doegen 0.1
DoEgen: A Python Library for Optimised Design of Experiment Generation and Evaluation
Requires Python: >=3.6

DoEgen: A Python Library for Optimised Design of Experiment Generation and Evaluation
=====================================================================================

DoEgen is a Python library aiming to assist in generating optimised
Design of Experiments (DoE), evaluating design efficiencies, and
analysing experiment results.

In a first step, optimised designs can be automatically generated and
efficiencies evaluated for any mixture of factor-levels for numeric and
categorical factors. Designs are automatically evaluated as function of
number of experiment runs and the most efficient designs are suggested.
In particular DoEgen provides computation of a wide range of design
efficiencies and allows to import and evaluate externally generated
designs as well.

The second part of DoEgen assists in analysing any derived experiment
results in terms of factor importance, correlations, and response
analysis for best parameter space selection.

Author: Sebastian Haan

Table of Contents
-----------------

-   [Definitions](#definitions)
-   [Functionality](#functionality)
-   [Installation And Requirements](#installation-and-requirements)
    -   [Requirements](#requirements)
    -   [User Templates](#user-templates)
    -   [Running tests](#running-tests)
    -   [Documentation](#documentation)
-   [Main Modules and Usage](#main-modules-and-usage)
    -   [Design Generation](#design-generation)
    -   [Design Efficiencies](#design-efficiencies)
    -   [Design Selection](#design-selection)
    -   [Experiment Result Analysis](#experiment-result-analysis)
-   [Use Case Study](#use-case-study)
-   [Comparison to Other DoE Tools](#comparison-to-other-doe-tools)
-   [Literature](#literature)
-   [Attribution and Acknowledgments](#attribution-and-acknowledgements)
-   [License](#license)

Definitions
-----------

An Experiment Design is typically defined by:

-   Number of Factors: the parameters or variates of the experiment
-   Number of Runs: the number of experiments
-   Levels: The number of value options for each factor, which can be
    either numeric values (discrete or continuous) or categorical.
    Discrete levels for continuous factors can be obtained by providing
    the minimum and maximum of the factor range and the number of
    levels. The more levels, the more “fine-grained” the experiment will
    evaluate this factor, but also more experimental runs are required.

The goal of optimising an experimental design is to provide an efficient
design that is near-optimal in terms of, e.g., orthogonality, level
balance, and two-way interaction coverage, yet can be performed with a
minimum number of experimental runs, which are often costly or
time-consuming.

Functionality
-------------

If you would like to jumpstart a new experiment and to skip the
technical details, you can find a summary of the main usage of DoEgen in
\[Case Study Use Case\].

Currently, the (preliminary) release contains several functions for
generating and evaluating designs. Importing and evaluating external
designs is supported (e.g. for comparison to other DoE generator tools).
DoE also implements several functions for experiment result analysis and
visualisation of parameter space.

The main functionalities are (sorted in order of typical experiment
process):

-   Reading Experiment Setup Table and Settings (Parameter Name, Levels
    for each factor, Maximum number of runs, Min/Max etc)
-   Generating optimised design arrays for a range of runs (given
    maximum number of runs, and optional computation-time constrains,
    see `settings_design.yaml`).
-   Evaluation and visualisation of more than ten design efficiencies
    such as level balance, orthogonality, D-efficiencies etc (see
    [Design Efficiencies](#design-efficiencies) for the complete list).
-   Automatic suggestion of minimum, optimal, and best designs within a
    given range of experiment runs.
-   Import and evaluation of externally generated design arrays.
-   Experiment result analysis: Template table for experiment results,
    multi-variant RMSE computation, best model/parameter selection,
    Factor Importance computation, pairwise response surface and
    correlation computation, factor correlation analysis and Two-way
    interaction response plots.
-   Visualisation of experiment results.

Installation And Requirements
-----------------------------

### Requirements

-   Python \>= 3.6
-   SWIG \>=3.0.12
-   OApackage
-   xlrd
-   XlsxWriter
-   Numpy
-   Pandas
-   PyYAML
-   scikit\_learn
-   matplotlib
-   seaborn

The DoEgen package is currently considered experimental and has been
tested with the libraries specified in `requirements.txt`.

