diff --git a/README.md b/README.md
index e2ced9a6..b1c72c15 100644
--- a/README.md
+++ b/README.md
@@ -1,14 +1,7 @@
-# STMO-ZOO
+# Genetic Algorithms
-Welcome to the STMO zoo! This is your final assignment for the course Selected Topics in Mathematical Optimization. Your goal is to implement an optimization method in Julia and contribute this to this repository. To pass, you have to:
+Jordi Verbruggen and Jietse Verweirder
-- fork this repo and create a pull request;
-- add a module to `src` with **at least one function**
-- add at least one unit test to the folder `test`;
-- document all your functions and add a page to the documentation page;
-- make a notebook in [Pluto](https://github.com/fonsp/Pluto.jl) and add it to `notebooks`;
-- perform a small code review of two other students.
+## Abstract
-Depending on the project you choose some of these individual assignments might be really minimalistic, with other parts larger. For example, if you want to develop an application, say solving the graph coloring problem with Tabu Search, you might have only a single function in the source code (e.g., generating an instance) but have a fairly large notebook with a tutorial. On the other hand, if you work on a method, e.g., implementing Bee Colony Optimization, you might have many functions in the source code, while your notebook is only a demonstration on the test functions.
-
-[](https://travis-ci.org/MichielStock/STMOZOO)[](https://coveralls.io/github/MichielStock/STMOZOO?branch=master)
\ No newline at end of file
+Genetic algorithms (GAs) are described as optimization algorithms that make use of concepts originated from biological evolution, such as natural selection and survival of the fittest. By introducing these concepts into the algotithm, a population will evolve to an optimal solution. The population is a representation of possible solutions, called chromosomes, to the problem in question. Each chromosome in their turn is comprised of genes, which are the actual number values of the solution. The algorithm will then apply evolutionary operators such as mutation, recombination and selection, over several generations, to converge the population to the best possible solution. A fitness function is used to determine which solution is the most optimal in the population, determining the objective function quality of the solution. Every generation, better solutions are created until the termination criteria are met or until a certain amount of generations has been run. The GA is terminated and the optimal solution should have been found. Although not guaranteed, most solutions will be of sufficient high quality.
\ No newline at end of file
diff --git a/docs/Project.toml b/docs/Project.toml
deleted file mode 100644
index 16656868..00000000
--- a/docs/Project.toml
+++ /dev/null
@@ -1,3 +0,0 @@
-[deps]
-Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-STMOZOO = "8e7dc78f-7190-4116-bf88-3d148ae9f088"
diff --git a/docs/make.jl b/docs/make.jl
deleted file mode 100644
index 21d4327e..00000000
--- a/docs/make.jl
+++ /dev/null
@@ -1,17 +0,0 @@
-using Documenter
-
-using STMOZOO
-using STMOZOO.Example
-
-makedocs(sitename="STMO ZOO",
- format = Documenter.HTML(),
- modules=[Example], # add your module
- pages=Any[
- "Example"=> "man/example.md", # add the page to your documentation
- ])
-
-#=
-deploydocs(
- repo = "github.com/michielstock/STMOZOO.jl.git",
- )
-=#
\ No newline at end of file
diff --git a/docs/src/index.md b/docs/src/index.md
deleted file mode 100644
index ad33d99d..00000000
--- a/docs/src/index.md
+++ /dev/null
@@ -1,7 +0,0 @@
-# STMO ZOO documentation
-
-This is the documentation page for the STMO ZOO packages (edition 2020-2021). This is the place for the **documentation**
-of your function. So explain the main functionality of your module and list the documentation of your funtions.
-
-```@contents
-```
\ No newline at end of file
diff --git a/docs/src/man/example.md b/docs/src/man/example.md
deleted file mode 100644
index 08857ecb..00000000
--- a/docs/src/man/example.md
+++ /dev/null
@@ -1,14 +0,0 @@
-## Example
-
-This is the example code, written by Michiel Stock. It contains some basic functionality
-to solve quadratic systems of the form:
-
-``\min_{\mathbf{x}} \frac{1}{2} \mathbf{x}^\intercal P\mathbf{x} + \mathbf{q} \cdot \mathbf{x} + r\,,``
-
-It contains a function to solve this optimization problem and a helper function that generates a quadratic function from
-the parameters in their canonical form.
-
-```@docs
-solve_quadratic_system
-quadratic_function
-```
\ No newline at end of file
diff --git a/instructions.md b/instructions.md
deleted file mode 100644
index 7264c9bc..00000000
--- a/instructions.md
+++ /dev/null
@@ -1,94 +0,0 @@
-# Assignments
-
-Edition 2020-2021
-
-This file gives a detailed overview of what you have to do for this project.
-
-## In brief
-
-For the exam project, you pick a optimization related topic of your interest that is *not* covered in detail in class. This can be an algorithm, an application you solve with methods seen the course or some theoretical aspect you want to study. You write some code that you add to the STMOZOO codebase (including documentation, tests etc.) and illustrate you application in a notebook.
-
-## Getting started
-
-- [ ] pick a project (take a look at `project ideas.md` or discuss with Michiel)
-- [ ] [fork](https://docs.github.com/en/enterprise-server@2.20/github/getting-started-with-github/fork-a-repo) this repo
-- [ ] rename your repo using a short indicative name, e.g., `GeneticProgramming.jl`. Add `.jl` to indicate this is a Julia package. **Don't use spaces in the name!**
-- [ ] make a local clone of the repository
-- [ ] add the repo with your project to the project sheet
-- [ ] update the `readme.md`
- - [ ] add title
- - [ ] add your names
- - [ ] add a small abstract/example of what the code should do
-
-## Source code
-
-Every project needs to have some source code, at least one function! You have to decide which parts belong in the source code (and can hence be readily loaded by other users) and which parts of your project will be in the notebook where people can see and interact with your code.
-
-Developing code can be done in any text editor, though we highly recommend [Visual Studio Code](https://code.visualstudio.com/), with Juno the environment for Julia. [Atom](https://atom.io/) is an alternative but is not supported anymore. When developing, you have to activate your project. Assuming that the location of the REPL is the project folder, open the Pkg manager (typing `]`) and type `activate .`. The dot indicated the current directory. If you use external packages in your project, for example, Zygote or LinearAlgebra, you have to add them using `add PACKAGE` in the package manager. This action will create a dependency and update the `Project.toml` file.
-
-Importantly, all your code should be in a [module](https://docs.julialang.org/en/v1/manual/modules/), where you export only the functions useful for the user.
-
-- [ ] In the `src` folder, add a new Julia file with your source code, for example `geneticprogramming.jl`. Don't use spaces or capitals in the file name.
-- [ ] Link your file in `STMOZOO.jl` using `include(filename)`, running the code.
-- [ ] Create a module environment in your file for all your code. Use [camel case](https://en.wikipedia.org/wiki/Camel_case) for the name.
- - use `module GeneticProgramming begin ... end` to wrap your code;
- - import everything you need from external packages: `using LinearAlgebra: norm`;
- - export your functions using `export`
-- [ ] write awesome code!
-- [ ] take a look at your code regarding the [Julia style guide](https://docs.julialang.org/en/v1/manual/style-guide/)
-- [ ] check the [Julia performance tips](https://docs.julialang.org/en/v1/manual/performance-tips/)
-- [ ] document *every* function! Make sure that an external user can understand everything! Be liberal with comments in your code. Take a look at the [guidelines](https://docs.julialang.org/en/v1/manual/documentation/)
-
-## Unit tests
-
-Great, we have written some code. The question is, does it work? Likely you have experimented in the REPL. For a larger project, we would like to have guarantees that it works, though. Luckily, this is very easy in Julia, where we can readily use [Unit testing](https://docs.julialang.org/en/v1/stdlib/Test/).
-
-You will have to write a file with some unit tests, ideally testing every function you have written! The fraction of functions that are tested is called [code coverage](https://en.wikipedia.org/wiki/Code_coverage). This project is monitored automatically using Travis (check the button on the readme page!). Currently, coverage is 100%, so help to keep this as high as possible!
-
-Tests can be executed using the `@test` macro. You evaluate some functions and check their results. The result should evaluate to `true`. For example: `@test 1+1 == 2` or `@test √(9) ≈ 3.0`.
-
-It makes sense to group several tests, which can be done using `@testset "names of tests" begin ... end`.
