{val}\\PY{o}{=}\\PY{l+m+mf}{0.0}\\PY{p}{)}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{setup\\PYZus{}partials}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{)}\\PY{p}{:}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{declare\\PYZus{}partials}\\PY{p}{(}\\PY{n}{of}\\PY{o}{=}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{n}{wrt}\\PY{o}{=}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x0}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x1}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\\PY{p}{)}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{compute}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{,} \\PY{n}{inputs}\\PY{p}{,} \\PY{n}{outputs}\\PY{p}{)}\\PY{p}{:}\n\\PY{+w}{ }\\PY{l+s+sd}{\\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\\PY{l+s+sd}{ Define the function f(xI, xC).}\n\n\\PY{l+s+sd}{ When Branin is used in a mixed integer problem, x0 is integer and x1 is continuous.}\n\\PY{l+s+sd}{ \\PYZdq{}\\PYZdq{}\\PYZdq{}}\n \\PY{n}{x0} \\PY{o}{=} \\PY{n}{inputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x0}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\n \\PY{n}{x1} \\PY{o}{=} \\PY{n}{inputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x1}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\n\n \\PY{n}{a} \\PY{o}{=} \\PY{l+m+mf}{1.0}\n \\PY{n}{b} \\PY{o}{=} \\PY{l+m+mf}{5.1}\\PY{o}{/}\\PY{p}{(}\\PY{l+m+mf}{4.0}\\PY{o}{*}\\PY{n}{np}\\PY{o}{.}\\PY{n}{pi}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2}\\PY{p}{)}\n \\PY{n}{c} \\PY{o}{=} \\PY{l+m+mf}{5.0}\\PY{o}{/}\\PY{n}{np}\\PY{o}{.}\\PY{n}{pi}\n \\PY{n}{d} \\PY{o}{=} \\PY{l+m+mf}{6.0}\n \\PY{n}{e} \\PY{o}{=} \\PY{l+m+mf}{10.0}\n \\PY{n}{f} \\PY{o}{=} \\PY{l+m+mf}{1.0}\\PY{o}{/}\\PY{p}{(}\\PY{l+m+mf}{8.0}\\PY{o}{*}\\PY{n}{np}\\PY{o}{.}\\PY{n}{pi}\\PY{p}{)}\n\n \\PY{n}{outputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]} \\PY{o}{=} \\PY{n}{a}\\PY{o}{*}\\PY{p}{(}\\PY{n}{x1} \\PY{o}{\\PYZhy{}} \\PY{n}{b}\\PY{o}{*}\\PY{n}{x0}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2} \\PY{o}{+} 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\\PY{l+m+mf}{5.1}\\PY{o}{/}\\PY{p}{(}\\PY{l+m+mf}{4.0}\\PY{o}{*}\\PY{n}{np}\\PY{o}{.}\\PY{n}{pi}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2}\\PY{p}{)}\n \\PY{n}{c} \\PY{o}{=} \\PY{l+m+mf}{5.0}\\PY{o}{/}\\PY{n}{np}\\PY{o}{.}\\PY{n}{pi}\n \\PY{n}{d} \\PY{o}{=} \\PY{l+m+mf}{6.0}\n \\PY{n}{e} \\PY{o}{=} \\PY{l+m+mf}{10.0}\n \\PY{n}{f} \\PY{o}{=} \\PY{l+m+mf}{1.0}\\PY{o}{/}\\PY{p}{(}\\PY{l+m+mf}{8.0}\\PY{o}{*}\\PY{n}{np}\\PY{o}{.}\\PY{n}{pi}\\PY{p}{)}\n\n \\PY{n}{partials}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x1}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]} \\PY{o}{=} \\PY{l+m+mf}{2.0}\\PY{o}{*}\\PY{n}{a}\\PY{o}{*}\\PY{p}{(}\\PY{n}{x1} \\PY{o}{\\PYZhy{}} \\PY{n}{b}\\PY{o}{*}\\PY{n}{x0}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2} \\PY{o}{+} \\PY{n}{c}\\PY{o}{*}\\PY{n}{x0} \\PY{o}{\\PYZhy{}} \\PY{n}{d}\\PY{p}{)}\n \\PY{n}{partials}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x0}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]} \\PY{o}{=} \\PY{l+m+mf}{2.0}\\PY{o}{*}\\PY{n}{a}\\PY{o}{*}\\PY{p}{(}\\PY{n}{x1} \\PY{o}{\\PYZhy{}} \\PY{n}{b}\\PY{o}{*}\\PY{n}{x0}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2} \\PY{o}{+} \\PY{n}{c}\\PY{o}{*}\\PY{n}{x0} \\PY{o}{\\PYZhy{}} \\PY{n}{d}\\PY{p}{)}\\PY{o}{*}\\PY{p}{(}\\PY{o}{\\PYZhy{}}\\PY{l+m+mf}{2.