The OApackage requires an installation of SWIG, which can be found at 
https://www.dev2qa.com/how-to-install-swig-on-macos-linux-and-windows/ 
or can be installed via conda

```sh
conda install swig
```

After installing `swig` and `numpy`, DoEgen can be installed locally with

``` sh
python setup.py build 
python setup.py install
```

Note that OAPackage can be also installed manually by following installation instructions and documentation for OApackage (tested with
OApackage 2.6.6), which can be found at https://pypi.org/project/OApackage/.


### User Templates

1.  The factor (parameter) settings of experiment are defined in an
    experiment setup table (see Experiment\_results\_template.xlsx). A
    new excel setup template table can be also created with
    create\_setupfile.py. Each factor is on a new row and specified by
    `Parameter Name`, `Parameter Type` , `Level Number`, `Minimum`,
    `Maximum`

2.  After the experiment is run, the results have to be filled in an
    experiment result table (see `Experiment_results_template.xlsx`). A
    new excel result template table can be also created with
    `create_resultfile.py` The result table allows to fill in multiple
    output properties (Y\_label: output target to be predicted) and
    experiment positions. The results have to be provided in the table
    with the following columns:

-   `Nexp`: Run\# of experiment, need to match Run\# in Experiment setup
    and design.
-   `PID`: Identifier\# of label of location (point) in experiment
    (e.g. if experiment is run at different locations simultaneously).
-   `Y Label`: Identifier\# or label of Y-Variate (target property that
    has to be predicted or evaluated, e.g. Rain and Temperature). This
    allows to include multi-output models with distinct target
    properties. Note that currently each Y variate is evaluated
    separately.
-   `Y Exp` The experiment result for Y
-   `Y Truth` (optional) if the true value available is available for Y.
    This is required to calculate the RMSE and to select best parameter
    space.
-   Not currently considered (yet) in result stats computation:
    `Std Y Exp`, `Std Y Truth`, `Weight PID`

<figure>
<img src="figures/Setup_header.png" width="600" alt="" /><figcaption>Experiment Setup Table Header.</figcaption>
</figure>

<figure>
<img src="figures/Result_header.png" width="600" alt="" /><figcaption>Experiment Result Table Header.</figcaption>
</figure>

### Running Tests

To verify that DoEgen works, you can run the example experiment

``` bash
$ python -m doegen.init_tests
$ python -m doegen.doegen test/settings_design_test.yaml
$ python -m doegen.doeval test/settings_expresults_test.yaml
```

### Documentation

Please do not modify `README.md`. Instead make any changes in the master
documentation file `MANUAL.md` (uses pandoc markdown syntax) and then
convert to the inferior Github markdown flavor (note thta the new
github-flavored markdown format gfm option does not correctly solve
figure caption and resize options):

``` bash
pandoc -f markdown -t markdown_github MANUAL.md -o README.md
```

and to pdf:

``` bash
pandoc -V geometry:margin=1.2in MANUAL.md -o docs/MANUAL.pdf
```

or as standalone html:

``` bash
pandoc MANUAL.md -o MANUAL.html
```

Main Modules and Usage
----------------------

### Design Generation

Design generation with `doegen.py`: Main model for generating optimised
designs and computation of efficiencies. Settings are specified in
settings yaml file `settings_design.yaml`. Before executing `doegen.py`,
two things have to be the done:

1.  fill in experiment setup table (see template provided
    `Experiment_setup_template.xlsx` or example in `test/` folder)
2.  provide settings in settings file (see `settings_design.yaml`) Then

``` bash
$ python doegen.py settings_design.yaml
```

This will produce a number of files for different experiment run length
(see folder `test/results/DesignArray_Nrun...`):

-   The optimised design array `EDarray_[factor_levelels]_Nrun.csv`.
-   A table of design efficiencies
    `Efficiencies_[factor_levelels]_Nrun.csv`
-   Table of Canonical Correlation Coefficients
    `Table_Canonical_Correlation.csv`
-   Table of two-way Interaction balance `Table_Interaction_Balance.txt`
-   Table of Pearson correlation coefficients between all factor pairs
    `Table_Pearson_Correlation.csv`
-   Plot of pairwise correlation including regression fit
    `pairwise_correlation.png` (see example plot below)