-
-Your assignments:
-- [ ] add a source file to the `test/` folder, the same name as your source code file.
-- [ ] add an `include(...)` with the filename in `runtests.jl`
-- [ ] in your file, add a block `@testset "MyModule" begin ... end` with a series of sensible unit tests. Use subblocks of `@testset` if needed.
-- [ ] run your tests, in the package manager, type `test`. It will run all tests and generate a report.
-
-Travis will automatically run your unit tests online when you push to the origin repo.
-
-## Documentation
-
-> **This part is optional!** If you just provide a couple of examples how to use your code in the readme, it is fine.
-
-Hopefully, you have already documented all your functions, so this should be a breeze! We will generate a documentation page using the [Documenter](https://juliadocs.github.io/Documenter.jl/stable/man/guide/) package. Since we will not put the project in the package manager, we won't host the documentation, though we generate HTML pages anyway.
-
-- [ ] add markdown file to `docs/src/man` with the documentation.
-- [ ] write a general introduction explaining the rationale of your code.
-- [ ] use a `@docs` block to add your functions with their documentation.
-- [ ] update the `make.jl` file, linking your page.
-- [ ] run the `make.jl` file to generate the documentation, an HTML file, not added to the repo.
-
-## Notebook
-
-Finally, you have to add a [Pluto](https://github.com/fonsp/Pluto.jl) notebook to the `notebook` folder. Again use the same name you used for your source code. Depending on the nature of your project, this will be the most extensive task! Make full use of Pluto's interactivity to illustrate your code. In contrast to the documentation page, this is not the place to explain your functions but rather show what you can do with your software or explain a concept.
-
-Alternatively, you may use [Literate](https://fredrikekre.github.io/Literate.jl/v2/) to have script with text annotation to explain your code/package. Up to you what you feel most comfortable with.
-
-## Code review
-
-Each of you will have to perform a code review of two other projects. You have till noon 13h of the exam date to do this, though it should not take too long. The aim is to **help** the other groups to make each other's project even better.
-
-- [ ] make a fork or local clone of the repo of the person you are reviewing;
-- [ ] check the source code, is the documentation clear? Anything obvious that can be improved.
-- [ ] run the tests. Do they work? Anything that could be tested but is not done so?
-- [ ] Is the documentation clear? Do you find any typos? Could an example be added?
-- [ ] Take a look at the notebook. Any suggestions there to improve this?
-
-Big things can be addressed by opening an issue. Small fixes and suggestions to the other person's code can be done immediately and via a pull request.
-
-Afterwards, you have the rest of the day to:
-- [ ] merge the entire request and fix any issues you find meaningful.
-- [ ] fill in a small questionnaire on Ufora about your project and the projects you have reviewed.
-
-When your code is final, you can [tag](https://docs.github.com/en/desktop/contributing-and-collaborating-using-github-desktop/managing-commits/managing-tags) your latest commit and mention Michiel you are finished (mention `@michielstock`).
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diff --git a/notebook/example.jl b/notebook/example.jl
deleted file mode 100644
index 950417f0..00000000
--- a/notebook/example.jl
+++ /dev/null
@@ -1,159 +0,0 @@
-### A Pluto.jl notebook ###
-# v0.14.8
-
-using Markdown
-using InteractiveUtils
-
-# ╔═╡ 5ad5c202-20f8-11eb-23f1-4f38b687c285
-using STMOZOO.Example
-
-# ╔═╡ d2d007b8-20f8-11eb-0ddd-1181d4565a85
-using Plots
-
-# ╔═╡ 45189a82-20fa-11eb-0423-05ce1b84639d
-using Zygote
-
-# ╔═╡ 171fee18-20f6-11eb-37e5-2d04caea8c35
-md"""
-# Example: solving quadratic systems
-
-By Michiel Stock
-
-## Introduction
-
-In this notebook, I have chosen to write code so minimize *quadratic functions* of the form:
-
-$$f(\mathbf{x}) = \frac{1}{2} \mathbf{x}^\intercal P\mathbf{x} + \mathbf{q} \cdot \mathbf{x} + r\,,$$
-
-where $P \succ 0$.
-
-Hence, solving
-
-$$\min_\mathbf{x}\, f(\mathbf{x})\,.$$
-"""
-
-# ╔═╡ fb4aeb8c-20f7-11eb-0444-259de7b76883
-md"""
-
-## Derivation
-
-The gradient of the quadratic function is
-
-$$\nabla f(\mathbf{x})=P\mathbf{x} +\mathbf{q}\,.$$
-
-Setting this to zero gives
-
-$$\mathbf{x}^\star=-P^{-1}\mathbf{q}\,.$$
-
-We also know that $\nabla^2f(\mathbf{x}) = P \succ 0$, so $\mathbf{x}^\star$ is a minimizer.
-"""
-
-# ╔═╡ 52e87238-20f8-11eb-2ea0-27ee1208d3c3
-md"""
-## Illustration
-
-We will use a simple 2D example to illustrate this code.
-"""
-
-# ╔═╡ e9a9d69e-20f8-11eb-0d9d-330ee5e9cf25
-P = [7 -1; -1 2]
-
-# ╔═╡ fdd4e550-20f8-11eb-227b-25f36708484d
-q = [-14.0, -2.0]
-
-# ╔═╡ 025fd6e8-20f9-11eb-3e7d-3519f3c4b58f
-r = 1
-
-# ╔═╡ 096eff98-20f9-11eb-1e61-99d5714895ba
-md"We have a function to generate the quadratic function."
-
-# ╔═╡ 165509ca-20f9-11eb-107c-550cbba0f0e9
-f_quadr = quadratic_function(P, q, r)
-
-# ╔═╡ 1fffc82a-20f9-11eb-198c-c160d7dac87d
-f_quadr([2, 1])
-
-# ╔═╡ 26ab6ce2-20f9-11eb-1836-1756b290e5e3
-md"No more need to remember the formulla for the minimizer! Just use `solve_quadratic_system`!"
-
-# ╔═╡ 49832a8e-20f9-11eb-0841-19a40a12db18
-x_star = solve_quadratic_system(P, q, r)
-
-# ╔═╡ 55e0e274-20f9-11eb-36c0-753f228f7e9b
-begin
- contourf(-20:0.1:20, -20:0.1:20, (x, y) -> f_quadr([x,y]), color=:speed)
- scatter!([x_star[1]], [x_star[2]], label="minimizer")
-end
-
-# ╔═╡ b1551758-20f9-11eb-3e8f-ff9a7127d7f8
-md"""
-## Approximating non-quadratic functions
-
-We can approximate non-quadratic functions by a quadratic function: The second order Taylor approximation $\hat{f}$ of a function $f$ at $\mathbf{x}$ is
-$$f(\mathbf{x}+\mathbf{v})\approx\hat{f}(\mathbf{x}+\mathbf{v}) = f(\mathbf{x}) + \nabla f(\mathbf{x})^\top \mathbf{v} + \frac{1}{2} \mathbf{v}^\top \nabla^2 f(\mathbf{x}) \mathbf{v}\,.$$
-
-Let us use this idea for the Rosenbrock function.
