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"source": [
"# Loop API Example on Hartmann6\n",
"\n",
"The loop API is the most lightweight way to do optimization in Ax. The user makes one call to `optimize`, which performs all of the optimization under the hood and returns the optimized parameters.\n",
"\n",
"For more customizability of the optimization procedure, consider the Service or Developer API."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
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""
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"output_type": "display_data"
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"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
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" \n",
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"source": [
"import numpy as np\n",
"\n",
"from ax.plot.contour import plot_contour\n",
"from ax.plot.trace import optimization_trace_single_method\n",
"from ax.service.managed_loop import optimize\n",
"from ax.metrics.branin import branin\n",
"from ax.utils.measurement.synthetic_functions import hartmann6\n",
"from ax.utils.notebook.plotting import render, init_notebook_plotting\n",
"\n",
"init_notebook_plotting()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Define evaluation function\n",
"\n",
"First, we define an evaluation function that is able to compute all the metrics needed for this experiment. This function needs to accept a set of parameter values and can also accept a weight. It should produce a dictionary of metric names to tuples of mean and standard error for those metrics."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true,
"execution": {
"iopub.execute_input": "2022-11-10T20:23:40.311254Z",
"iopub.status.busy": "2022-11-10T20:23:40.310138Z",
"iopub.status.idle": "2022-11-10T20:23:40.316366Z",
"shell.execute_reply": "2022-11-10T20:23:40.314981Z"
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"outputs": [],
"source": [
"def hartmann_evaluation_function(parameterization):\n",
" x = np.array([parameterization.get(f\"x{i+1}\") for i in range(6)])\n",
" # In our case, standard error is 0, since we are computing a synthetic function.\n",
" return {\"hartmann6\": (hartmann6(x), 0.0), \"l2norm\": (np.sqrt((x ** 2).sum()), 0.0)}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If there is only one metric in the experiment – the objective – then evaluation function can return a single tuple of mean and SEM, in which case Ax will assume that evaluation corresponds to the objective. It can also return only the mean as a float, in which case Ax will treat SEM as unknown and use a model that can infer it. For more details on evaluation function, refer to the \"Trial Evaluation\" section in the docs."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Run optimization\n",
"The setup for the loop is fully compatible with JSON. The optimization algorithm is selected based on the properties of the problem search space."
]
},
{
"cell_type": "code",
"execution_count": 3,
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"execution": {
"iopub.execute_input": "2022-11-10T20:23:40.320146Z",
"iopub.status.busy": "2022-11-10T20:23:40.319641Z",
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"shell.execute_reply": "2022-11-10T20:25:52.240225Z"
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[ParameterConstraint(1.0*x1 + 1.0*x2 <= 20.0)]).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 12 trials, GPEI for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/runner/work/Ax/Ax/ax/core/observation.py:274: FutureWarning:\n",
"\n",
"In a future version of pandas, a length 1 tuple will be returned when iterating over a groupby with a grouper equal to a list of length 1. Don't supply a list with a single grouper to avoid this warning.\n",
"\n",
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:23:40] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.14/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:306: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.'), OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.'), OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.'), OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.14/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:328: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 11-10 20:23:56] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:24:02] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:24:08] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:24:15] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:24:22] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:24:27] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.14/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:306: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.14/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:328: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 11-10 20:24:40] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:24:46] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.14/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:306: RuntimeWarning:\n",
"\n",
"Optimization failed in `gen_candidates_scipy` with the following warning(s):\n",
"[OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.'), OptimizationWarning('Optimization failed within `scipy.optimize.minimize` with status 9.')]\n",
