{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"customInput": null,
"hidden_ranges": [],
"originalKey": "95e7a97a-bf78-48d4-a0c1-c0e8dfc4fed9",
"showInput": true
},
"source": [
"# Multi-Objective Optimization Ax API\n",
"### Using the Service API\n",
"For Multi-objective optimization (MOO) in the `AxClient`, objectives are specified through the `ObjectiveProperties` dataclass. An `ObjectiveProperties` requires a boolean `minimize`, and also accepts an optional floating point `threshold`. If a `threshold` is not specified, Ax will infer it through the use of heuristics. If the user knows the region of interest (because they have specs or prior knowledge), then specifying the thresholds is preferable to inferring it. But if the user would need to guess, inferring is preferable.\n",
"\n",
"\n",
"To learn more about how to choose a threshold, see [Set Objective Thresholds to focus candidate generation in a region of interest](#Set-Objective-Thresholds-to-focus-candidate-generation-in-a-region-of-interest). See the [Service API Tutorial](/tutorials/gpei_hartmann_service.html) for more infomation on running experiments with the Service API."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"code_folding": [],
"customInput": null,
"execution": {
"iopub.execute_input": "2022-11-10T21:07:21.908495Z",
"iopub.status.busy": "2022-11-10T21:07:21.907994Z",
"iopub.status.idle": "2022-11-10T21:07:24.718985Z",
"shell.execute_reply": "2022-11-10T21:07:24.718194Z"
},
"hidden_ranges": [],
"originalKey": "06bf2029-0ea4-40b4-aced-956f1411cb6e",
"showInput": true
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
},
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ax.service.ax_client import AxClient\n",
"from ax.service.utils.instantiation import ObjectiveProperties\n",
"\n",
"import torch\n",
"\n",
"# Plotting imports and initialization\n",
"from ax.utils.notebook.plotting import render, init_notebook_plotting\n",
"from ax.plot.pareto_utils import compute_posterior_pareto_frontier\n",
"from ax.plot.pareto_frontier import plot_pareto_frontier\n",
"init_notebook_plotting()\n",
"\n",
"# Load our sample 2-objective problem\n",
"from botorch.test_functions.multi_objective import BraninCurrin\n",
"branin_currin = BraninCurrin(negate=True).to(\n",
" dtype=torch.double, \n",
" device= torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\"),\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"code_folding": [],
"customInput": null,
"execution": {
"iopub.execute_input": "2022-11-10T21:07:24.792399Z",
"iopub.status.busy": "2022-11-10T21:07:24.791051Z",
"iopub.status.idle": "2022-11-10T21:07:24.805912Z",
"shell.execute_reply": "2022-11-10T21:07:24.805068Z"
},
"executionStartTime": 1628191188673,
"executionStopTime": 1628191188746,
"hidden_ranges": [],
"originalKey": "c687973d-1b09-4a8f-9108-1f74adf64d4d",
"requestMsgId": "ea523260-8896-48e4-a62f-3530d268b209",
"showInput": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] 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 11-10 21:07:24] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. 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 21:07:24] 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 21:07:24] 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])], parameter_constraints=[]).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.core.experiment: The is_test flag has been set to True. This flag is meant purely for development and integration testing purposes. If you are running a live experiment, please set this flag to False\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] 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 21:07:24] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+MOO', steps=[Sobol for 5 trials, MOO for subsequent trials]). Iterations after 5 will take longer to generate due to model-fitting.\n"
]
}
],
"source": [
"ax_client = AxClient()\n",
"ax_client.create_experiment(\n",
" name=\"moo_experiment\",\n",
" parameters=[\n",
" {\n",
" \"name\": f\"x{i+1}\",\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" }\n",
" for i in range(2)\n",
" ],\n",
" objectives={\n",
" # `threshold` arguments are optional\n",
" \"a\": ObjectiveProperties(minimize=False, threshold=branin_currin.ref_point[0]), \n",
" \"b\": ObjectiveProperties(minimize=False, threshold=branin_currin.ref_point[1])\n",
" },\n",
" overwrite_existing_experiment=True,\n",
" is_test=True,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"customInput": null,
"hidden_ranges": [],
"originalKey": "70fd45e1-a2ce-4034-bb44-086507833472",
"showInput": true