-"""
-
-# ╔═╡ 41d8f1dc-20fa-11eb-3586-a989427c1fd6
-f_nonquadr((x1, x2); a=1, b=5) = (a-x1)^2 + b * (x2 - x1^2)^2
-
-# ╔═╡ 4ed4215e-20fa-11eb-11ee-f7741591163c
-x = [0.0, 0.0]
-
-# ╔═╡ 56af99ee-20fa-11eb-0240-69c675efb78c
-fx = f_nonquadr(x)
-
-# ╔═╡ 6c5473b4-20fa-11eb-327b-51ac560530eb
-∇fx = f_nonquadr'(x)
-
-# ╔═╡ 7518c2c0-20fa-11eb-32c0-a9db2a91cbc5
-∇²fx = Zygote.hessian(f_nonquadr, x)
-
-# ╔═╡ 34027942-20fb-11eb-261e-3b991ce4c9f8
-v = solve_quadratic_system(∇²fx, ∇fx, fx)
-
-# ╔═╡ 3bbeb85c-20fc-11eb-04d0-fb12d8ace50a
-f̂(x′) = quadratic_function(∇²fx, ∇fx, fx)(x′ .- x)
-
-# ╔═╡ 8623ac1a-20fa-11eb-2d45-49cce0fdac86
-begin
- plot_nonquadr = contourf(-2:0.01:2, -2:0.01:2, (x, y) -> f_nonquadr([x,y]), color=:speed, title="non-quadratic function")
- scatter!(plot_nonquadr, [x[1]], [x[2]], label="x")
- scatter!(plot_nonquadr, [x[1]+v[1]], [x[2]+v[2]], label="x + v")
-
- plot_approx = contourf(-2:0.01:2, -2:0.01:2, (x, y) -> f̂([x,y]), color=:speed,
- title="quadratic approximation")
- scatter!(plot_approx, [x[1]], [x[2]], label="x")
- scatter!(plot_approx, [x[1]+v[1]], [x[2]+v[2]], label="x + v")
-
- plot(plot_nonquadr, plot_approx, layout=(2,1), size=(600, 800))
-
-end
-
-
-# ╔═╡ Cell order:
-# ╟─171fee18-20f6-11eb-37e5-2d04caea8c35
-# ╠═5ad5c202-20f8-11eb-23f1-4f38b687c285
-# ╠═d2d007b8-20f8-11eb-0ddd-1181d4565a85
-# ╟─fb4aeb8c-20f7-11eb-0444-259de7b76883
-# ╟─52e87238-20f8-11eb-2ea0-27ee1208d3c3
-# ╠═e9a9d69e-20f8-11eb-0d9d-330ee5e9cf25
-# ╠═fdd4e550-20f8-11eb-227b-25f36708484d
-# ╠═025fd6e8-20f9-11eb-3e7d-3519f3c4b58f
-# ╟─096eff98-20f9-11eb-1e61-99d5714895ba
-# ╠═165509ca-20f9-11eb-107c-550cbba0f0e9
-# ╠═1fffc82a-20f9-11eb-198c-c160d7dac87d
-# ╟─26ab6ce2-20f9-11eb-1836-1756b290e5e3
-# ╠═49832a8e-20f9-11eb-0841-19a40a12db18
-# ╠═55e0e274-20f9-11eb-36c0-753f228f7e9b
-# ╟─b1551758-20f9-11eb-3e8f-ff9a7127d7f8
-# ╠═41d8f1dc-20fa-11eb-3586-a989427c1fd6
-# ╠═45189a82-20fa-11eb-0423-05ce1b84639d
-# ╠═4ed4215e-20fa-11eb-11ee-f7741591163c
-# ╠═56af99ee-20fa-11eb-0240-69c675efb78c
-# ╠═6c5473b4-20fa-11eb-327b-51ac560530eb
-# ╠═7518c2c0-20fa-11eb-32c0-a9db2a91cbc5
-# ╠═34027942-20fb-11eb-261e-3b991ce4c9f8
-# ╠═3bbeb85c-20fc-11eb-04d0-fb12d8ace50a
-# ╟─8623ac1a-20fa-11eb-2d45-49cce0fdac86
diff --git a/notebook/geneticalgorithms.jl b/notebook/geneticalgorithms.jl
new file mode 100644
index 00000000..921b9149
--- /dev/null
+++ b/notebook/geneticalgorithms.jl
@@ -0,0 +1,2509 @@
+### A Pluto.jl notebook ###
+# v0.17.1
+
+using Markdown
+using InteractiveUtils
+
+# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
+macro bind(def, element)
+ quote
+ local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
+ local el = $(esc(element))
+ global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
+ el
+ end
+end
+
+# ╔═╡ c80a0f15-2c37-4c40-a543-2e6c3fead1be
+using Images, StatsBase, Plots, PlutoUI, Distributions, Random
+
+# ╔═╡ 171fee18-20f6-11eb-37e5-2d04caea8c35
+md"""
+# Genetic Algorithms
+
+*By Jordi Verbruggen & Jietse Verweirder*
+
+## Introduction
+
+**Genetic algorithms (GAs)** are described as optimization algorithms that make use of concepts originated from biological evolution, such as natural selection and survival of the fittest.
+By introducing these concepts into the algotithm, a population will evolve to an optimal solution.
+**The population** is a representation of possible solutions, called chromosomes, to the problem in question. Each chromosome in their turn is comprised of genes, which are the actual number values of the solution. The algorithm will then apply evolutionary operators such as **mutation, recombination and selection**, over several generations, to converge the population to the best possible solution.
+**A fitness function** is used to determine which solution is the most optimal in the population, determining the objective function quality of the solution. Every generation, better solutions are created until **the termination criteria** are met or until a certain amount of generations has been run. The GA is terminated and the optimal solution should have been found. Although not guaranteed, most solutions will be of sufficient high quality.
+
+A schematic overview of all the steps in the process is portrayed below.
+"""
+
+# ╔═╡ 98b278e9-5cc9-4e36-9d1a-75eb9f4158de
+md"""
+
+
+"""
+
+# ╔═╡ d89c31c5-f2b3-4b52-8e47-580c62979687
+md"""
+During this presentation we will introduce the general concepts of GAs. We will build up a GA by introducing all its different aspects. Along the way, the option will be given to experiment with the different parameters and evaluate their effect on the algorithm. As a running example, to explain the concept, we will make use of the **Himmelblau's function** where we will try to find one of its four minima. The function is written as follows:
+
+```math
+\begin{equation}
+ f(x,y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2
+\end{equation}
+```
+A visualization of the function is given. *(Use the sliders to move the plot around.)*
+"""
+
+# ╔═╡ ba845736-b141-484a-9b10-fc73ecf31db3
+md"""
+Angle 1:
+$(@bind ca1 Slider(0:90,default=50,show_value=true))
+
+Angle 2:
+$(@bind ca2 Slider(1:90,default=75,show_value=true))
+"""
+
+# ╔═╡ cccaf5fb-3c95-4ea9-b699-0cee2f12542e
+md"""
+
+The function takes x and y coordinates that have real number values. Therefore the representation of the individuals will be a tuple of the x and y coordinates. In principle all techniques that are discussed here, are applicable to any function represented by chromosomes with real numbers. Bit string representations are also often used in GAs, and most of what is discussed further can be applied to that, but not all, which is important to keep in mind. To illustrate the implementation with bitstrings, figures of this process have been added.
+
+In a last part of the notebook functionality has been added where custom objectives can be found via a genetic algorithm. Here you can write your function and by setting up some parameters, the extremeties of the objective can be found. **Important to mention here is that the functions have to be 2D or 3D.**
+"""
+
+# ╔═╡ 8212a676-3167-438a-944d-5eeae72d54d8
+md"""
+## Initial population
+
+The first step in creating a genetic algorithm is defining the **initial population.** Each individual in the population contains a set of variables, descibed as genes. These genes as a whole form a chromosome, which can be seen as a possible solution. In most of the cases simple binary values are used to represent the genes. An example is portrayed below.
+
+"""
+
+# ╔═╡ 9365760a-10e5-48a4-ae77-b3f1a686f8e3
+md"""
+
+
+"""
+
+# ╔═╡ a8cd1caa-feb2-442f-ba8f-27619bfbff84
+md"""
+
+A few things have to be taken into account, when designing the initial population:
+
+- **The population size:** A smaller population has a higher chance for a premature convergence, while a large population on the other hand asks for more computing time.
+
+- **The diversity:** A low diverstity will also result in a premature convergence. Diversity in this context means that the individuals differ greatly in their genome.
+
+Overall, there are two primary methods to initialize a population in a GA:
+
+- **Random Initialization:** Populate the initial population with completely random solutions.
+
+- **Heuristic initialization:** Populate the initial population using a known heuristic for the problem. The population exists of solutions that are already guided a few steps closer to the exact solution of the problem.