"Trying again with a new set of initial conditions.\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.8.14/x64/lib/python3.8/site-packages/botorch/optim/optimize.py:328: RuntimeWarning:\n",
"\n",
"Optimization failed on the second try, after generating a new set of initial conditions.\n",
"\n",
"[INFO 11-10 20:25:00] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:06] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:12] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:17] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:22] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:28] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:35] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:41] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 20:25:46] ax.service.managed_loop: Running optimization trial 30...\n"
]
}
],
"source": [
"best_parameters, values, experiment, model = optimize(\n",
" parameters=[\n",
" {\n",
" \"name\": \"x1\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" \"value_type\": \"float\", # Optional, defaults to inference from type of \"bounds\".\n",
" \"log_scale\": False, # Optional, defaults to False.\n",
" },\n",
" {\n",
" \"name\": \"x2\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x3\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x4\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x5\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" {\n",
" \"name\": \"x6\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" },\n",
" ],\n",
" experiment_name=\"test\",\n",
" objective_name=\"hartmann6\",\n",
" evaluation_function=hartmann_evaluation_function,\n",
" minimize=True, # Optional, defaults to False.\n",
" parameter_constraints=[\"x1 + x2 <= 20\"], # Optional.\n",
" outcome_constraints=[\"l2norm <= 1.25\"], # Optional.\n",
" total_trials=30, # Optional.\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can introspect optimization results:"
]
},
{
"cell_type": "code",
"execution_count": 4,
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"execution": {
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"text/plain": [
"{'x1': 0.23736426993933266,\n",
" 'x2': 0.19799462806099588,\n",
" 'x3': 0.4694112887455931,\n",
" 'x4': 0.28292969955853714,\n",
" 'x5': 0.31303917887204047,\n",
" 'x6': 0.6648016400854645}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
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"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
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"data": {
"text/plain": [
"{'l2norm': 0.9674182421059508, 'hartmann6': -3.2780568157580374}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"means, covariances = values\n",
"means"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For comparison, minimum of Hartmann6 is:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2022-11-10T20:25:52.260991Z",
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"source": [
"hartmann6.fmin"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Plot results\n",
"Here we arbitrarily select \"x1\" and \"x2\" as the two parameters to plot for both metrics, \"hartmann6\" and \"l2norm\"."
]
},
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"Arm 0_0
hartmann6: -0.19066 (SEM: 0)
x1: 0.0286128
x2: 0.0771406
x3: 0.277624
x4: 0.300056
x5: 0.823706
x6: 0.521663",
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hartmann6: -0.0161924 (SEM: 0)
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x5: 0.774861
x6: 0.267701",
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hartmann6: -0.382524 (SEM: 0)
x1: 0.108757
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x3: 0.74072
x4: 0.799608
x5: 0.320434
x6: 0.856731",
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hartmann6: -0.832638 (SEM: 0)
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x4: 0.217251
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x6: 0.429171",
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hartmann6: -1.06934 (SEM: 0)
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hartmann6: -1.31319 (SEM: 0)
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x5: 0.47979
x6: 0.508543",
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hartmann6: -1.57761 (SEM: 0)
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hartmann6: -1.77078 (SEM: 0)
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x6: 0.619974",
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hartmann6: -1.94065 (SEM: 0)
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x4: 0.21411
x5: 0.351629
x6: 0.647001",
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hartmann6: -1.64427 (SEM: 0)
x1: 4.52094e-18
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x4: 0.22061
x5: 0.36999
x6: 0.615052",
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hartmann6: -2.29821 (SEM: 0)
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hartmann6: -0.148934 (SEM: 0)
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x5: 0.337182
x6: 0.363433",
"Arm 20_0
hartmann6: -2.322 (SEM: 0)
x1: 0
x2: 0.325513
x3: 0.542879
x4: 0.247725
x5: 0.250146
x6: 0.729299",
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hartmann6: -2.39858 (SEM: 0)
x1: 1.66419e-17
x2: 0.324552
x3: 0.563504
x4: 0.2238
x5: 0.313028
x6: 0.72905",
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hartmann6: -2.28072 (SEM: 0)
