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"source": [
"# Visualizations\n",
"\n",
"This tutorial illustrates the core visualization utilities available in Ax."
]
},
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""
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"text": [
"[INFO 05-02 05:16:33] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
},
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"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:33] ax.utils.notebook.plotting: Please see\n",
" (https://ax.dev/tutorials/visualizations.html#Fix-for-plots-that-are-not-rendering)\n",
" if visualizations are not rendering.\n"
]
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" \n",
" "
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"source": [
"import numpy as np\n",
"\n",
"from ax.modelbridge.cross_validation import cross_validate\n",
"from ax.plot.contour import interact_contour\n",
"from ax.plot.diagnostic import interact_cross_validation\n",
"from ax.plot.scatter import interact_fitted, plot_objective_vs_constraints, tile_fitted\n",
"from ax.plot.slice import plot_slice\n",
"from ax.service.ax_client import AxClient, ObjectiveProperties\n",
"from ax.utils.measurement.synthetic_functions import hartmann6\n",
"from ax.utils.notebook.plotting import init_notebook_plotting, render\n",
"\n",
"init_notebook_plotting()"
]
},
{
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"id": "d9852c74",
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"showInput": true,
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"source": [
"## 1. Create experiment and run optimization\n",
"\n",
"The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials"
]
},
{
"cell_type": "markdown",
"id": "2d5f015f",
"metadata": {
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"tags": []
},
"source": [
"#### 1a. Define search space and evaluation function"
]
},
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"source": [
"noise_sd = 0.1\n",
"param_names = [f\"x{i+1}\" for i in range(6)] # x1, x2, ..., x6\n",
"\n",
"\n",
"def noisy_hartmann_evaluation_function(parameterization):\n",
" x = np.array([parameterization.get(p_name) for p_name in param_names])\n",
" noise1, noise2 = np.random.normal(0, noise_sd, 2)\n",
"\n",
" return {\n",
" \"hartmann6\": (hartmann6(x) + noise1, noise_sd),\n",
" \"l2norm\": (np.sqrt((x**2).sum()) + noise2, noise_sd),\n",
" }"
]
},
{
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"id": "50caa7a2",
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"tags": []
},
"source": [
"#### 1b. Create Experiment"
]
},
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"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] 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=[]).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR since there is at least one ordered parameter and there are no unordered categorical parameters.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=6 num_trials=None use_batch_trials=False\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: `verbose`, `disable_progbar`, and `jit_compile` are not yet supported when using `choose_generation_strategy` with ModularBoTorchModel, dropping these arguments.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 12 trials, BoTorch for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.\n"
]
}
],
"source": [
"ax_client = AxClient()\n",
"ax_client.create_experiment(\n",
" name=\"test_visualizations\",\n",
" parameters=[\n",
" {\n",
" \"name\": p_name,\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" }\n",
" for p_name in param_names\n",
" ],\n",
" objectives={\"hartmann6\": ObjectiveProperties(minimize=True)},\n",
" outcome_constraints=[\"l2norm <= 1.25\"],\n",
")"
]
},
{
"cell_type": "markdown",
"id": "15ca0871",
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"showInput": false,
"tags": []
},
"source": [
"#### 1c. Run the optimization and fit a GP on all data"
]
},
{
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"execution_count": 4,
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.020896, 'x2': 0.904968, 'x3': 0.000168, 'x4': 0.49008, 'x5': 0.194316, 'x6': 0.651144} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.130186, 0.1), 'l2norm': (1.251495, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.254904, 'x2': 0.276718, 'x3': 0.568393, 'x4': 0.137626, 'x5': 0.391328, 'x6': 0.024703} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.056309, 0.1), 'l2norm': (0.892053, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.351547, 'x2': 0.844315, 'x3': 0.191608, 'x4': 0.697669, 'x5': 0.313083, 'x6': 0.296609} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-1.19481, 0.1), 'l2norm': (1.296905, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.832836, 'x2': 0.349403, 'x3': 0.238205, 'x4': 0.109476, 'x5': 0.005529, 'x6': 0.822927} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.193561, 0.1), 'l2norm': (1.256255, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.563354, 'x2': 0.082045, 'x3': 0.68168, 'x4': 0.419048, 'x5': 0.321608, 'x6': 0.149029} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.209781, 0.1), 'l2norm': (1.2362, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.991218, 'x2': 0.712046, 'x3': 0.752436, 'x4': 0.873299, 'x5': 0.324084, 'x6': 0.921131} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.181936, 0.1), 'l2norm': (1.971424, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.380349, 'x2': 0.962953, 'x3': 0.238626, 'x4': 0.032358, 'x5': 0.284958, 'x6': 0.949175} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.177029, 0.1), 'l2norm': (1.613896, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.208664, 'x2': 0.846691, 'x3': 0.267054, 'x4': 0.969681, 'x5': 0.688151, 'x6': 0.634725} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (0.090669, 0.1), 'l2norm': (1.578328, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.946795, 'x2': 0.012834, 'x3': 0.325507, 'x4': 0.724636, 'x5': 0.891541, 'x6': 0.861132} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (0.065115, 0.1), 'l2norm': (1.706824, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.285428, 'x2': 0.250466, 'x3': 0.780617, 'x4': 0.386558, 'x5': 0.664229, 'x6': 0.263374} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.199322, 0.1), 'l2norm': (1.218192, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.989678, 'x2': 0.572212, 'x3': 0.975391, 'x4': 0.558608, 'x5': 0.022497, 'x6': 0.521227} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.06357, 0.1), 'l2norm': (1.755731, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.651035, 'x2': 0.364688, 'x3': 0.082868, 'x4': 0.353762, 'x5': 0.399629, 'x6': 0.966862} using model Sobol.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.666637, 0.1), 'l2norm': (1.334875, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:40] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.279645, 'x2': 0.749335, 'x3': 0.154641, 'x4': 0.581262, 'x5': 0.27916, 'x6': 0.295518} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:40] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-0.862992, 0.1), 'l2norm': (0.967496, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:50] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.328462, 'x2': 0.794214, 'x3': 0.17621, 'x4': 0.63412, 'x5': 0.302644, 'x6': 0.281129} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:50] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.236234, 0.1), 'l2norm': (1.124293, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:59] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.392765, 'x2': 0.797215, 'x3': 0.18389, 'x4': 0.634274, 'x5': 0.312027, 'x6': 0.232323} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:16:59] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.536154, 0.1), 'l2norm': (1.122452, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:03] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.443493, 'x2': 0.783815, 'x3': 0.162403, 'x4': 0.595586, 'x5': 0.292667, 'x6': 0.222745} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:03] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.686711, 0.1), 'l2norm': (1.276556, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:13] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.432242, 'x2': 0.736396, 'x3': 0.198184, 'x4': 0.579148, 'x5': 0.317132, 'x6': 0.169138} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:13] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.983579, 0.1), 'l2norm': (1.02437, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:21] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.461549, 'x2': 0.722245, 'x3': 0.222253, 'x4': 0.587152, 'x5': 0.335408, 'x6': 0.102965} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:21] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.348686, 0.1), 'l2norm': (1.208449, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:28] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.489926, 'x2': 0.721081, 'x3': 0.226895, 'x4': 0.53872, 'x5': 0.345407, 'x6': 0.049004} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:28] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.427052, 0.1), 'l2norm': (1.106857, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:36] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.522741, 'x2': 0.671707, 'x3': 0.232624, 'x4': 0.62002, 'x5': 0.341954, 'x6': 0.030279} using model BoTorch.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:36] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-1.548812, 0.1), 'l2norm': (1.058702, 0.1)}.\n"
]
}
],
"source": [
"for i in range(20):\n",
" parameters, trial_index = ax_client.get_next_trial()\n",
" # Local evaluation here can be replaced with deployment to external system.\n",
" ax_client.complete_trial(\n",
" trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters)\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "d7f351da",
"metadata": {
"originalKey": "72f4d3e7-fa04-43d0-8451-ded292e705df",
"papermill": {
"duration": 0.047521,
"end_time": "2024-05-02T05:17:36.332947",
"exception": false,
"start_time": "2024-05-02T05:17:36.285426",
"status": "completed"
},
"tags": []
},
"source": [
"## 2. Contour plots\n",
"\n",
"The plot below shows the response surface for `hartmann6` metric as a function of the `x1`, `x2` parameters.\n",
"\n",
"The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "2deffc91",
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2024-05-02T05:17:36.405698Z",
"iopub.status.busy": "2024-05-02T05:17:36.405098Z",
"iopub.status.idle": "2024-05-02T05:17:37.324237Z",
"shell.execute_reply": "2024-05-02T05:17:37.323410Z"
},
"executionStartTime": 1627654870209,
"executionStopTime": 1627654871972,
"hidden_ranges": [],
"originalKey": "843df85c-965d-4a83-9fe1-696225d81c0f",
"papermill": {
"duration": 0.959901,
"end_time": "2024-05-02T05:17:37.328905",
"exception": false,
"start_time": "2024-05-02T05:17:36.369004",
"status": "completed"
},
"requestMsgId": "4a643541-867c-46b6-868d-64337920c2a3",
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 05-02 05:17:36] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n"
]
},
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hartmann6: -0.130186 (SEM: 0.1)
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"# this could alternately be done with `ax.plot.contour.plot_contour`\n",
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"Arm 0_0
hartmann6: -0.130186 (SEM: 0.1)
x1: 0.0208963
x2: 0.904968
x3: 0.000168421
x4: 0.49008
x5: 0.194316
x6: 0.651144",
"Arm 1_0
hartmann6: -0.0563094 (SEM: 0.1)
x1: 0.254904
x2: 0.276718
x3: 0.568393
x4: 0.137626
x5: 0.391328
x6: 0.0247035",
"Arm 2_0
hartmann6: -1.19481 (SEM: 0.1)
x1: 0.351547
x2: 0.844315
x3: 0.191608
x4: 0.697669
x5: 0.313083
x6: 0.296609",
"Arm 3_0
hartmann6: -0.193561 (SEM: 0.1)
x1: 0.832836
x2: 0.349403
x3: 0.238205
x4: 0.109476
x5: 0.0055285
x6: 0.822927",
"Arm 4_0
hartmann6: -0.209781 (SEM: 0.1)
x1: 0.563354
x2: 0.0820451
x3: 0.68168
x4: 0.419048
x5: 0.321608
x6: 0.149029",
"Arm 5_0
hartmann6: -0.181936 (SEM: 0.1)
x1: 0.991218
x2: 0.712046
x3: 0.752436
x4: 0.873299
x5: 0.324084
x6: 0.921131",
"Arm 6_0
hartmann6: -0.177029 (SEM: 0.1)
x1: 0.380349
x2: 0.962953
x3: 0.238626
x4: 0.0323582
x5: 0.284958
x6: 0.949175",
"Arm 7_0
hartmann6: 0.0906694 (SEM: 0.1)
x1: 0.208664
x2: 0.846691
x3: 0.267054
x4: 0.969681
x5: 0.688151
x6: 0.634725",
"Arm 8_0
hartmann6: 0.0651147 (SEM: 0.1)
x1: 0.946795
x2: 0.0128335
x3: 0.325507
x4: 0.724636
x5: 0.891541
x6: 0.861132",
"Arm 9_0
hartmann6: -0.199322 (SEM: 0.1)
x1: 0.285428
x2: 0.250466
x3: 0.780617
x4: 0.386558
x5: 0.664229
x6: 0.263374",
"Arm 10_0
hartmann6: 0.0635697 (SEM: 0.1)
x1: 0.989678
x2: 0.572212
x3: 0.975391
x4: 0.558608
x5: 0.0224965
x6: 0.521227",
"Arm 11_0
hartmann6: -0.666637 (SEM: 0.1)
x1: 0.651035
x2: 0.364688
x3: 0.0828684
x4: 0.353762
x5: 0.399629
x6: 0.966862",
"Arm 12_0
hartmann6: -0.862992 (SEM: 0.1)
x1: 0.279645
x2: 0.749335
x3: 0.154641
x4: 0.581262
x5: 0.27916
x6: 0.295518",
"Arm 13_0
hartmann6: -1.23623 (SEM: 0.1)
x1: 0.328462
x2: 0.794214
x3: 0.17621
x4: 0.63412
x5: 0.302644
x6: 0.281129",
"Arm 14_0
hartmann6: -1.53615 (SEM: 0.1)
x1: 0.392765
x2: 0.797215
x3: 0.18389
x4: 0.634274
x5: 0.312027
x6: 0.232323",
"Arm 15_0
hartmann6: -1.68671 (SEM: 0.1)
x1: 0.443493
x2: 0.783815
x3: 0.162403
x4: 0.595586
x5: 0.292667
x6: 0.222745",
"Arm 16_0
hartmann6: -1.98358 (SEM: 0.1)
x1: 0.432242
x2: 0.736396
x3: 0.198184
x4: 0.579148
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"Arm 0_0
hartmann6: -0.130186 (SEM: 0.1)
x1: 0.0208963
x2: 0.904968
x3: 0.000168421
x4: 0.49008
x5: 0.194316
x6: 0.651144",
"Arm 1_0
hartmann6: -0.0563094 (SEM: 0.1)
x1: 0.254904
x2: 0.276718
x3: 0.568393
x4: 0.137626
x5: 0.391328
x6: 0.0247035",
"Arm 2_0
hartmann6: -1.19481 (SEM: 0.1)
x1: 0.351547
x2: 0.844315
x3: 0.191608
x4: 0.697669
x5: 0.313083
x6: 0.296609",
"Arm 3_0
hartmann6: -0.193561 (SEM: 0.1)
x1: 0.832836
x2: 0.349403
x3: 0.238205
x4: 0.109476
x5: 0.0055285
x6: 0.822927",
"Arm 4_0
hartmann6: -0.209781 (SEM: 0.1)
x1: 0.563354
x2: 0.0820451
x3: 0.68168
x4: 0.419048
x5: 0.321608
x6: 0.149029",
"Arm 5_0
hartmann6: -0.181936 (SEM: 0.1)
x1: 0.991218
x2: 0.712046
x3: 0.752436
x4: 0.873299
x5: 0.324084
x6: 0.921131",
"Arm 6_0
hartmann6: -0.177029 (SEM: 0.1)
x1: 0.380349
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