+
+*The code to initialize goes as folows:*
+"""
+
+# ╔═╡ eba0c158-54d3-4f56-8b1a-5d3ddba001db
+"""
+ random_init_pop(ps, gs, i_x, i_y)
+
+Inputs:
+
+ - ps: Population Size: The desired size of the population
+ - gs: Genome Size: The desired size of the genome. Options: 1 or 2 (integers)
+ - i_x: Interval to define the range of the generated float numbers on the x-axis
+ - i_y: Interval to define the range of the generated float numbers on the y-axis
+
+Output:
+
+ - pop: A random initial population
+"""
+function random_init_pop(ps, gs, i_x, i_y)
+
+ if gs == 2
+ pop = [
+ [rand(Uniform(i_x[1], i_x[2])),rand(Uniform(i_y[1],i_y[2]))] for _ in 1:ps
+ ]
+ else
+ pop = [[rand(Uniform(i_x[1], i_x[2]))] for _ in 1:ps]
+ end
+
+ return pop
+
+end;
+
+# ╔═╡ 41dd8e8d-0f4c-407e-90c5-6f450fe318fe
+population = random_init_pop(100, 2, [-4,4], [-4,4])
+
+# ╔═╡ 37b9fce9-e99c-424f-a614-8169b7edf0d6
+md"""
+## Fitness
+
+As we want to improve our population over time, it is of absolute importance to select individuals that have a high **fitness level**. To determine the fitness level of an individual, we have to implement a **fitness function**. This function takes a candidate solution to the problem as input and produces a numeric value as output indicating how “fit” our how “good” the solution is.
+
+Due to the fact that the fitness value has to be calculated after each generation, the fitness function should not only correlate closely with the designer's goal, but it also should be computationally efficient.
+
+**The fitness function used as example here is based on the himmelblau's optimization function:**
+
+$$f(x, y) = (x^2 + y − 11)^2 + (x + y^2 − 7)^2$$
+
+The x and y values respectively were the first
+and second gene in the chromosome of the individual.
+
+*(As we want to calculate the minima of the Himmelblau function, we take the negative of the function as its fitness value.)*
+
+"""
+
+# ╔═╡ f4969be8-815e-43bc-adaf-a6e1eeec1226
+"""
+ fitness(p, ff, extremeties)
+
+Inputs:
+
+ - p: The population you are working with
+ - ff: The fitness function
+ - extremeties: Indicate if you want to calculate the minima of maxima of the
+ function. Options: "minima" or "maxima"
+
+Output:
+
+ - pf: A calculated fitness score for each individual in
+ the population based on the fitness function
+
+
+"""
+function fitness(p, ff, extremeties)
+ @assert(extremeties == "minima" || extremeties == "maxima", "extremeties has to be one of the following values: 'minima' or 'maxima' (without quotation marks)")
+
+ d = length(p[1])
+ @assert(d == 1 || d == 2, "function has to be 2d or 3d")
+
+ if d == 2
+ if extremeties == "minima"
+ pf = [[[ind[1], ind[2]], -ff(ind[1], ind[2])] for ind in p]
+ else
+ pf = [[[ind[1], ind[2]], ff(ind[1],ind[2])] for ind in p]
+ end
+ else
+ if extremeties == "minima"
+ pf = [[[ind[1]], -ff(ind[1])] for ind in p]
+ else
+ pf = [[[ind[1]], ff(ind[1])] for ind in p]
+ end
+ end
+
+ return pf
+end;
+
+# ╔═╡ ccb197ff-f322-4f14-acb5-ba64a343d234
+md"""
+## Termination criteria
+
+Eventually the run of the algorithm will have to come to an end. Therefore certain conditions have to be determined that halt the algoritm, when these criteria are met. It has been observed that initially, the GA progresses very fast with better solutions coming in every few iterations, but this tends to saturate in the later stages, where the improvements are very small. We usually want a termination condition such that our solution is close to the optimal, at the end of the run.
+
+**Usually, we keep one of the following termination conditions:**
+
+- *No improvement in the population for X iterations.*
+
+- *An absolute number of generations is reached.*
+
+- *The objective function value has reached a certain pre-defined value.*
+
+*The code goes as follows:*
+"""
+
+# ╔═╡ 2bcdbbf0-2473-40d9-8c85-cec3b6ca4b31
+"""
+ check_term(pf, σ, nmax)
+
+Inputs:
+
+ - pf: Population_fitness: The fitness scores per individual determinded by
+ the fitness function
+ - σ: Treshold for the standard deviation
+ - nmax: The number of generations the maximal fitness has not changed
+
+Output:
+
+ - bool: Depending on the fact that the criteria were met or not
+
+"""
+function check_term(pf, σ, nmax)
+
+ return std([x[2] for x in pf]) < σ && nmax >= 5
+
+end;
+
+# ╔═╡ c6155621-9a86-4747-b0ec-65e779670b57
+md"""
+## Selection
+
+During selection, the parent chromosomes are choosen for later on "breeding purposes", this is implemented by **the crossover operator.** Different methods of selection are available and some are discussed below. Important to note here is that an individual can be selected more than one time, otherwise the population would not change. When each individual can only be selected once, the least fit individuals would also be selected for the mating pool. Therefore convergence of the algorithm would be hindered.
+"""
+
+# ╔═╡ 953edf56-a957-4c61-8a89-9709dc6dfd65
+md"""
+
+### Roulette Wheel Selection
+
+As the name suggests, this way of selecting parents is based on turning a roulette wheel. The chance of selecting an individual is proportional to its fitness. The higher its fitness the bigger its pocket will be on the roulette wheel and thus resulting in a higher chance of being selected.
+
+**The chance for an individual to be selected can be mathematically written as:**
+
+```math
+\begin{equation}
+ p_i = \frac{f_i}{\sum_{j=1}^{N} f_j}
+\end{equation}
+```
+
+Where:
+- *pᵢ is the probability for choosing individual i*
+- *fᵢ is the fitness of individual i*
+- *N is the size of the population*
+
+*We implement this in code:*
+"""
+
+# ╔═╡ 79eb48df-26de-4965-b078-9bb20313247a
+"""
+
+ roulette_wheel_selection(population_fitness)
+
+Input:
+
+ - population_fitness: A list where each element consists of the individual
+ and its corresponding fitness
+
+Output:
+
+ - pool: A list with the selected individuals for the mating pool
+
+"""
+function roulette_wheel_selection(population_fitness)
+
+ # extract the individuals from the list
+ p = [pf[1] for pf in population_fitness]
+
+ # extract the weights from the list, which are its fitness proportions
+ fitness = [pf[2] for pf in population_fitness]
+ w = [fᵢ / sum(fitness) for fᵢ in fitness]
+
+ # randomly choose the same number of individuals but with its chance of being
+ # choosen proportional to its fitness
+ pool = sample(p, Weights(w), length(population_fitness))
+
+ return pool
+
+end;
+
+# ╔═╡ 8623b228-c627-4f81-8f6f-6de074b8ec20
+md"""
+### Rank Selection
+
+In **rank selection** individuals are ranked based on their fitness. The individual with the worst fitness is given rank one, the individual with the best fitness is given rank N. In rank selection, the fitness values can be negative.
+
+**The probability with which an individual can be selected can then be given by:**
+
+```math
+\begin{equation}
+ p_i = \frac{r_i}{n(n-1)}
+\end{equation}
+```
+
+Where:
+- *pᵢ is the probability for choosing individual i*
+- *rᵢ is the rank of individual i*
+- *n the total number of ranks, which is equal to the number of individuals in the population*
+
+*We implement this in code:*
+"""
+
+# ╔═╡ 84d49f43-8ac3-4e73-991c-a54bb9fe9b5f
+md"""
+### Steady State Selection
+
+During **steady state selection** a proportion of individuals with the highest fitness is choosen as mating pool. An equal proportion of individual with the lowest fitness values is removed from the population and replaced by the offspring of the mating pool.
+
+*We can write the code as follows:*
+
+"""
+
+# ╔═╡ 07e1c8b6-c3fd-4f5f-bbb0-fe6595813d55
+"""
+ steady_state_selection(pf, Δ)
+
+Input:
+
+ - pf: Population Fitness: A list where each element consists of the individual
+ and its corresponding fitness
+ - Δ: The proportion of fittest individuals that need to be selected
+
+Output:
+
+ - pool: A list with the selected individuals for the mating pool
+"""
+function steady_state_selection(pf, Δ)
+ @assert(Δ <= 0.5, "Proportion of selected individuals has to be smaller than 0.5")
+
+ # sort the population based on fitness in descending order
+ sorted_population_fitness = sort(pf, by=pf->pf[2], rev=true)
+
+ # calculate the number of individuals that need to be selected
+ n_ind = trunc(Int, Δ * length(pf))
+
+ # return the mating pool
+ pool = [spf[1] for spf in sorted_population_fitness[1:n_ind]]
+
+ return pool
+end;
+
+# ╔═╡ 307af9a7-6b0c-44ad-a5b0-d9b0c18b5db4
+md"""
+### Tournament Selection
+
+As a last selection technique, we have tournament selection. Here selection happens by means of **tournaments between randomly choosen individuals** from the population. In the tournament, the individual with the biggest fitness is chosen with the biggest probability, the individual with the second highest probability has the second best probability to be chosen and so on.