x1: 2.7846e-18
x2: 0.304196
x3: 0.573527
x4: 0.164343
x5: 0.284048
x6: 0.699994",
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hartmann6: -2.61253 (SEM: 0)
x1: 0.0767156
x2: 0.327633
x3: 0.568126
x4: 0.237868
x5: 0.318556
x6: 0.742623",
"Arm 24_0
hartmann6: -2.54234 (SEM: 0)
x1: 0.128745
x2: 0.327399
x3: 0.594802
x4: 0.234856
x5: 0.313228
x6: 0.783238",
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hartmann6: -2.82694 (SEM: 0)
x1: 0.109401
x2: 0.313538
x3: 0.530444
x4: 0.250487
x5: 0.324304
x6: 0.720496",
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hartmann6: -3.14027 (SEM: 0)
x1: 0.180492
x2: 0.265285
x3: 0.485177
x4: 0.269241
x5: 0.322647
x6: 0.689258",
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hartmann6: -3.27806 (SEM: 0)
x1: 0.237364
x2: 0.197995
x3: 0.469411
x4: 0.28293
x5: 0.313039
x6: 0.664802",
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hartmann6: -3.26655 (SEM: 0)
x1: 0.224838
x2: 0.126057
x3: 0.50484
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x5: 0.329991
x6: 0.676571",
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hartmann6: -0.094178 (SEM: 0)
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x6: 0.416601",
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hartmann6: -0.00391722 (SEM: 0)
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x2: 0.614076
x3: 0.47361
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hartmann6: -0.0802372 (SEM: 0)
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x2: 0.919363
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x5: 0.844018
x6: 0.530008",
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hartmann6: -0.167187 (SEM: 0)
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hartmann6: -0.112497 (SEM: 0)
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hartmann6: -0.26256 (SEM: 0)
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x6: 0.244129",
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hartmann6: -0.00879909 (SEM: 0)
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hartmann6: -0.19066 (SEM: 0)
x1: 0.0286128
x2: 0.0771406
x3: 0.277624
x4: 0.300056
x5: 0.823706
x6: 0.521663",
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hartmann6: -0.0161924 (SEM: 0)
x1: 0.678451
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x5: 0.774861
x6: 0.267701",
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hartmann6: -0.382524 (SEM: 0)
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x4: 0.799608
x5: 0.320434
x6: 0.856731",
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hartmann6: -0.832638 (SEM: 0)
x1: 0.0353861
x2: 0.344902
x3: 0.384472
x4: 0.217251
x5: 0.546153
x6: 0.429171",
"Arm 13_0
hartmann6: -1.06934 (SEM: 0)
x1: 0.00847715
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x3: 0.41666
x4: 0.222798
x5: 0.512353
x6: 0.468813",
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hartmann6: -1.31319 (SEM: 0)
x1: 0
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x3: 0.446335
x4: 0.221935
x5: 0.47979
x6: 0.508543",
"Arm 15_0
hartmann6: -1.57761 (SEM: 0)
x1: 0
x2: 0.435432
x3: 0.481044
x4: 0.214305
x5: 0.440377
x6: 0.557716",
"Arm 16_0
hartmann6: -1.77078 (SEM: 0)
x1: 0
x2: 0.467446
x3: 0.526882
x4: 0.20112
x5: 0.389847
x6: 0.619974",
"Arm 17_0
hartmann6: -1.94065 (SEM: 0)
x1: 0
x2: 0.442396
x3: 0.608848
x4: 0.21411
x5: 0.351629
x6: 0.647001",
"Arm 18_0
hartmann6: -1.64427 (SEM: 0)
x1: 4.52094e-18
x2: 0.446613
x3: 0.704595
x4: 0.22061
x5: 0.36999
x6: 0.615052",
"Arm 19_0
hartmann6: -2.29821 (SEM: 0)
x1: 1.1877e-18
x2: 0.375347
x3: 0.588315
x4: 0.234966
x5: 0.304392
x6: 0.680022",
"Arm 1_0
hartmann6: -0.148934 (SEM: 0)
x1: 0.0265269
x2: 0.266673
x3: 0.62365
x4: 0.774008
x5: 0.337182
x6: 0.363433",
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hartmann6: -2.322 (SEM: 0)
x1: 0
x2: 0.325513
x3: 0.542879
x4: 0.247725
x5: 0.250146
x6: 0.729299",
"Arm 21_0
hartmann6: -2.39858 (SEM: 0)
x1: 1.66419e-17
x2: 0.324552
x3: 0.563504
x4: 0.2238
x5: 0.313028
x6: 0.72905",
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hartmann6: -2.28072 (SEM: 0)
x1: 2.7846e-18
x2: 0.304196
x3: 0.573527
x4: 0.164343
x5: 0.284048
x6: 0.699994",
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hartmann6: -2.61253 (SEM: 0)
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x2: 0.327633
x3: 0.568126
x4: 0.237868
x5: 0.318556
x6: 0.742623",
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hartmann6: -2.54234 (SEM: 0)
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x2: 0.327399
x3: 0.594802
x4: 0.234856
x5: 0.313228
x6: 0.783238",
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hartmann6: -2.82694 (SEM: 0)
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x3: 0.530444
x4: 0.250487
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hartmann6: -3.14027 (SEM: 0)
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x3: 0.485177
x4: 0.269241
x5: 0.322647
x6: 0.689258",
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hartmann6: -3.27806 (SEM: 0)
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x4: 0.28293
x5: 0.313039
x6: 0.664802",
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hartmann6: -3.26655 (SEM: 0)
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hartmann6: -0.094178 (SEM: 0)
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hartmann6: -0.00391722 (SEM: 0)
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