Besides the default optimisation (based on function
`doegen.optimize_design`), DoEgen also allows the to construct full
orthogonal designs using the function `doegen.gen_highD`, which is based
on OApackage orthogonal arrays and extensions. However, this works only
for special cases with limited number of factors and design levels.
Thus, it is currently not fully automated but might assist advanced
users to construct optimal designs.

### Design Selection

DoEgen will select by default three designs based on the following
citeria:

1.  minimum Design with the criteria:

-   number of runs \>= number of factors + 1
-   center balance \> 95%
-   level balance \> 95%
-   Orthogonal Balance \> 90%
-   Two Level interaction Balance \> 90%
-   Two Level Interaction Minimum One = 100%

1.  optimal Design with the criteria:

-   center balance \> 98%
-   level balance \> 98%
-   Orthogonal Balance \> 95%
-   Two Level interaction Balance \> 95%
-   Two Level Interaction Minimum One = 100%

1.  best design which is based on best score that is sum of efficiencies
    above and includes a small penalty for runsize relative to maximum
    runsize

This will deliver (see folder `test/results/`):

-   Overview summary of the three designs and their main efficiencies:
    `Experiment_Design_selection_summary.txt`
-   Three tables (`Designtable_minimum/optimal/best...csv`) for the
    there suggested designs that are converted in the actual level
    values
-   An overview of the efficiencies is plotted as function of exp run
    and saved in `Efficiencies_[factor_levels].png`

In case the user wants to select another design for a different run
size, one can covert the design array into a design table with the
function `doegen.array2valuetable()`.

<figure>
<img src="figures/Efficiencies.png" width="400" alt="" /><figcaption>Example overview plot of the main efficiencies (from 0=worst to 100=best) as function of number of experiments.</figcaption>
</figure>

### Design Efficiencies

EoDgen computes more than ten efficiencies and saves them as .csv file
for each generated design arrays. All indicators, except for the
canonical correlations, ave a range from 0 (worst possible) to 1
(optimal):

-   Center Balance: 100% \[1 - Sum(Center-Deviation)/Array Size\],
    i.e. ,the average center balance over all factors.
-   Level Balance: Defined as 100% \[1 - Sum(Imbalance)/Array Size\],
    the average level balance over all factors.
-   Orthogonality: Defined as 100% \[1 - Orthogonality\], i.e. the
    average orthogonality over all factor pairs.
-   Two-way Interaction Balance: Similar to level balance but for
    pairwise factor balance.
-   Two-way Interaction with at least one occurrence: 100% \[1 - Sum(Not
    at least one pairwise factor occurrence)/number of pairwise
    combinations\]; 100% if all factor-level pair combinations occur at
    least once.
-   D-Eff: D-Efficiency (model includes main term and quadratic).
-   D1 Eff: only main terms
-   D2 Eff: main, quadratic, and interaction terms
-   A-Eff: A-efficiency (main term and quadratic)
-   A1-Eff: only main terms
-   A2-Eff: main, quadratic, and interaction terms
-   Acor\_can\_avg: average canonical correlation efficiency
-   Acor\_can\_max: maximal canonical correlation coefficient

For further inspection, `doegen.evaluate_design2` creates also the
following tables and plots:

-   Table of Canonical Correlation
-   Table of Pearson Correlation (same as above if normalised discrete
    variables)
-   Table of Two-way Interaction Balance
-   Cornerplot of pairwise factor relation with Y

<figure>
<img src="figures/pairwise_correlation.png" width="600" alt="" /><figcaption>Pairwise factor correlation plot of an example 8 factor design array with a mix of 3- and 2-level factors. The lines and blue shadows correspond to the linear regression fit and its uncertainty. Two pairs are 100% orthogonal if the linear regression line is horizontal. The diagonal bar charts show the histogram of level values for each factor (perfect level balance if histogram is flat).</figcaption>
</figure>