+
+**The probability with which the individual with the highest fitness is chosen, is a given value and can be written as:**
+
+```math
+\begin{equation}
+ p_i = P * (1-P)^{i-1}
+\end{equation}
+```
+
+Where:
+- *pᵢ is the selection probability for the i-th fittest individual in the tournament*
+- *P is the selection probability for the best individual in the tournament with 0 < P ≤ 1*
+
+Each individual has the same chance to be chosen for a tournament. Selection continues until a mating pool with the same size as the population has been formed.
+
+*We write the code as follows:*
+"""
+
+# ╔═╡ 6cf8534b-2fa1-4762-9526-bd3c2da99843
+"""
+ tournament_selection(population_fitness, k, prob)
+
+Input:
+
+ - population_fitness: A list where each element consists of the individual and
+ its corresponding fitness
+ - k: The tournament size. The number of individuals selected for the
+ tournament
+ - prob: The probability with which the fittest individual in the tournament is
+ selected
+
+Output:
+
+ - pool: A list with the selected individuals for the mating pool
+"""
+function tournament_selection(population_fitness, k, prob)
+ @assert(0 < prob <= 1, "prob has to be between 0 and 1 (1 included)")
+
+ @assert(k <= length(population_fitness), "the tournament has to be smaller then the population size!")
+
+ pool = Array{Float64}[]
+ while length(pool) < length(population_fitness)
+
+ # build the tournament by randomly selecting k individuals from the population
+ # each individual can only be selected once for a tournament
+ t = sample(population_fitness, k, replace=true)
+
+ # sort the tournament based on the fitness values
+ sorted_t = sort(t, by=t->t[2], rev=true)
+
+ # get all individuals
+ p = [pf[1] for pf in population_fitness]
+
+ # get their weights (selection probabilities)
+ w = [prob * (1-prob)^i for i in 0:k-1]
+
+ # add the choosen individual to the mating pool
+ push!(pool, sample(p, Weights(w)))
+ end
+
+ return pool
+
+end;
+
+# ╔═╡ 5096d7c0-0189-4c89-9ec0-13e7aac9aa8a
+md"""
+## Crossover
+
+After selection the most significant way to stochastically generate new solutions from an existing population is by **recombination (crossover)** of parental chromosomes.
+
+There exist a few different types of crossover:
+
+- **Single Point Crossover:** A crossover point on the parent organism string is selected. All data beyond that point in the organism string is swapped between the two parent organisms. Strings are characterized by Positional Bias.
+
+- **Two-Point Crossover:** This is a specific case of a N-point Crossover technique. Two random points are chosen on the individual chromosomes (strings) and the genetic material is exchanged at these points.
+
+- **Uniform Crossover:** Each gene (bit) is selected randomly from one of the corresponding genes of the parent chromosomes. Tossing of a coin can be seen as an example technique.
+
+For this example we introduce the "Single Point Crossover"
+"""
+
+# ╔═╡ 0be0a442-8c9f-4035-b926-998f0c63ade7
+md"""
+
+
+"""
+
+# ╔═╡ 9c2f897a-663e-4408-8364-1582ef6cba9c
+md"""
+This method of recombination is implemented by introducing two equatations:
+
+$$C_1 = \alpha P_1 + (1 − \alpha)P_2$$
+
+$$C_2 = (1 − \alpha)P_1 + \alpha P_2$$
+
+Where:
+- *P1 is the gene of parent one*
+- *P2 is the gene of parent two*
+- *C1 is the gene of child/offspring one*
+- *C2 is the gene of child/offspring two*
+- *α is a factor by wich the parental genes are divided*
+
+This technique is also called **whole arithmetic crossover** and goes as follows:
+
+First the mating pool is shuffled to make random pairings of parents and two parents are selected that are adjacent in the mating pool list. Then the genome of the parents is divided over the offspring with a factor α, resulting in two children. Eventually the whole population is replaced by the offsprings.
+
+*The code goes as follows:*
+"""
+
+# ╔═╡ 1e7552ac-9c46-479d-b26e-5d776e3cc5af
+"""
+ crossover(pool, α)
+
+Inputs:
+
+ - pool: The mating pool that is selected for further breeding
+ - α: the crossover rate: A float between 0 and 1 to determine the part of
+ the genome that is going to be crossed
+
+Output:
+
+ - offspring: Next generation of individuals (population) that replaces
+ the previous population
+"""
+function crossover(pool, α)
+ @assert(0<α<1, "crossover rate has to be between 0 and 1")
+
+ # shuffle the mating pool
+ shuffle(pool)
+
+ # create offspring
+ offspring = Array{Float64}[]
+
+ # go over the mating pool
+ for i in 1:2:length(pool)
+ child1 = []
+ child2 = []
+ for (j, gene) in enumerate(pool[i])
+ # divide the genome of the parents over the children with a factor α
+ push!(child1, (α * gene + (1-α) * pool[i + 1][j]))
+ push!(child2, (α * pool[i + 1][j] + (1 - α) * gene))
+ end
+ push!(offspring, child1)
+ push!(offspring, child2)
+ end
+
+ return offspring
+
+end;
+
+# ╔═╡ 3347f3d5-dd43-40ff-bbed-f8f06532be47
+md"""
+## Mutation
+
+During **mutation** small changes are introduced to the genes of the chromosomes. By doing this, genetic diversity is maintained within the population. When not applying mutation, the genetic diversity would go down with each generation of the algorithm. The applied changes can not be to large, otherwise a perfectly good solution would be changed completely, destroying the work that already had been put into it. To ensure the changes are not to big a creep mutational operator can be used. Hereby only a small amount is added or substracted from the gene value, often a Gaussian deviate. Also important is the fact that after a lot of generations, the change is getting smaller so that the solution can be finetuned. **The mutation rate gives the proportion of genes that need to be mutated.** When applying mutation to a bitstring, a flip of one bit can be applied to introduce the change.
+"""
+
+# ╔═╡ 82b5a573-6013-408f-99c9-f105708f948e
+md"""
+
+
+"""
+
+# ╔═╡ 0b598ee8-8671-4b99-87b8-1a65a2d63aa2
+md"""
+*We code this as follows:*
+"""
+
+# ╔═╡ 1b6763ba-ae24-4f63-b7e8-545364ddab89
+"""
+ mutation(offspring, pm, generation)
+
+Input
+
+ - offspring: List of individuals after crossover
+ - pm: Mutation rate, the proportion of genes that need to be mutated
+ - generation: The generation the algorithm is currently in
+
+Output
+
+ - offspring: List of individuals with mutated genes
+"""
+function mutation(offspring, pm, generation)
+
+ # initiate a Gaussian distribution
+ gd = truncated(Normal(0.0, 1/(generation + 1)), 0.0, Inf)
+
+ # the number of chromosomes in the population
+ n_ind = length(offspring)
+
+ # the number of genes in each chromosome
+ n_genes = length(offspring[1])
+
+ # based on the mutation rate, calculate exact number of genes that should mutate
+ nmut = trunc(Int, n_ind * n_genes * pm)
+
+ # keep track of what genes are already mutated and of the number of mutated genes
+ used, mutated = Tuple{Int, Int}[], 0
+
+ # go on as long as there are still genes that need to be mutated
+ while mutated < nmut
+ ind = rand(1:n_ind) # choose a random individual (index)
+ g = rand(1:n_genes) # choose a random gene (index)
+ if !((ind,g) in used) # when not mutated yet, mutate the gene
+ gene = offspring[ind][g] # select the gene (value)
+ gene += rand(gd) # add random Gaussian deviate to the gene
+ offspring[ind][g] = gene # change the gene
+ push!(used, (ind,g)) # keep track of mutated genes
+ mutated += 1 # keep track of number of mutated genes
+ end
+ end
+
+ return offspring
+
+end;
+
+# ╔═╡ 6a60527b-0f46-4bf0-bd6f-91e509737a32
+md"""
+## The complete algorithm
+
+Now that we have been introduced to the different aspects of a genetic algorithm, it it time to put it all together and start seeking the minima of our Himmelblau's function:
+
+"""
+
+# ╔═╡ 97af696e-d076-40b3-a5d5-ec363350d7b7
+md"""
+
+To better understand the influences of the different parameters, you can change them below. Alter the parameters and look in which way they change the efficiency of the algorithm. What is the effect of the population size or mutation rate for example?