},
"source": [
"### Create an Evaluation Function\n",
"In the case of MOO experiments, evaluation functions can be any arbitrary function that takes in a `dict` of parameter names mapped to values and returns a `dict` of objective names mapped to a `tuple` of mean and SEM values."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"code_folding": [],
"customInput": null,
"execution": {
"iopub.execute_input": "2022-11-10T21:07:24.809521Z",
"iopub.status.busy": "2022-11-10T21:07:24.808993Z",
"iopub.status.idle": "2022-11-10T21:07:24.813722Z",
"shell.execute_reply": "2022-11-10T21:07:24.812993Z"
},
"executionStartTime": 1628191201840,
"executionStopTime": 1628191201871,
"hidden_ranges": [],
"originalKey": "a0e4fa8d-ebc7-4dc6-b370-ed4a83e3208f",
"requestMsgId": "9cfd336d-c317-4d1c-a028-42d45903bac6",
"showInput": true
},
"outputs": [],
"source": [
"def evaluate(parameters):\n",
" evaluation = branin_currin(torch.tensor([parameters.get(\"x1\"), parameters.get(\"x2\")]))\n",
" # In our case, standard error is 0, since we are computing a synthetic function.\n",
" # Set standard error to None if the noise level is unknown.\n",
" return {\"a\": (evaluation[0].item(), 0.0), \"b\": (evaluation[1].item(), 0.0)}"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"customInput": null,
"hidden_ranges": [],
"originalKey": "4200cd7c-8e13-4cbf-b0c1-72b52d900aaf",
"showInput": true
},
"source": [
"### Run Optimization"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"customInput": null,
"execution": {
"iopub.execute_input": "2022-11-10T21:07:24.817407Z",
"iopub.status.busy": "2022-11-10T21:07:24.816888Z",
"iopub.status.idle": "2022-11-10T21:07:59.064977Z",
"shell.execute_reply": "2022-11-10T21:07:59.064142Z"
},
"executionStartTime": 1628191208271,
"executionStopTime": 1628191238749,
"originalKey": "f91b1a1e-c78a-4262-a211-a13115c007c1",
"requestMsgId": "842a1cf8-97a3-43d6-83a3-f258ea96ae20",
"showInput": true
},
"outputs": [
{
"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 21:07:24] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.904733, 'x2': 0.900744}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Completed trial 0 with data: {'a': (-139.696442, 0.0), 'b': (-4.378954, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.971915, 'x2': 0.130264}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Completed trial 1 with data: {'a': (-0.939132, 0.0), 'b': (-9.983678, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.475125, 'x2': 0.336992}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Completed trial 2 with data: {'a': (-8.374448, 0.0), 'b': (-9.19126, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.981195, 'x2': 0.55417}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Completed trial 3 with data: {'a': (-31.934563, 0.0), 'b': (-6.059327, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.489548, 'x2': 0.957582}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:24] ax.service.ax_client: Completed trial 4 with data: {'a': (-132.888977, 0.0), 'b': (-4.79389, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:25] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.0, 'x2': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:25] ax.service.ax_client: Completed trial 5 with data: {'a': (-308.129059, 0.0), 'b': (-3.0, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:26] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.0, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:26] ax.service.ax_client: Completed trial 6 with data: {'a': (-17.508297, 0.0), 'b': (-1.180408, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:27] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.0, 'x2': 0.810116}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:27] ax.service.ax_client: Completed trial 7 with data: {'a': (-38.081207, 0.0), 'b': (-1.381634, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:28] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.117739, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:28] ax.service.ax_client: Completed trial 8 with data: {'a': (-6.698983, 0.0), 'b': (-4.801826, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:30] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.053286, 'x2': 0.956613}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:30] ax.service.ax_client: Completed trial 9 with data: {'a': (-5.677922, 0.0), 'b': (-3.332395, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:31] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.734744, 'x2': 0.379224}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:31] ax.service.ax_client: Completed trial 10 with data: {'a': (-40.322601, 0.0), 'b': (-7.786732, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:32] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.024022, 'x2': 0.9742}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:32] ax.service.ax_client: Completed trial 11 with data: {'a': (-11.711469, 0.0), 'b': (-2.193388, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:34] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.090306, 'x2': 0.921506}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:34] ax.service.ax_client: Completed trial 12 with data: {'a': (-1.683393, 0.0), 'b': (-4.546085, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:35] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.0, 'x2': 0.424165}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:35] ax.service.ax_client: Completed trial 13 with data: {'a': (-129.901917, 0.0), 'b': (-2.077045, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:38] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.038255, 'x2': 0.985463}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:38] ax.service.ax_client: Completed trial 14 with data: {'a': (-7.918545, 0.0), 'b': (-2.722753, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:39] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.068927, 'x2': 0.971073}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:39] ax.service.ax_client: Completed trial 15 with data: {'a': (-3.530133, 0.0), 'b': (-3.796133, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:42] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.012105, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:42] ax.service.ax_client: Completed trial 16 with data: {'a': (-13.798748, 0.0), 'b': (-1.673965, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:44] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.028978, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:44] ax.service.ax_client: Completed trial 17 with data: {'a': (-9.511669, 0.0), 'b': (-2.342496, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:47] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.111208, 'x2': 0.878688}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:47] ax.service.ax_client: Completed trial 18 with data: {'a': (-0.767756, 0.0), 'b': (-5.176579, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:48] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.21908, 'x2': 0.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:48] ax.service.ax_client: Completed trial 19 with data: {'a': (-91.569672, 0.0), 'b': (-13.798164, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:50] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.045953, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:50] ax.service.ax_client: Completed trial 20 with data: {'a': (-6.314091, 0.0), 'b': (-2.969521, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:52] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.05963, 'x2': 0.993683}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:52] ax.service.ax_client: Completed trial 21 with data: {'a': (-4.561624, 0.0), 'b': (-3.444644, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:54] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.005949, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:54] ax.service.ax_client: Completed trial 22 with data: {'a': (-15.621313, 0.0), 'b': (-1.423648, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:56] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.07902, 'x2': 0.947881}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:56] ax.service.ax_client: Completed trial 23 with data: {'a': (-2.56357, 0.0), 'b': (-4.159083, 0.0)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:59] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.018447, 'x2': 1.0}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 11-10 21:07:59] ax.service.ax_client: Completed trial 24 with data: {'a': (-12.062981, 0.0), 'b': (-1.929054, 0.0)}.\n"
]
}
],
"source": [
"for i in range(25):\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(trial_index=trial_index, raw_data=evaluate(parameters))"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"customInput": null,
"hidden_ranges": [],
"originalKey": "e0a6feb4-8c38-42e4-9d7c-62b79307e043",
"showInput": false
},
"source": [
"### Plot Pareto Frontier"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"code_folding": [],
"customInput": null,
"execution": {
"iopub.execute_input": "2022-11-10T21:07:59.069226Z",
"iopub.status.busy": "2022-11-10T21:07:59.068399Z",