### Experiment Result Analysis

Experiment Result Analysis with `doeval.py`: The experiment results have
to be provided in a result table with the format as specified in
\#user-templates, and specifications in the `settings_expresults.yaml`
file. Then run

``` bash
$ python dovale.py settings_expresults.yaml
```

This will create the following stats tables and plots (see folder
`test/expresults/` as example):

-   A valuation of the factors in term of “importance”, which is defined
    by the maximum change (range) in the average Y between any factor
    levels. Results are visualized in bar plot and saved as csv,
    including, min, max, std deviation across all levels
-   Computes RMSE between experiment result and ground truth; results
    saved as csv.
-   Ranks list of top experiments and their parameters based on RMSE
-   Computes average and variance of best parameters weighted with RMSE;
    saved to csv file
-   An overview plot of all the correlation plots between Y and each
    factor (see function `plot_regression`)
-   Moreover it will plot Y value for each pairwise combination of
    factors (see function `plot_3dmap`), which allows the user to
    visualise categorical factors

<figure>
<img src="figures/Expresult_correlation_X_1.png" width="600" alt="" /><figcaption>Overview plot of X-Y Correlation for each factor as function of their level values. On top the linear regression coefficient <code>r</code> is shown along the linear regression fit and its uncertainty (line and shadow).</figcaption>
</figure>

<figure>
<img src="figures/Expresult_pairwise-correlation_1.png" width="600" alt="" /><figcaption>Cornerplot of pairwise factor relation with Y. The color(bar) indicates the value of Y.</figcaption>
</figure>

Use Case Study
--------------

Here we demonstrate a typical use case where we would like to first
generate and select an optimal experiment design. Then subsequently
after running the experiment we would like to answer the question which
is the best parameter space and what parameters are important. Our case
study is given by the test example, which consists of 8 factors
(parameters) that are specified in the experiment setup table
`Experiment_setup_test.xlsx`.

<figure>
<img src="figures/Setup_header_test.png" width="600" alt="" /><figcaption>Test Experiment Setup Table with 6 discrete and 2 categorical factors. Each factor can have a certain number of levels (values), which are here either 3 or 2</figcaption>
</figure>

The first goal is to generate an efficient design with only a fraction
of the entire parameter combination (in our case the full factorial
would be 3<sup>6</sup> × 2<sup>2</sup> = 2916). The maximum number of
experiments (in this case we choose 150) is set in the file
`settings_design_test.yaml`, which also specifies input and output
directory names, as well as the maximum time for optimising one run (in
this case 100seconds per design optimisation). This configuration will
generate and optimize a range of experiments with different designs run
sizes from 12 to 150, in steps of 6 runsizes (since the lowest common
multiple of our mix of 2 and 3 factor levels is 6). Note that the user
can also choose a different stepsize, which can done by setting the
value in the setting parameter `delta_nrun`. Now we are all setup to
start the experiment design generation and optimisation script, which we
do by running the script doegen.py with the settings file as argument:

``` bash
$ cd DoEgen
$ python doegen.py test/settings_design_test.yaml
```

This will generate for each runsize an optimised design array and a list
of efficiencies and diagnostic tables and plots (see [Design
Generation](#design-generation) for more details). To simplify the
selection of the generated experiment designs, DoEgen suggests
automatically three designs: 1) one minimum design (lowest number of
runs at given efficiency threshold), 2) one optimal design, and 3) one
best design (either equal or has larger experiment run number than
optimal design). In our case the three design are selected for run
numbers 30 (minimum), 72 (optimal), 90 (best). Since the optimal design
has basically almost the same efficiencies as the best design (see
figure below) but at a lower cost of experiment runs, we choose for our
experiment the optimal design, which is given in the table
`Designtable_optimal_Nrun72.csv`.

