@@ -7,27 +7,25 @@ Genetic Algorithms such as NSGA2 are even less trivial.

Their implementation in the [mgo](https://github.com/openmole/mgo) used in [OpenMole](https://openmole.org/) was adapted so they are efficient for computation on clusters or grids.

This leaves a lot of uncertainty to the user on what really happens.

Why should you, as a user, trust this implementation?

The answer is simple: you should not.

Any implementation in scientific computing should be verified.

The answer is simple: you should not.

Any implementation in scientific computing should be verified to be trusted.

## Test Functions

Many functions named "Test Functions" were proposed over time to test and compare multi-objective optimization algorithmls.

Many functions named "Test Functions" were proposed over time to test and compare multi-objective optimization algorithms.

The [wikipedia page](https://en.wikipedia.org/wiki/Test_functions_for_optimization) lists several of them.

A test function is an optimization function which you can propose as the problem to optimize to your implementation.

Functions test:

A test function is an function you can use as the problem to optimize, for which the expected results are known.

Test functions might test:

- problems with multiple parameters and multiple objectives

- problems with constraints: a part of the space of parameter leads to computation errors as a result, so the algorithm should achieve to deal with it

- problems with parts of the space of solution that are tricky to detect, either because they are statistically unlikely to find, or because they are is a part of the space of solutions which is heavily constrained, etc.

- problems with constraints: a part of the space of solutions can not be computed, so the algorithm should achieve to deal with it

- problems with parts of the space of solution that are tricky to detect, either because they are statistically unlikely to find, or because they are in a part of the space of solutions which is heavily constrained, etc.

Test tunctions enable the testing of several aspects including:

The results of a test function are usually compared in both terms of:

- coverage of the Pareto front,

- speed of convergence

Once a test function was explored by an implementation of an algorithm, you should compare the Pareto front obtained withou your implementation with the one expected in literature.

## Test and Learn

...

...

@@ -35,14 +33,22 @@ Test functions have another role: they constitute a simple example of optimizati

As a user, you can also learn to tune the parameters of the genetic algorithm as check when convergence

occurs.

## Test Workflows for OpenMole

We provide here a few examples of test functions which you can open with OpenMole.

For each workflow:

- Choose a test function.

- Run the workflow.

- Open the files with the solutions, check you understand them.

- Graph them and compare them with the literature (you have these results in the [wikipedia page](https://en.wikipedia.org/wiki/Test_functions_for_optimization)).

- ConstrEx

- CP1

- Schaffer N1

- Schaffer N2

To run a test

- Choose one of the workflows starting with "test function"

- Run the workflow

- Update the view on the left using the "refresh" button

- Download the graph of the last Pareto front, and compare it with the literature (you might use the [wikipedia page](https://en.wikipedia.org/wiki/Test_functions_for_optimization) )

You might then tune the parameters of the optimization algorithm and analyze the results, to understand how to better use the optimization method.