+
+"""
+
+# ╔═╡ 6ba87a23-5114-4126-b6a2-0981992d8a46
+md"""
+Population size:
+$(@bind pop_size_h Slider(0:250,default=100,show_value=true))
+
+Standard deviation σ for the termination criteria:
+$(@bind σₕ NumberField(0:0.00000001:1,default=0.001))
+
+The crossover rate α determines the proportion of dividing the parent genes during crossover:
+$(@bind αₕ Slider(0:0.01:1,default=0.5,show_value=true))
+
+The mutation rate: proportion of the genes that need to undergo mutation each generation:
+$(@bind pmₕ Slider(0:0.01:1,default=0.10,show_value=true))
+"""
+
+# ╔═╡ 48a851ce-fd14-4516-a172-c720f24bf153
+md"""
+We will visualize the different generations in order to get a better understanding of the inner workings of the algorithm.
+The visualization of the different steps of the solution can be seen here, you might need to fiddle with the angles again to get a good viewing point.
+We recommend looking at where your solution is converging too and using the first plot to set the values for both angles (they are the same angles in both plots).
+Moreover, to control the speed of the animation, you can alter the frames per second and the number of generations shown. Together these two will also decide how long it will run.
+"""
+
+# ╔═╡ 34360486-0f98-46bf-bdb6-550164e3b051
+md"""
+
+On the animation, we clearly see how the algorithm works. The initial population is drawn to one of the minima while also exploring other directions. In the beginning all points are randomly distributed, which is normal behaviour. After some generations, the points begin to huddle together forming a more uniform front. Then they start to migrate towards one of the minima in the plot. The later generations are finetuning of the solutions and making all solutions in the population as identical as possible (depending on the σ value given to the algorithm).
+
+"""
+
+# ╔═╡ 22c1df68-673f-4791-a705-0b45a42da211
+md"""
+## Custom functions
+
+To enable people to enter their own functions, we rewrite the algorithm more generally. Here you can again play with the different parameters but also give in your custom function. The functions can be 2D or 3D, which needs to be indicated by the genome size. A genome size of 1 resembles a 2D function (one variable) and a genome size of 2 resembles a 3D function (two variables).
+
+"""
+
+# ╔═╡ 5af46f82-c323-4472-aa68-76d253eb35b9
+md"""
+Population size:
+$(@bind pop_size_c Slider(0:250,default=100,show_value=true))
+
+Genome size:
+$(@bind gs Select([1, 2]))
+
+Interval to search in:
+
+X-axis:
+From
+$(@bind i_lower_x NumberField(-1000000:1000000, default=-1))
+To
+$(@bind i_upper_x NumberField(-1000000:1000000, default=1))
+
+Y-axis (for functions in 3D):
+From
+$(@bind i_lower_y NumberField(-1000000:1000000, default=-1))
+To
+$(@bind i_upper_y NumberField(-1000000:1000000, default=1))
+
+Which extremeties are you looking for:
+$(@bind extr Select(["minima", "maxima"]))
+
+Standard deviation σ for the termination criteria:
+$(@bind σ_custom NumberField(0:0.00000001:1,default=0.001))
+
+The crossover rate α determines the proportion of dividing the parent genes during crossover:
+$(@bind α_custom Slider(0:0.01:1,default=0.5,show_value=true))
+
+The mutation rate: proportion of the genes that need to undergo mutation each generation:
+$(@bind pm_custom Slider(0:0.01:1,default=0.10,show_value=true))
+"""
+
+# ╔═╡ cc6edd6d-0328-4692-834d-aa5258076d21
+# write your function here: f(x) = ... if genome size = 1 or f(x,y) = ... if genome size = 2 then save to execute the algorithm
+f(x) = x^2
+
+# ╔═╡ 3ff092e2-7af2-4b4b-bd29-2b0310cae48f
+md"""
+## Appendices
+"""
+
+# ╔═╡ b4a64a85-640d-4386-b7ad-87d87671aac9
+function plot_himmelblau(ca1, ca2, points=Array{Float64}[])
+ f(x,y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2
+ x=range(-4.6,stop=4.6,length=100)
+ y=range(-4.6,stop=4.6,length=100)
+ cg = cgrad([
+ :black,
+ :lightblue,
+ :blue,
+ :darkblue,
+ :lightgreen,
+ :green,
+ :darkgreen,
+ :yellow,
+ :orange,
+ :red,
+ :brown
+ ])
+ q = plot(
+ x,y,f,
+ st=:surface,
+ c = cg,
+ camera = (ca1,ca2),
+ zlim = (0,200),
+ xlab = "x",
+ ylab = "y",
+ )
+ if length(points) != 0
+ x = [p[1] for p in points]
+ y = [p[2] for p in points]
+ z = [f(p[1], p[2]) for p in points]
+ plot!(q,x,y,z,seriestype=:scatter, legend=false, zlim = (0,200), c=:white)
+ end
+ return q
+end
+
+# ╔═╡ d73ee58d-536b-4d19-bb3a-cae8c3bcc4c8
+plot_himmelblau(ca1, ca2)
+
+# ╔═╡ 1cef7433-e0a8-4ec7-a7a7-e7bd24efa20f
+function plot_3d(ca1, ca2, f, i_lower_x, i_upper_x, i_lower_y, i_upper_y, points=Array{Float64}[])
+ x=range(i_lower_x,stop=i_upper_x,length=100)
+ y=range(i_lower_y,stop=i_upper_y,length=100)
+ cg = cgrad([
+ :black,
+ :lightblue,
+ :blue,
+ :darkblue,
+ :lightgreen,
+ :green,
+ :darkgreen,
+ :yellow,
+ :orange,
+ :red,
+ :brown
+ ])
+ q = plot(
+ x,y,f,
+ st=:surface,
+ c = cg,
+ camera = (ca1,ca2),
+ zlim = (f(i_lower_x,i_lower_y), f(i_upper_x, i_upper_y)),
+ xlab = "x",
+ ylab = "y",
+ )
+ if length(points) != 0
+ x = [p[1] for p in points]
+ y = [p[2] for p in points]
+ z = [f(p[1], p[2]) for p in points]
+ plot!(q,x,y,z,seriestype=:scatter, legend=false, zlim=(f(i_lower_x,i_lower_y), f(i_upper_x, i_upper_y)), c=:white)
+ end
+ return q
+end
+
+# ╔═╡ c4838943-8a9d-46f9-88d5-6df92b66c8d4
+function plot_2d(i_lower_x, i_upper_x, f, points=Array{Float64}[])
+ x = range(i_lower_x, i_upper_x, length=100)
+ r = plot(
+ x,f,
+ c = :black,
+ xlab = "x",
+ ylab = "y",
+ )
+ if length(points) != 0
+ x = [p[1] for p in points]
+ y = [f(p[1]) for p in points]
+ plot!(r,x,y,seriestype=:scatter, legend=false, c=:white)
+ end
+ return r
+end
+
+# ╔═╡ 46862350-c094-4489-83a2-ea4b670a16c0
+f_himmelblau(x,y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2
+
+# ╔═╡ 2daddc2a-bc0e-4e8e-adde-f99660c9ac10
+population_fitness = fitness(population, f_himmelblau, "minima")
+
+# ╔═╡ 3bc3a212-fe9f-4416-9b95-9d061d50a08d
+pool_roulette = roulette_wheel_selection(population_fitness)
+
+# ╔═╡ a6da65cb-817d-4637-b7a7-0830488696e0
+"""
+ rank_selection(pf)
+
+Input:
+
+ - pf: Population Fitness: A list where each element consists of the individual
+ and its corresponding fitness
+
+Output:
+
+ - pool: A list with the selected individuals for the mating pool
+"""
+function rank_selection(pf)
+
+ # the number of ranks
+ n = length(population_fitness)
+
+ # initiate the lists containing the individuals
+ # and their weights (selection probability)
+ p, w = Array{Float64}[], Float64[]
+ for (rank, ind) in enumerate(sort(pf, by=pf->pf[2]))
+ push!(p, ind[1])
+ push!(w, (rank / (n * (n - 1))))
+ end
+
+ # select the mating pool based on their selection probabilities
+ pool = sample(p, Weights(w), n)
+
+ return pool
+end;
+
+# ╔═╡ fc0a7329-5d93-4519-ace0-626aa376fc1b
+"""
+ minima_himmelblau(pop_size, σ, α, pm, ff)
+
+Input:
+
+ - pop_size: The population size
+ - σ: The standarddeviation used to determine the termination criteria
+ - α: The crossover rate
+ - pm: The mutation rate
+ - ff: Fitness Function
+
+Output:
+
+ - generations: A list with the population in every generation
+"""
+function minima_himmelblau(pop_size, σ, α, pm, ff)
+
+ # counters
+ generation, generation_max = 0, 0
+
+ # the initial population
+ population = random_init_pop(pop_size, 2, [-4,4], [-4,4])
+
+ # population with its fitness values
+ f_pop = fitness(population, ff, "minima")
+
+ # the maximal fitness value
+ max_fitness = maximum([x[2] for x in f_pop])
+
+ # keep track of each population in each generation
+ generations = Array{Array{Float64}}[]
+ push!(generations, population)
+
+ # keep going untill termination criteria are true or
+ # until 1 milion generations
+ while !check_term(f_pop, σ, generation_max) && generation < 1000000
+
+ # keep track of the number of generations the maximal fitness does not change
+ if maximum([x[2] for x in f_pop]) > max_fitness
+ max_fitness = maximum([x[2] for x in f_pop])
+ generation_max = 0
+ else
+ generation_max += 1
+ end
+
+ # selection
+ mate_pool = rank_selection(f_pop)
+
+ # crossover
+ offspring = crossover(mate_pool, α)
+
+ # mutation
+ population = mutation(offspring, pm, generation)
+
+ # track each population in each generation
+ push!(generations, population)
+
+ # fitness of new population
+ f_pop = fitness(population, ff, "minima")
+
+ # track the number of generations
+ generation += 1
+
+ end
+
+ return generations
+end;
+
+# ╔═╡ c75e7eb2-ea7c-4448-ad5b-54955ee5cd8c
+"""
+ genetic_algorithm(pop_size, gs, i_x, i_y, extremeties, σ, α, pm, ff)
+
+Input:
+
+ - pop_size: The population size
+ - gs: Genome Size: Indicates wheter the function is 2d or 3d
+ - i_x: Interval: Interval in which the extrema need to be searched on the x-axis
+ - i_y: Interval: Interval in which the extrema need to be searched on the y-axis
+ - extremeties: Wheter the minima or maxima need to be searched: Options: "minima"
+ or "maxima"
+ - σ: The standarddeviation used to determine the termination criteria
+ - α: The crossover rate
+ - pm: The mutation rate
+ - ff: Fitness Function
+
+Output:
+
+ - generations: A list with the population in every generation
+"""
+function genetic_algorithm(pop_size, gs, i_x, i_y, extremeties, σ, α, pm, ff)
+
+ # counters
+ generation, generation_max = 0, 0
+
+ # the initial population
+ population = random_init_pop(pop_size, gs, i_x, i_y)
+
+ # population with its fitness values
+ f_pop = fitness(population, ff, extremeties)
+
+ # the maximal fitness value
+ max_fitness = maximum([x[2] for x in f_pop])
+
+ # keep track of each population in each generation
+ generations = Array{Array{Float64}}[]
+ push!(generations, population)
+
+ # keep going untill termination criteria are true or
+ # until 1 milion generations
+ while !check_term(f_pop, σ, generation_max) && generation < 1000000
+
+ # keep track of the number of generations the maximal fitness does not change
+ if maximum([x[2] for x in f_pop]) > max_fitness
+ max_fitness = maximum([x[2] for x in f_pop])
+ generation_max = 0
+ else
+ generation_max += 1
+ end
+
+ # selection
+ mate_pool = rank_selection(f_pop)
+
+ # crossover
+ offspring = crossover(mate_pool, α)
+
+ # mutation
+ population = mutation(offspring, pm, generation)
+
+ # track each population in each generation
+ push!(generations, population)
+
+ # fitness of new population
+ f_pop = fitness(population, ff, extremeties)
+
+ # track the number of generations
+ generation += 1
+
+ end
+
+ return generations
+end;
+
+# ╔═╡ 23000c68-7864-409f-b5fe-b43b9a2164c3
+pool_rank = rank_selection(population_fitness)
+
+# ╔═╡ fa31ea0c-b3dd-4145-bb35-3698308371a7
+offspring = crossover(pool_rank, 0.5)
+
+# ╔═╡ 93634846-dc90-4021-bf4c-de1b13f476cc
+offspring_mutated = mutation(offspring, 0.9, 1)
+
+# ╔═╡ ba2820c1-649f-4551-98d8-ce113e309b22
+pool_steady_state = steady_state_selection(population_fitness, 0.4)
+
+# ╔═╡ 4408b037-e336-4382-8468-28d1746c23d3
+pool_tournament = tournament_selection(population_fitness,50,0.9)
+
+# ╔═╡ 5aed7665-1131-4715-90ca-dca12c038a68
+generations_himmelblau = minima_himmelblau(pop_size_h, σₕ, αₕ, pmₕ, f_himmelblau)
+
+# ╔═╡ 7dbb864c-b3d9-4cd1-8c48-9a61be67334f
+md"""
+
+Number of generations to show:
+$(@bind g NumberField(1:length(generations_himmelblau),default=50))
+
+Frames per second:
+$(@bind fps NumberField(1:50, default=5))
+
+Angle 1:
+$(@bind ca3 NumberField(1:90,default=50))
+
+Angle 2:
+$(@bind ca4 NumberField(1:90,default=75))
+"""
+
+# ╔═╡ 453b235b-bd4f-446f-b767-b71a197cc66c
+begin
+ anim = @animate for (i,s) in enumerate(generations_himmelblau[1:g])
+ plot_himmelblau(ca3, ca4, s)
+ plot!(title="Generation: $i")
+ end
+ gif(anim, fps=fps)
+end
+
+# ╔═╡ 5f1b386d-daf0-46ca-a90a-89c954eb2d11
+generations_custom = genetic_algorithm(pop_size_c, gs, [i_lower_x,i_upper_x], [i_lower_y,i_upper_y], extr, σ_custom, α_custom, pm_custom, f)
+
+# ╔═╡ 26f2bdca-e7bc-4e80-86ca-d4dc29d71aa0
+md"""
+
+Number of generations to show:
+$(@bind ge NumberField(1:length(generations_custom),default=1))
+
+Frames per second:
+$(@bind frps NumberField(1:50, default=5))
+
+Only relevant for 3D functions:
+
+Angle 1:
+$(@bind ca5 NumberField(1:90,default=50))
+Angle 2:
+$(@bind ca6 NumberField(1:90,default=75))
+"""
+
+# ╔═╡ 19b91d8e-d03d-4b76-8358-5a4b1e90604d
+begin
+ anima = @animate for (i,s) in enumerate(generations_custom[1:ge])
+ if gs == 2
+ plot_3d(ca5,ca6,f,i_lower_x,i_upper_x,i_lower_y,i_upper_y,s)
+ else
+ plot_2d(i_lower_x,i_upper_x,f,s)
+ end
+ plot!(title="Generation: $i")
+ end
+ gif(anima, fps=frps)
+end
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+
+[compat]
+Distributions = "~0.25.37"
+Images = "~0.25.0"
+Plots = "~1.25.4"
+PlutoUI = "~0.7.27"
+StatsBase = "~0.33.14"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
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+version = "1.0.1"
+
+[[AbstractPlutoDingetjes]]
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+
+[[Adapt]]
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+version = "3.3.2"
+
+[[ArgTools]]
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+
+[[ArnoldiMethod]]
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+version = "0.2.0"
+
+[[ArrayInterface]]
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+
+[[Artifacts]]
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+
+[[AxisAlgorithms]]
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+deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "e08890d19787ec25029113e88c34ec20cac1c91e"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "2.0.0"
+
+[[StackViews]]
+deps = ["OffsetArrays"]
+git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
+uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
+version = "0.1.1"
+
+[[Static]]
+deps = ["IfElse"]
+git-tree-sha1 = "7f5a513baec6f122401abfc8e9c074fdac54f6c1"
+uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
+version = "0.4.1"
+
+[[StaticArrays]]
+deps = ["LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "de9e88179b584ba9cf3cc5edbb7a41f26ce42cda"
+uuid = "90137ffa-7385-5640-81b9-e52037218182"
+version = "1.3.0"
+
+[[Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[StatsAPI]]
+git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.2.0"
+
+[[StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.33.14"
+
+[[StatsFuns]]
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "0.9.14"
+
+[[StructArrays]]
+deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
+git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
+uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+version = "0.6.3"
+
+[[SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
+[[TOML]]
+deps = ["Dates"]
+uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
+
+[[TableTraits]]
+deps = ["IteratorInterfaceExtensions"]
+git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
+uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
+version = "1.0.1"
+
+[[Tables]]
+deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
+git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
+uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
+version = "1.6.1"
+
+[[Tar]]
+deps = ["ArgTools", "SHA"]
+uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
+
+[[TensorCore]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
+uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
+version = "0.1.1"
+
+[[Test]]
+deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
+uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[TiffImages]]
+deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
+git-tree-sha1 = "991d34bbff0d9125d93ba15887d6594e8e84b305"
+uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
+version = "0.5.3"
+