<figure>
<img src="figures/Results_overview.png" width="600" alt="" /><figcaption>Result Overview of Experiment Design Generation and the three suggested choices. The most important criteria for a good design are orthogonality (100% means that all factor pairs are 100% orthogonal to each other), level/center balance (100% is best) and two-way interaction balance (100% is best). We also want to make sure that at each pairwise interaction occurs at least one (100% Two-Level Min Efficiency). D-efficiency maximises the determinant of the information matrix <span class="math inline">|<em>X</em><sup><em>T</em></sup><em>X</em>|</span>, which corresponds to minimizing the generalized variance of the parameter estimates for a pre-specified model <span class="math inline"><em>X</em></span>. Here, D1-efficiency defines the model with only the main effects, while D-efficiency includes also all quadratic terms in the model <span class="math inline"><em>X</em></span>. Typically D1-efficiency should be larger than 60%, while D-efficiency only increases if number of experiments is much larger than the number of model terms. In this case study we consider only D1-efficiency given that we want to minimize the number of experiments.</figcaption>
</figure>

<figure>
<img src="figures/Designtable_optimal_Nrun72.png" width="600" alt="" /><figcaption>Header with first 5 rows of the optimal design with 72 experiments</figcaption>
</figure>

Now it is time to run the experiment. In our example, we produce just
some random data for the 72 experiments with 10 sensor locations (PID 1
to 10) and one output variable Y (e.g. temperature). To analyse the
experiment, the results have to written in a structured table with the
format as given in `experiment_results_Nrun72.xlsx` (see description in
figure below).

<figure>
<img src="figures/Experiment_result_Nrun72_header.png" width="600" alt="" /><figcaption>Header with first rows of the experiment result table for 72 experiments. Note that the <code>Nexp</code> number has to match the experiment design table <code>Nexp</code>. Each experiment (label <code>Nexp</code>) can have multiple locations or points (identifier# <code>PID</code>), e.g., if experiment is run at different locations simultaneously. In addition, it is possible that one has multiple output Y-variates, labeled with identifier <code>Y :abel</code> (target property that has to be predicted or evaluated, e.g. Rain and Temperature). The column <code>Y Exp</code> holds the experiment result for Y while the column <code>Y Truth</code>holds the ground truth value, which is required to calculate the RMSE and to select best parameter space.</figcaption>
</figure>

To run the experiment analysis script, settings such as for input output
directory names are given in the settings file
`settings_expresults_test.yaml`, and we can now run the analysis script
with

``` bash
$ python doeval.py test/settings_expresults_test.yaml
```

This analysis produces a range of diagnostic tables and result plots for
each output variable Y (in our case we have only one Y). One of the
question of this example use case is to identify what factors are
important, which is given in the figure `Ybarplot.png`. The “importance”
basically indicates how much a factor changes Y (defined by the maximum
average change in Y between any levels). This has the advantage to
identify also important factors that have either a low linear regression
coefficients with Y (see r values in plot `Expresult_correlation_X.png`)
or are categorical. Such insight can be valuable to determine, e.g.,
which factors should be investigated in more detail in a subsequent
experiment or to estiamate which factors have no effect on Y.

<figure>
<img src="figures/Ybarplot_1.png" width="600" alt="" /><figcaption>Factor Importance ranked from maximum to lowest change (range) in Y</figcaption>
</figure>

Another important question is what are the best parameter values based
on the obtained experiment results so far? This question can be answered
by computing the Root-Mean-Square-Error between experiment results and
ground truth (or alternatively the likelihood if the model predictions
include also uncertainties). Table `Experiment_1_RMSE_Top10_sorted.csv`
provides an overview of the top 10 experiments sorted as function of
their RMSE. Moroever we can calculate the (RMSE-weighted) average of
each factor for the top experiments as shown in bar plot below.

<figure>
<img src="figures/Top10.png" width="600" alt="" /><figcaption>Picture of Table <code>Experiment_1_RMSE_Top10_sorted.csv</code> which shows the factor values of the top 10 experiments based on their RSME values.</figcaption>
</figure>

<figure>
<img src="figures/BestFactor_Avg1.png" width="600" alt="" /><figcaption>Factor values of the top 10 experiments based on their RSME values. The bar heights indicate the top factor’s average value and the dark lines their standard deviation. Note that the average and their standard deviation are computed with the weights <span class="math inline"><em>R</em><em>M</em><em>S</em><em>E</em><sup> − 2</sup></span>.</figcaption>
</figure>

Furthermore, multiple other diagnostics plots such as factor-Y
correlation and pairwise correlation maps are generated (see [Experiment
Result Analysis](#experiment-result-analysis) for more details).

