CHORES: pre-commit

00_intro.md

@@ -69,20 +69,20 @@ awaits you in this primer:
 
 1. [Installation](#01-installation): Quick installation guide.
 2. [Example](#02-example): A short example, showing the usage of CP-SAT.
-3. [Alternatives](#03-big-picture): An overview of the different
-   optimization techniques and tools available. Putting CP-SAT into context.
+3. [Alternatives](#03-big-picture): An overview of the different optimization
+   techniques and tools available. Putting CP-SAT into context.
 4. [Modelling](#04-modelling): An overview of variables, objectives, and
    constraints. The constraints make the most important part.
 5. [Parameters](#05-parameters): How to specify CP-SATs behavior, if needed.
    Timelimits, hints, assumptions, parallelization, ...
-6. [Coding Patterns](#06-coding-patterns): Basic design
-   patterns for creating maintainable algorithms.
+6. [Coding Patterns](#06-coding-patterns): Basic design patterns for creating
+   maintainable algorithms.
 7. [How does it work?](#07-under-the-hood): After we know what we can do with
    CP-SAT, we look into how CP-SAT will do all these things.
-8. [Benchmarking your Model](#08-benchmarking): How to benchmark your
-   model and how to interpret the results.
-9. [Large Neighborhood Search](#09-lns):
-   The use of CP-SAT to create more powerful heuristics.
+8. [Benchmarking your Model](#08-benchmarking): How to benchmark your model and
+   how to interpret the results.
+9. [Large Neighborhood Search](#09-lns): The use of CP-SAT to create more
+   powerful heuristics.
 
 ---
 
@@ -108,14 +108,14 @@ awaits you in this primer:
 > write me a quick mail to `krupked@gmail.com`.
 
 > **Want to Contribute?** If you are interested in contributing, please open an
-> issue or email me with a brief description of your proposal. We can
-> then discuss the details. I welcome all assistance and am open to expanding
-> the content. Contributors to any section or similar input will be recognized
-> as coauthors.
+> issue or email me with a brief description of your proposal. We can then
+> discuss the details. I welcome all assistance and am open to expanding the
+> content. Contributors to any section or similar input will be recognized as
+> coauthors.
 
 > **Want to use/share this content?** This tutorial can be freely used under
 > [CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/). Smaller parts can
 > even be copied without any acknowledgement for non-commercial, educational
 > purposes.
 
----
+---

01_installation.md

@@ -1,8 +1,9 @@
 <!-- EDIT THIS PART VIA 01_installation.md -->
 
-## Installation
 <a name="01-installation"></a>
 
+## Installation
+
 We are using Python 3 in this primer and assume that you have a working Python 3
 installation as well as the basic knowledge to use it. There are also interfaces
 for other languages, but Python 3 is, in my opinion, the most convenient one, as

02_example.md

@@ -1,8 +1,9 @@
 <!-- EDIT THIS PART VIA 02_example.md -->
 
-## Example
 <a name="02-example"></a>
 
+## Example
+
 Before we dive into any internals, let us take a quick look at a simple
 application of CP-SAT. This example is so simple that you could solve it by
 hand, but know that CP-SAT would (probably) be fine with you adding a thousand
@@ -193,4 +194,4 @@ higher-level constraints, such as conditional constraints that are only enforced
 if some variable is set to true, in MIPs yourself, because the computer is not
 very good at that).
 
----
+---

03_big_picture.md

@@ -1,8 +1,8 @@
 <!-- EDIT THIS PART VIA 03_big_picture.md -->
-<a name="section-alternatives"></a>
+
+<a name="section-alternatives"></a> <a name="03-big-picture"></a>
 
 ## Alternatives: CP-SAT's Place in the World of Optimization
-<a name="03-big-picture"></a>
 
 When you begin exploring optimization, you will encounter a plethora of tools,
 techniques, and communities. It can be overwhelming, as these groups, while
@@ -165,4 +165,4 @@ problems, you should definitely get familiar with CP-SAT. It is good enough for
 most problems, and superior for some, which is amazing for a free and
 open-source tool.
 
----
+---

04_modelling.md

@@ -1,7 +1,9 @@
 <!--EDIT THIS PART VIA 04_modelling.md -->
-## Modelling
+
 <a name="04-modelling"></a>
 
+## Modelling
+
 CP-SAT provides us with much more modelling options than the classical
 MIP-solver. Instead of just the classical linear constraints (<=, ==, >=), we
 have various advanced constraints such as `AllDifferent` or
@@ -142,8 +144,8 @@ variables needed.
 However, CP-SAT employs a lazy creation strategy for these boolean variables.
 This means it only generates them as needed, based on the solver's
 decision-making process. Therefore, an integer variable with a wide range - say,
-from 0 to 100 - will not immediately result in 200 boolean variables. It might lead
-to the creation of only a few, depending on the solver's requirements.
+from 0 to 100 - will not immediately result in 200 boolean variables. It might
+lead to the creation of only a few, depending on the solver's requirements.
 
 Limiting the domain of a variable can have drawbacks. Firstly, defining a domain
 explicitly can be computationally costly and increase the model size drastically
@@ -1023,8 +1025,8 @@ model.Minimize(y)
 
 This can be quite tedious, but luckily, I wrote a small helper class that will
 do this automatically for you. You can find it in
-[./utils/piecewise_functions](https://github.com/d-krupke/cpsat-primer/blob/main/utils/piecewise_functions/). Simply copy it into
-your code.
+[./utils/piecewise_functions](https://github.com/d-krupke/cpsat-primer/blob/main/utils/piecewise_functions/).
+Simply copy it into your code.
 