"iopub.status.idle": "2022-11-10T21:08:13.494395Z",
"shell.execute_reply": "2022-11-10T21:08:13.493470Z"
},
"executionStartTime": 1628191262231,
"executionStopTime": 1628191270720,
"hidden_ranges": [],
"originalKey": "c2c2b222-6b68-4f1a-839f-16b50019ada4",
"requestMsgId": "563d345b-573c-4d93-a480-5db88a283250",
"showInput": true
},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": false
},
"data": [
{
"error_x": {
"array": [
0.050974216532408155,
0.050974216532408155,
0.03503435309646542,
0.05097421662040848,
0.049717646115883724,
0.03646544881070412,
0.05097421659107504,
0.050974216532408155,
0.05097421667907536,
0.05097421662040848,
0.050974216532408155,
0.05097421659107504,
0.050974216532408155,
0.050974216649741916,
0.050974216532408155,
0.04161584268279902,
0.05097421659107504,
0.050974216532408155,
0.05097421667907536,
0.0509742165617416
],
"color": "rgba(128,177,211,0.4)",
"thickness": 2,
"type": "data"
},
"error_y": {
"array": [
0.0022798128840634878,
0.002279812891413774,
0.0015840897723668652,
0.002279812891413774,
0.002126669256373018,
0.0016826133603470754,
0.002279812890188726,
0.002279812891413774,
0.0022798128840634878,
0.002279812891413774,
0.002279812891413774,
0.0022798128889636783,
0.002279812891413774,
0.0022798128950889166,
0.002279812891413774,
0.001869136055996454,
0.0022798128950889166,
0.002279812891413774,
0.0022798128889636783,
0.002279812891413774
],
"color": "rgba(128,177,211,0.4)",
"thickness": 2,
"type": "data"
},
"hoverinfo": "text",
"legendgroup": "mean",
"marker": {
"color": "rgba(128,177,211,1)"
},
"mode": "markers",
"name": "mean",
"text": [
"Parameterization 0
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 2.201686790780075e-15
x2: 1.0",
"Parameterization 1
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 1.0",
"Parameterization 2
a: -12.329 [-12.364, -12.294]
b: -1.889 [-1.891, -1.888]
Parameterization:
x1: 0.017448307142270542
x2: 1.0",
"Parameterization 3
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 9.278955900190044e-18
x2: 1.0",
"Parameterization 4
a: -5.278 [-5.327, -5.228]
b: -3.228 [-3.230, -3.226]
Parameterization:
x1: 0.05351015825595366
x2: 1.0",
"Parameterization 5
a: -11.017 [-11.054, -10.981]
b: -2.092 [-2.094, -2.091]
Parameterization:
x1: 0.022562713646356407
x2: 1.0",
"Parameterization 6
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 6.2938309131930216e-15
x2: 0.9999999999999996",
"Parameterization 7
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 1.0",
"Parameterization 8
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 6.371636918164192e-16
x2: 0.9999999999999996",
"Parameterization 9
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 7.331349539991468e-17
x2: 1.0",
"Parameterization 10
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 1.0",
"Parameterization 11
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 1.834957857489735e-15
x2: 0.9999999999999998",
"Parameterization 12
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 1.0",
"Parameterization 13
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 0.999999999999998",
"Parameterization 14
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 1.0",
"Parameterization 15
a: -6.689 [-6.731, -6.648]
b: -2.885 [-2.887, -2.884]
Parameterization:
x1: 0.04358262654799556
x2: 1.0",
"Parameterization 16
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 4.554780001795659e-16
x2: 0.9999999999999996",
"Parameterization 17
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 0.0
x2: 1.0",
"Parameterization 18
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 5.868376724612924e-17
x2: 1.0",
"Parameterization 19
a: -17.506 [-17.557, -17.455]
b: -1.18 [-1.182, -1.178]
Parameterization:
x1: 7.759762682599398e-18
x2: 1.0"
],
"type": "scatter",
"x": [
-17.505566921334434,
-17.505566921312504,
-12.328590726962041,
-17.505566921310496,
-5.277718822933721,
-11.017102439476758,
-17.505566921331866,
-17.505566921312504,
-17.50556692132441,
-17.505566921334623,
-17.505566921312504,
-17.50556692132842,
-17.505566921312504,
-17.505566921316387,
-17.505566921312504,
-6.689314177501608,
-17.505566921318454,
-17.505566921312504,
-17.50556692131858,
-17.505566921312504
],
"y": [
-1.1801644574586314,
-1.180164457458226,
-1.889161060899189,
-1.180164457458226,
-3.2281714557134493,
-2.0922916690203976,
-1.1801644574593078,
-1.180164457458226,
-1.1801644574580146,
-1.1801644574584667,
-1.180164457458226,
-1.1801644574585635,
-1.180164457458226,
-1.180164457457427,
-1.180164457458226,
-2.8854299414582885,
-1.1801644574585346,
-1.180164457458226,
-1.1801644574584667,