}\\PY{o}{*}\\PY{n}{b}\\PY{o}{*}\\PY{n}{x0} \\PY{o}{+} \\PY{n}{c}\\PY{p}{)} \\PY{o}{\\PYZhy{}} \\PY{n}{e}\\PY{o}{*}\\PY{p}{(}\\PY{l+m+mf}{1.}\\PY{o}{\\PYZhy{}}\\PY{n}{f}\\PY{p}{)}\\PY{o}{*}\\PY{n}{np}\\PY{o}{.}\\PY{n}{sin}\\PY{p}{(}\\PY{n}{x0}\\PY{p}{)}\n\\end{Verbatim}\n", "application/papermill.record/text/plain": "class Branin(om.ExplicitComponent):\n \"\"\"\n The Branin test problem. This version is the standard version and\n contains two continuous parameters.\n \"\"\"\n\n def setup(self):\n \"\"\"\n Define the independent variables, output variables, and partials.\n \"\"\"\n # Inputs\n self.add_input('x0', 0.0)\n self.add_input('x1', 0.0)\n\n # Outputs\n self.add_output('f', val=0.0)\n\n def setup_partials(self):\n self.declare_partials(of='f', wrt=['x0', 'x1'])\n\n def compute(self, inputs, outputs):\n \"\"\"\n Define the function f(xI, xC).\n\n When Branin is used in a mixed integer problem, x0 is integer and x1 is continuous.\n \"\"\"\n x0 = inputs['x0']\n x1 = inputs['x1']\n\n a = 1.0\n b = 5.1/(4.0*np.pi**2)\n c = 5.0/np.pi\n d = 6.0\n e = 10.0\n f = 1.0/(8.0*np.pi)\n\n outputs['f'] = a*(x1 - b*x0**2 + c*x0 - d)**2 + e*(1-f)*np.cos(x0) + e\n\n def compute_partials(self, inputs, partials):\n \"\"\"\n Provide the Jacobian.\n \"\"\"\n x0 = inputs['x0']\n x1 = inputs['x1']\n\n a = 1.0\n b = 5.1/(4.0*np.pi**2)\n c = 5.0/np.pi\n d = 6.0\n e = 10.0\n f = 1.0/(8.0*np.pi)\n\n partials['f', 'x1'] = 2.0*a*(x1 - b*x0**2 + c*x0 - d)\n partials['f', 'x0'] = 2.0*a*(x1 - b*x0**2 + c*x0 - d)*(-2.*b*x0 + c) - e*(1.-f)*np.sin(x0)" }, "metadata": { "scrapbook": { "mime_prefix": "application/papermill.record/", "name": "code_src15" } }, "output_type": "display_data" } ], "source": [ "from openmdao.utils.notebook_utils import get_code\n", "from myst_nb import glue\n", "glue(\"code_src15\", get_code(\"openmdao.test_suite.components.branin.Branin\"), display=False)" ] }, { "cell_type": "markdown", "id": "49f9629f", "metadata": { "papermill": { "duration": 0.001773, "end_time": "2026-10-02T14:42:05.105377+00:00", "exception": false, "start_time": "2026-10-02T14:42:05.103604+00:00", "status": "completed" }, "tags": [] }, "source": [ ":::{dropdown} `Branin` class definition \n", "\n", "{glue:}`code_src15`\n", ":::" ] }, { "cell_type": "code", "execution_count": 6, "id": "9016697c", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:05.109999Z", "iopub.status.busy": "2026-10-02T14:42:05.109792Z", "iopub.status.idle": "2026-10-02T14:42:05.178677Z", "shell.execute_reply": "2026-10-02T14:42:05.177660Z" }, "papermill": { "duration": 0.072213, "end_time": "2026-10-02T14:42:05.179301+00:00", "exception": false, "start_time": "2026-10-02T14:42:05.107088+00:00", "status": "completed" }, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "Problem: problem2\n", "Driver: DifferentialEvolutionDriver\n", " success : True\n", " iterations : 241\n", " runtime : 5.8878E-02 s\n", " model_evals : 241\n", " model_time : 1.1275E-02 s\n", " deriv_evals : 0\n", " deriv_time : 0.0000E+00 s\n", " exit_status : SUCCESS" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import openmdao.api as om\n", "from openmdao.test_suite.components.branin import Branin\n", "\n", "prob = om.Problem()\n", "model = prob.model\n", "\n", "model.add_subsystem('comp', Branin(), promotes_inputs=[('x0', 'xI'), ('x1', 'xC')])\n", "\n", "model.add_design_var('xI', lower=-5.0, upper=10.0)\n", "model.add_design_var('xC', lower=0.0, upper=15.0)\n", "model.add_objective('comp.f')\n", "\n", "prob.driver = om.DifferentialEvolutionDriver()\n", "prob.driver.options['max_gen'] = 5\n", "\n", "prob.setup()\n", "prob.run_driver()" ] }, { "cell_type": "markdown", "id": "97fc61c0", "metadata": { "papermill": { "duration": 0.001876, "end_time": "2026-10-02T14:42:05.183203+00:00", "exception": false, "start_time": "2026-10-02T14:42:05.181327+00:00", "status": "completed" }, "tags": [] }, "source": [ "You can change the population size by setting the “pop_size” option. The default value for pop_size is 0, which means that the driver automatically computes a population size that is 20 times the total number of input variables." ] }, { "cell_type": "code", "execution_count": 7, "id": "a872ac59", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:05.187952Z", "iopub.status.busy": "2026-10-02T14:42:05.187767Z", "iopub.status.idle": "2026-10-02T14:42:05.528620Z", "shell.execute_reply": "2026-10-02T14:42:05.527237Z" }, "papermill": { "duration": 0.34474, "end_time": "2026-10-02T14:42:05.529829+00:00", "exception": false, "start_time": "2026-10-02T14:42:05.185089+00:00", "status": "completed" }, "tags": [ "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "Problem: problem3\n", "Driver: DifferentialEvolutionDriver\n", " success : True\n", " iterations : 1011\n", " runtime : 3.3249E-01 s\n", " model_evals : 1011\n", " model_time : 6.9063E-02 s\n", " deriv_evals : 0\n", " deriv_time : 0.0000E+00 s\n", " exit_status : SUCCESS" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import openmdao.api as om\n", "from openmdao.test_suite.components.branin import Branin\n", "\n", "prob = om.Problem()\n", "model = prob.model\n", "\n", "model.add_subsystem('comp', Branin(), promotes_inputs=[('x0', 'xI'), ('x1', 'xC')])\n", "\n", "model.add_design_var('xI', lower=-5.0, upper=10.0)\n", "model.add_design_var('xC', lower=0.0, upper=15.0)\n", "model.add_objective('comp.f')\n", "\n", "prob.driver = om.DifferentialEvolutionDriver()\n", "prob.driver.options['pop_size'] = 10\n", "\n", "prob.setup()\n", "prob.run_driver()" ] } ], "metadata": { "celltoolbar": "Tags", "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": "3.13.14" }, "nbsphinx": { "timeout": 90 }, "orphan": true, "papermill": { "default_parameters": {}, "duration": 17.036168, "end_time": "2026-10-02T14:42:06.349687+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/building_blocks/drivers/differential_evolution.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/building_blocks/drivers/differential_evolution.ipynb", "parameters": {}, "start_time": "2026-10-02T14:41:49.313519+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }