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"cell_type": "markdown",
"metadata": {},
"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": {},
"outputs": [
{
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""
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"metadata": {},
"output_type": "display_data"
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"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:10] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
},
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"data": {
"text/html": [
" \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
},
"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,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] 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 04-26 20:09:11] ax.service.managed_loop: Started full optimization with 30 steps.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 1...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 2...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 3...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 4...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 5...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 6...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 7...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 8...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 9...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 10...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 11...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 12...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:11] ax.service.managed_loop: Running optimization trial 13...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/hostedtoolcache/Python/3.7.12/x64/lib/python3.7/site-packages/gpytorch/lazy/lazy_tensor.py:1741: UserWarning:\n",
"\n",
"torch.triangular_solve is deprecated in favor of torch.linalg.solve_triangularand will be removed in a future PyTorch release.\n",
"torch.linalg.solve_triangular has its arguments reversed and does not return a copy of one of the inputs.\n",
"X = torch.triangular_solve(B, A).solution\n",
"should be replaced with\n",
"X = torch.linalg.solve_triangular(A, B). (Triggered internally at ../aten/src/ATen/native/BatchLinearAlgebra.cpp:1672.)\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:17] ax.service.managed_loop: Running optimization trial 14...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:23] ax.service.managed_loop: Running optimization trial 15...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:30] ax.service.managed_loop: Running optimization trial 16...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:36] ax.service.managed_loop: Running optimization trial 17...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:42] ax.service.managed_loop: Running optimization trial 18...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:48] ax.service.managed_loop: Running optimization trial 19...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:09:54] ax.service.managed_loop: Running optimization trial 20...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:01] ax.service.managed_loop: Running optimization trial 21...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:07] ax.service.managed_loop: Running optimization trial 22...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:13] ax.service.managed_loop: Running optimization trial 23...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:18] ax.service.managed_loop: Running optimization trial 24...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:23] ax.service.managed_loop: Running optimization trial 25...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:28] ax.service.managed_loop: Running optimization trial 26...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:35] ax.service.managed_loop: Running optimization trial 27...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:40] ax.service.managed_loop: Running optimization trial 28...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:44] ax.service.managed_loop: Running optimization trial 29...\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 04-26 20:10:49] 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,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'x1': 0.4076336950751692,\n",
" 'x2': 0.9025745948037075,\n",
" 'x3': 0.18501790637296855,\n",
" 'x4': 0.5539181749333645,\n",
" 'x5': 0.44872971190026884,\n",
" 'x6': 0.04304143492213628}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'l2norm': 1.2349385505454658, 'hartmann6': -3.071102782450379}"
]
},
"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": {},
"outputs": [
{
"data": {
"text/plain": [
"-3.32237"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hartmann6.fmin"
]
},
{
"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\"."
]
},
{
"cell_type": "code",
"execution_count": 7,
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"Arm 0_0
hartmann6: -0.177779 (SEM: 0)
x1: 0.398423
x2: 0.767501
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hartmann6: -0.0536031 (SEM: 0)
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x6: 0.401669",
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hartmann6: -0.0172144 (SEM: 0)
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x6: 0.108675",
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hartmann6: -0.0590564 (SEM: 0)
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hartmann6: -0.91023 (SEM: 0)
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hartmann6: -0.0219373 (SEM: 0)
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x6: 0.689943",
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hartmann6: -2.67815 (SEM: 0)
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x5: 0.860386
x6: 0.0149064",
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x5: 0.906839
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hartmann6: -0.0980761 (SEM: 0)
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x6: 0.523842",
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hartmann6: -1.68057 (SEM: 0)
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x5: 0.745872
x6: 0.0681874",
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hartmann6: -2.02872 (SEM: 0)
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x5: 0.777158
x6: 0.0574868",
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hartmann6: -2.59202 (SEM: 0)
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x6: 0.0179569",
