## Sequences of Pareto reflections

**What are sequences of Pareto reflections?**
Sequences of Pareto reflections are a Pythonic implementation of a mathematical (possibly finite) sequence
of Pareto reflections.

**Why using sequences of Pareto reflections?**
With sequences of Pareto reflections we can target different (possibly excluding) properties of Pareto points
within one MOO run. For example, we have Pareto reflections which target a certain corner of the Pareto front.
By constructing a sequence of Pareto reflections using different Pareto reflections which target different corners
we can construct a sequence which targets all corners.

**How do we use sequences of Pareto reflections?**
This is done by calling the ``apply_to_sequence`` method of some MOO algorithm (implemented in the ``ParefMOO``
interface)
to the sequence of Pareto reflections.

```python
from paref.moo_algorithms.minimizer.gpr_minimizer import GPRMinimizer
from paref.moo_algorithms.stopping_criteria.max_iterations_reached import MaxIterationsReached
from paref.pareto_reflection_sequences.multi_dimensional.find_edge_points_sequence import FindEdgePointsSequence

moo = GPRMinimizer()
reflection = FindEdgePointsSequence()
stopping_criteria = MaxIterationsReached(max_iterations=1)
moo.apply_to_sequence(blackbox_function=bbf,
                      sequence_pareto_reflections=reflection,
                      stopping_criteria=stopping_criteria)
```

All sequences are found within the ``paref.pareto_reflection_sequences`` module.
You can access the Pareto points fitting the properties best by calling the ``best_fits`` attribute.
Currently, Paref includes implementations of the following sequences of Pareto reflections
(illustrated by their corresponding property):

|                                                 Property                                                  |                                     Graphic                                     |              Sequence               | Supported target space dimension |       Note       |
|:---------------------------------------------------------------------------------------------------------:|:-------------------------------------------------------------------------------:|:-----------------------------------:|:--------------------------------:|:----------------:|
|                                       Filling gaps of Pareto front                                        | ![Fill Gaps](../graphics/plots/reflections/FillGapsOfParetoFrontSequence2D.svg) | ``FillGapsOfParetoFrontSequence2D`` |                2                 |                  |
|                                 Being the edge points of the Pareto front                                 |    ![Edge Points](../graphics/plots/reflections/FindEdgePointsSequence.svg)     |     ``FindEdgePointsSequence``      |               All                |                  |
|                           Being minimal in some component (for all components)                            |  ![1 Pareto Points](../graphics/plots/reflections/FindEdgePointsSequence.svg)   |     ``FindEdgePointsSequence``      |               All                |                  |
|                            Repeating a (list of) Pareto reflections (generic)                             |                                                                                 |        ``RepeatingSequence``        |               All                | Generic sequence |
| Repeating a single Pareto reflection of a list of reflections until a stopping criterion is met (generic) |                                                                                 |   ``NextWhenStoppingCriteriaMet``   |               All                | Generic Sequence |