Comparison to Other DoE Tools
-----------------------------

The aim of DoEgen is to provide an open-source tool for researchers to
create optimised designs and a framework for transparent evaluation of
experiment designs. Moreover, DoEgen aims to assist the result analysis
that may allow the researcher a subsequent factor selection, parameter
fine-tuning, or model building. The design generation function of DoEgen
is build upon the excellent package `OApackage` and extends it further
in terms of design efficiency evaluation, filtering, automation, and
experiment analysis. There are multiple other tools available for DoE;
the table below provides a brief (preliminary) summary of the main
advantages and disadvantages for each tool that has been tested.

| Feature                   |  SAS JMP  |  pyDOE2 | OApackage |   DoEgen   |
|---------------------------|:---------:|:-------:|:---------:|:----------:|
| Open-Source               | no (paid) |   yes   |    yes    |     yes    |
| Design Optimisation Score | very good | limited |    good   |    good    |
| Optimal Runsize Finder    |     no    |    no   |     no    |     yes    |
| Design Efficiency Eval    |    yes    |    no   |  limited  |     yes    |
| Exp Result Analysis       |    yes    |    no   |     no    |     yes    |
| Development Stage         |  advanced |  early  |  moderate | very early |

Literature
----------

[OApackage: A Python package for generation and analysis of orthogonal
arrays, optimal designs and conference
designs](https://doi.org/10.21105/joss.01097), P.T. Eendebak, A.R.
Vazquez, Journal of Open Source Software, 2019

[pyDOE2: An experimental design package for
python](https://github.com/clicumu/pyDOE2)

Dean, A., Morris, M., Stufken, J. and Bingham, D. eds., 2015. Handbook
of design and analysis of experiments (Vol. 7). CRC Press.

Goos, P. and Jones, B., 2011. Optimal design of experiments: a case
study approach. John Wiley & Sons.

Kuhfeld, W.F., 2010. Discrete choice. SAS Technical Papers, 2010,
pp.285-663.

Zwerina, K., Huber, J. and Kuhfeld, W.F., 1996. A general method for
constructing efficient choice designs. Durham, NC: Fuqua School of
Business, Duke University.

Cheong, Y.P. and Gupta, R., 2005. Experimental design and analysis
methods for assessing volumetric uncertainties. SPE Journal, 10(03),
pp.324-335.

JMP, A. and Proust, M., 2010. Design of experiments guide. Cary, NC: SAS
Institute Inc.

Attribution and Acknowledgments
-------------------------------

Acknowledgments are an important way for us to demonstrate the value we
bring to your research. Your research outcomes are vital for ongoing
funding of the Sydney Informatics Hub.

If you make use of this code for your research project, please include
the following acknowledgment:

“This research was supported by the Sydney Informatics Hub, a Core
Research Facility of the University of Sydney.”

Contributors
------------

We would like to thank Dietmar Muller (School of Geophyics, University
of Sydney) for suggesting the need for this library, Danial Azam (School
of Geophyics, University of Sydney) for testing DOEgen on real-world
cases, Christopher Howden (SIH, University of Sydney) for
statistical consultancy, literature suggestions, and documentation
review, and Joel Nothman for the code review. 

DoEgen has benefited from the OApackage library
[OApackage](https://github.com/eendebakpt/oapackage) for the design
optimisation code and we would like to thank the researchers who have
made their code available as open-source.

License
-------

Copyright 2020 Sebastian Haan, The University of Sydney

DoEgen is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License (AGPL version 3) as published by the Free Software Foundation.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Affero General Public License for more details.

You should have received a copy of the GNU Affero General Public License along with this program (see LICENSE.md). If not, see [https://www.gnu.org/licenses/](https://www.gnu.org/licenses/).