-1.180164457458226
]
}
],
"layout": {
"height": 500,
"hovermode": "closest",
"legend": {
"orientation": "h"
},
"margin": {
"b": 75,
"l": 225,
"pad": 4,
"t": 75
},
"template": {
"data": {
"bar": [
{
"error_x": {
"color": "#2a3f5f"
},
"error_y": {
"color": "#2a3f5f"
},
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "bar"
}
],
"barpolar": [
{
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "barpolar"
}
],
"carpet": [
{
"aaxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"baxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"type": "carpet"
}
],
"choropleth": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "choropleth"
}
],
"contour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"type": "contour"
}
],
"contourcarpet": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "contourcarpet"
}
],
"heatmap": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"type": "heatmap"
}
],
"heatmapgl": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"type": "heatmapgl"
}
],
"histogram": [
{
"marker": {
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "histogram"
}
],
"histogram2d": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"type": "histogram2d"
}
],
"histogram2dcontour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"type": "histogram2dcontour"
}
],
"mesh3d": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "mesh3d"
}
],
"parcoords": [
{
"line": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "parcoords"
}
],
"pie": [
{
"automargin": true,
"type": "pie"
}
],
"scatter": [
{
"fillpattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
},
"type": "scatter"
}
],
"scatter3d": [
{
"line": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatter3d"
}
],
"scattercarpet": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattercarpet"
}
],
"scattergeo": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattergeo"
}
],
"scattergl": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattergl"
}
],
"scattermapbox": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattermapbox"
}
],
"scatterpolar": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatterpolar"
}
],
"scatterpolargl": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatterpolargl"
}
],
"scatterternary": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatterternary"
}
],
"surface": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"type": "surface"
}
],
"table": [
{
"cells": {
"fill": {
"color": "#EBF0F8"
},
"line": {
"color": "white"
}
},
"header": {
"fill": {
"color": "#C8D4E3"
},
"line": {
"color": "white"
}
},
"type": "table"
}
]
},
"layout": {
"annotationdefaults": {
"arrowcolor": "#2a3f5f",
"arrowhead": 0,
"arrowwidth": 1
},
"autotypenumbers": "strict",
"coloraxis": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"colorscale": {
"diverging": [
[
0,
"#8e0152"
],
[
0.1,
"#c51b7d"
],
[
0.2,
"#de77ae"
],
[
0.3,
"#f1b6da"
],
[
0.4,
"#fde0ef"
],
[
0.5,
"#f7f7f7"
],
[
0.6,
"#e6f5d0"
],
[
0.7,
"#b8e186"
],
[
0.8,
"#7fbc41"
],
[
0.9,
"#4d9221"
],
[
1,
"#276419"
]
],
"sequential": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
],
"sequentialminus": [
[
0.0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1.0,
"#f0f921"
]
]
},
"colorway": [
"#636efa",
"#EF553B",
"#00cc96",
"#ab63fa",
"#FFA15A",
"#19d3f3",
"#FF6692",
"#B6E880",
"#FF97FF",
"#FECB52"
],
"font": {
"color": "#2a3f5f"
},
"geo": {
"bgcolor": "white",
"lakecolor": "white",
"landcolor": "#E5ECF6",
"showlakes": true,
"showland": true,
"subunitcolor": "white"
},
"hoverlabel": {
"align": "left"
},
"hovermode": "closest",
"mapbox": {
"style": "light"
},
"paper_bgcolor": "white",
"plot_bgcolor": "#E5ECF6",
"polar": {
"angularaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"bgcolor": "#E5ECF6",
"radialaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
}
},
"scene": {
"xaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"yaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"zaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
}
},
"shapedefaults": {
"line": {
"color": "#2a3f5f"
}
},
"ternary": {
"aaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"baxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"bgcolor": "#E5ECF6",
"caxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
}
},
"title": {
"x": 0.05
},
"xaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
},
"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "Pareto Frontier"
},
"width": 750,
"xaxis": {
"ticksuffix": "",
"title": {
"text": "a"
},
"zeroline": true
},
"yaxis": {
"ticksuffix": "",
"title": {
"text": "b"
},
"zeroline": true
}
}
},
"text/html": [
"