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hartmann6: -2.75562 (SEM: 0)
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x5: 0.656819
x6: 1.81822e-16",
"Arm 17_0
hartmann6: -1.97162 (SEM: 0)
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x5: 0.665566
x6: 2.21194e-18",
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hartmann6: -2.82433 (SEM: 0)
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x6: 7.81084e-18",
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hartmann6: -2.63814 (SEM: 0)
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x6: 1.20092e-18",
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hartmann6: -2.92621 (SEM: 0)
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x6: 4.17018e-08",
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hartmann6: -2.9469 (SEM: 0)
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x6: 2.73128e-09",
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hartmann6: -2.92463 (SEM: 0)
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hartmann6: -2.97156 (SEM: 0)
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"Arm 28_0
hartmann6: -3.06918 (SEM: 0)
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hartmann6: -0.177779 (SEM: 0)
x1: 0.398423
x2: 0.767501
x3: 0.985177
x4: 0.739179
x5: 0.28668
x6: 0.895158",
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hartmann6: -0.0536031 (SEM: 0)
x1: 0.490791
x2: 0.319897
x3: 0.262714
x4: 0.599394
x5: 0.798092
x6: 0.401669",
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hartmann6: -0.0172144 (SEM: 0)
x1: 0.962786
x2: 0.240473
x3: 0.585971
x4: 0.012025
x5: 0.417127
x6: 0.108675",
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hartmann6: -0.392451 (SEM: 0)
x1: 0.79478
x2: 0.205626
x3: 0.063052
x4: 0.3554
x5: 0.217532
x6: 0.355469",
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hartmann6: -0.143018 (SEM: 0)
x1: 0.357024
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x6: 0.55288",
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hartmann6: -0.0590564 (SEM: 0)
x1: 0.20969
x2: 0.892688
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x5: 0.992038
x6: 0.772372",
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hartmann6: -0.91023 (SEM: 0)
x1: 0.213147
x2: 0.560835
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x4: 0.248569
x5: 0.387296
x6: 0.773546",
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hartmann6: -0.0219373 (SEM: 0)
x1: 0.38589
x2: 0.36064
x3: 0.111445
x4: 0.637104
x5: 0.764981
x6: 0.689943",
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hartmann6: -2.67815 (SEM: 0)
x1: 0.389215
x2: 0.78592
x3: 0.0981495
x4: 0.552126
x5: 0.860386
x6: 0.0149064",
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hartmann6: -0.00128769 (SEM: 0)
x1: 0.860403
x2: 0.28761
x3: 0.50627
x4: 0.701542
x5: 0.906839
x6: 0.560025",
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hartmann6: -0.242474 (SEM: 0)
x1: 0.863283
x2: 0.389635
x3: 0.464657
x4: 0.0582119
x5: 0.158668
x6: 0.496087",
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hartmann6: -0.0980761 (SEM: 0)
x1: 0.0544792
x2: 0.446555
x3: 0.727651
x4: 0.684284
x5: 0.806846
x6: 0.523842",
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hartmann6: -1.68057 (SEM: 0)
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x2: 0.665032
x3: 0.0652667
x4: 0.469641
x5: 0.745872
x6: 0.0681874",
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hartmann6: -2.04775 (SEM: 0)
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x2: 0.718178
x3: 0.0722093
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x5: 0.781005
x6: 0.0572178",
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hartmann6: -2.02872 (SEM: 0)
x1: 0.454816
x2: 0.714113
x3: 0.0702674
x4: 0.472493
x5: 0.777158
x6: 0.0574868",
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hartmann6: -2.59202 (SEM: 0)
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x2: 0.755947
x3: 0.0143918
x4: 0.555892
x5: 0.705888
x6: 0.0179569",
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hartmann6: -2.75562 (SEM: 0)
x1: 0.377738
x2: 0.804521
x3: 0.000338175
x4: 0.574505
x5: 0.656819
x6: 1.81822e-16",
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hartmann6: -1.97162 (SEM: 0)
x1: 0.26208
x2: 0.815253
x3: 2.30907e-18
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x5: 0.665566
x6: 2.21194e-18",
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hartmann6: -2.82433 (SEM: 0)
x1: 0.387343
x2: 0.85686
x3: 0.0402197
x4: 0.516549
x5: 0.623467
x6: 7.81084e-18",
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hartmann6: -2.63814 (SEM: 0)
x1: 0.382419
x2: 0.866178
x3: 7.02691e-18
x4: 0.4794
x5: 0.693406
x6: 1.20092e-18",
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hartmann6: -2.92621 (SEM: 0)
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x2: 0.845492
x3: 0.0843073
x4: 0.558285
x5: 0.584994
x6: 4.17018e-08",
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hartmann6: -2.9469 (SEM: 0)
x1: 0.394943
x2: 0.848788
x3: 0.100135
x4: 0.578934
x5: 0.574615
x6: 2.73128e-09",
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hartmann6: -2.90201 (SEM: 0)
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x2: 0.841434
x3: 0.160252
x4: 0.575449
x5: 0.59524
x6: 0",
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hartmann6: -2.92463 (SEM: 0)
x1: 0.411299
x2: 0.835806
x3: 0.128652
x4: 0.562756
x5: 0.586708
x6: 0",
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hartmann6: -3.0158 (SEM: 0)
x1: 0.398095
x2: 0.859741
x3: 0.112079
x4: 0.578565
x5: 0.574823
x6: 0.0557957",
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x1: 0.397592
x2: 0.854616
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x4: 0.56879
x5: 0.570605
x6: 0.0567597",
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x1: 0.404703
x2: 0.882664
x3: 0.124501
x4: 0.569074
x5: 0.470929
x6: 0.0882684",
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hartmann6: -0.73788 (SEM: 0)
x1: 0.410855
x2: 0.984604
x3: 0.0192436
x4: 0.51246
x5: 0.430491
x6: 0.349133",
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hartmann6: -3.06918 (SEM: 0)
x1: 0.4036
x2: 0.877685
x3: 0.139064
x4: 0.57802
x5: 0.493861
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"# `plot_single_method` expects a 2-d array of means, because it expects to average means from multiple \n",
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" optimum=hartmann6.fmin,\n",
" title=\"Model performance vs. # of iterations\",\n",
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