 This code does some further optimizations:
 

05_parameters.md

@@ -1,8 +1,9 @@
 <!-- EDIT THIS PART VIA 05_parameters.md -->
 
-## Parameters
 <a name="05-parameters"></a>
 
+## Parameters
+
 The CP-SAT solver has a lot of parameters to control its behavior. They are
 implemented via
 [Protocol Buffer](https://developers.google.com/protocol-buffers) and can be
@@ -38,9 +39,9 @@ we run the solver:
 solver.parameters.max_time_in_seconds = 60  # 60s timelimit
 ```
 
-We now of course have the problem, that maybe we will not have an optimal solution,
-or a solution at all, we can continue on. Thus, we need to check the status of
-the solver.
+We now of course have the problem, that maybe we will not have an optimal
+solution, or a solution at all, we can continue on. Thus, we need to check the
+status of the solver.
 
 ```python
 status = solver.Solve(model)
@@ -76,8 +77,8 @@ $abs(O - B) / max(1, abs(O))$ of the bound (B). To stop as soon as we are within
 solver.parameters.relative_gap_limit = 0.05
 ```
 
-Now we may want to stop after we did not make progress for some time or whatever.
-In this case, we can make use of the solution callbacks.
+Now we may want to stop after we did not make progress for some time or
+whatever. In this case, we can make use of the solution callbacks.
 
 > For those familiar with Gurobi: Unfortunately, we can only abort the solution
 > progress and not add lazy constraints or similar. For those not familiar with
@@ -513,4 +514,4 @@ some conflicts.
 > it performed worse. Further, I assume that CP-SAT can learn the best strategy
 > (Gurobi does such a thing, too) much better dynamically on its own.
 
----
+---

06_coding_patterns.md

@@ -1,8 +1,9 @@
-
 <!-- EDIT THIS PART VIA 06_coding_patterns.md -->
-## Coding Patterns for Optimization Problems
+
 <a name="06-coding-patterns"></a>
 
+## Coding Patterns for Optimization Problems
+
 In this section, we will explore various coding patterns that are essential for
 structuring implementations for optimization problems using CP-SAT. While we
 will not delve into the modeling of specific problems, our focus will be on
@@ -664,4 +665,4 @@ class KnapsackSolver:
   any logic to decide which variables are needed upfront, simplifying the model
   construction process.
 
----
+---

07_under_the_hood.md

@@ -1,8 +1,9 @@
 <!-- EDIT THIS PART VIA 07_under_the_hood.md -->
 
-## How does it work?
 <a name="07-under-the-hood"></a>
 
+## How does it work?
+
 CP-SAT is a versatile _portfolio_ solver, centered around a _Lazy Clause
 Generation (LCG)_ based Constraint Programming Solver, although it encompasses a
 broader spectrum of technologies.
@@ -180,4 +181,4 @@ such as modulo constraints. However, it's noteworthy that I am not aware of any
 alternative solver capable of efficiently addressing these specific constraints.
 At times, NP-hard problems inherently pose formidable challenges, leaving us
 with no alternative but to seek more manageable modeling approaches instead of
-looking for better solvers.
+looking for better solvers.

08_benchmarking.md

@@ -1,8 +1,9 @@
 <!-- EDIT THIS PART VIA 08_benchmarking.md -->
 
-## Benchmarking your Model
 <a name="08-benchmarking"></a>
 
+## Benchmarking your Model
+
 Benchmarking is an essential step if your model is not yet meeting the
 performance standards of your application or if you are aiming for an academic
 publication. This process involves analyzing your model's performance,
@@ -207,8 +208,8 @@ and research questions. Here are some strategies to keep things organized:
 - **Experiment Flexibility**: Design experiments to be interruptible and
   extendable, allowing for easy resumption or modification. This is especially
   important for exploratory studies, where you may need to make frequent
-  adjustments. However, if your workhorse study takes a long time to run, you
-  do not want to repeat it from scratch if you want to add a further solver.
+  adjustments. However, if your workhorse study takes a long time to run, you do
+  not want to repeat it from scratch if you want to add a further solver.
 - **Utilizing Technology**: Employ tools like slurm for efficient distribution
   of experiments across computing clusters, saving time and resources. The
   faster you have your results, the faster you can act on them.
@@ -406,4 +407,4 @@ and nice plots on which we can base our decisions.
 > The general problem of selecting the right strategy for a specific instance is
 > called
 > [Algorithm Selection](https://en.wikipedia.org/wiki/Algorithm_selection)
-> problem and can be surprisingly complex, too.
+> problem and can be surprisingly complex, too.

09_lns.md

@@ -1,8 +1,9 @@
 <!-- EDIT THIS PART VIA 08_lns.md -->
 
-## Using CP-SAT for Bigger Problems with Large Neighborhood Search
 <a name="09-lns"></a>
 
+## Using CP-SAT for Bigger Problems with Large Neighborhood Search
+
 CP-SAT is great at solving small and medium-sized problems. But what if you have
 a really big problem on your hands? One option might be to use a special kind of
 algorithm known as a "meta-heuristic", like a
@@ -11,8 +12,8 @@ can be hard to set up and might not even give you good results.
 
 Sometimes you will see new algorithms with cool-sounding names in scientific
 papers. While tempting, these are often just small twists on older methods and
-might leave out key details that make them work. If you are interested, there's a
-discussion about this issue in a paper by Sörensen, called
+might leave out key details that make them work. If you are interested, there's
+a discussion about this issue in a paper by Sörensen, called
 ["Metaheuristics – The Metaphor Exposed"](http://onlinelibrary.wiley.com/doi/10.1111/itor.12001/).
 
 The good news? You do not have to implement an algorithm that simulates the