+[[TiledIteration]]
+deps = ["OffsetArrays"]
+git-tree-sha1 = "5683455224ba92ef59db72d10690690f4a8dc297"
+uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
+version = "0.3.1"
+
+[[TranscodingStreams]]
+deps = ["Random", "Test"]
+git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
+uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
+version = "0.9.6"
+
+[[URIs]]
+git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
+uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
+version = "1.3.0"
+
+[[UUIDs]]
+deps = ["Random", "SHA"]
+uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
+
+[[UnPack]]
+git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
+uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+version = "1.0.2"
+
+[[Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+
+[[UnicodeFun]]
+deps = ["REPL"]
+git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
+uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
+version = "0.4.1"
+
+[[Unzip]]
+git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.1.2"
+
+[[Wayland_jll]]
+deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
+uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
+version = "1.19.0+0"
+
+[[Wayland_protocols_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
+uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
+version = "1.23.0+0"
+
+[[WoodburyMatrices]]
+deps = ["LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
+uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
+version = "0.5.5"
+
+[[XML2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
+uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
+version = "2.9.12+0"
+
+[[XSLT_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
+git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
+uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
+version = "1.1.34+0"
+
+[[Xorg_libX11_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
+git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
+uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
+version = "1.6.9+4"
+
+[[Xorg_libXau_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
+uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
+version = "1.0.9+4"
+
+[[Xorg_libXcursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
+uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
+version = "1.2.0+4"
+
+[[Xorg_libXdmcp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
+uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
+version = "1.1.3+4"
+
+[[Xorg_libXext_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
+uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
+version = "1.3.4+4"
+
+[[Xorg_libXfixes_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
+version = "5.0.3+4"
+
+[[Xorg_libXi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
+version = "1.7.10+4"
+
+[[Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
+git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
+version = "1.1.4+4"
+
+[[Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
+version = "1.5.2+4"
+
+[[Xorg_libXrender_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
+uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
+version = "0.9.10+4"
+
+[[Xorg_libpthread_stubs_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
+uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
+version = "0.1.0+3"
+
+[[Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
+git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.13.0+3"
+
+[[Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
+version = "1.1.0+4"
+
+[[Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.2+4"
+
+[[Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.27.0+4"
+
+[[Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.4.0+3"
+
+[[Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+
+[[Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.0+0"
+
+[[libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.1+0"
+
+[[libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+0"
+
+[[libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+1"
+
+[[nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+
+[[p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+
+[[x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "0.9.1+5"
+"""
+
+# ╔═╡ Cell order:
+# ╠═c80a0f15-2c37-4c40-a543-2e6c3fead1be
+# ╟─171fee18-20f6-11eb-37e5-2d04caea8c35
+# ╟─98b278e9-5cc9-4e36-9d1a-75eb9f4158de
+# ╟─d89c31c5-f2b3-4b52-8e47-580c62979687
+# ╟─d73ee58d-536b-4d19-bb3a-cae8c3bcc4c8
+# ╟─ba845736-b141-484a-9b10-fc73ecf31db3
+# ╟─cccaf5fb-3c95-4ea9-b699-0cee2f12542e
+# ╟─8212a676-3167-438a-944d-5eeae72d54d8
+# ╟─9365760a-10e5-48a4-ae77-b3f1a686f8e3
+# ╟─a8cd1caa-feb2-442f-ba8f-27619bfbff84
+# ╠═eba0c158-54d3-4f56-8b1a-5d3ddba001db
+# ╠═41dd8e8d-0f4c-407e-90c5-6f450fe318fe
+# ╟─37b9fce9-e99c-424f-a614-8169b7edf0d6
+# ╠═f4969be8-815e-43bc-adaf-a6e1eeec1226
+# ╠═2daddc2a-bc0e-4e8e-adde-f99660c9ac10
+# ╟─ccb197ff-f322-4f14-acb5-ba64a343d234
+# ╠═2bcdbbf0-2473-40d9-8c85-cec3b6ca4b31
+# ╟─c6155621-9a86-4747-b0ec-65e779670b57
+# ╟─953edf56-a957-4c61-8a89-9709dc6dfd65
+# ╠═79eb48df-26de-4965-b078-9bb20313247a
+# ╠═3bc3a212-fe9f-4416-9b95-9d061d50a08d
+# ╟─8623b228-c627-4f81-8f6f-6de074b8ec20
+# ╠═a6da65cb-817d-4637-b7a7-0830488696e0
+# ╠═23000c68-7864-409f-b5fe-b43b9a2164c3
+# ╟─84d49f43-8ac3-4e73-991c-a54bb9fe9b5f
+# ╠═07e1c8b6-c3fd-4f5f-bbb0-fe6595813d55
+# ╠═ba2820c1-649f-4551-98d8-ce113e309b22
+# ╟─307af9a7-6b0c-44ad-a5b0-d9b0c18b5db4
+# ╠═6cf8534b-2fa1-4762-9526-bd3c2da99843
+# ╠═4408b037-e336-4382-8468-28d1746c23d3
+# ╠═5096d7c0-0189-4c89-9ec0-13e7aac9aa8a
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diff --git a/notebook/geneticalgorithms.jl.html b/notebook/geneticalgorithms.jl.html
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+ ⚡ Pluto.jl ⚡
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diff --git "a/notebook/\360\237\216\210 geneticalgorithms.jl \342\200\224 Pluto.jl.pdf" "b/notebook/\360\237\216\210 geneticalgorithms.jl \342\200\224 Pluto.jl.pdf"
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diff --git a/project ideas.md b/project ideas.md
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-# Project ideas
-
-Here are some suggestions for projects to do. Either pick something from this list or use it as inspiration.
-
-If you choose a project use strikthrought to remove it -> ~~crossed~~
-
-## Teaching 👨🏫
-
-Explain an optimization method not covered in the course though an interactive notebook. Gold standard is [Distill](https://distill.pub/2017/momentum/)
-
-- Conjugate gradient descent
-- [Cross-entropy method](https://en.wikipedia.org/wiki/Cross-Entropy_Method)
-- Levenberg–Marquardt algorithm (for nonlinear regression and inverse kinematics)
-- training adverserial neural networks
-- Q-learning
-- link between [fractals and the Newton method](https://www.youtube.com/watch?v=-RdOwhmqP5s)
-- [MAP-elites](https://arxiv.org/abs/1504.04909)
-- [information-geometric opitmization algorithms](http://www.cmap.polytechnique.fr/~anne.auger/teaching-slides/05_DFO-IGO.pdf)
-- the big deal with multi-objective optimization
-- Thompson sampling: optimal gambling 🎲
-- ...
-
-## Tools 🔧
-
-Solve a problem using a method from the course or a new one.
-
-- time table scheduling
-- my own RNA folder!
-- color transfer using optimal transportation done right
-- analytic solution of a ODE using genetic programming
-- graph matching using simulated annealing
-- optimal task for every person using the Hungarian algorithm
-- finding negative cycles using the Bellman–Ford algorithm
-- multiple sequence alignment using Genetic Algorithms
-- using MaxEnt to find the best probability distribution
-- finding design patterns in phage lytic proteins using evolutionary algorithms
-- homebrew SVM
-- recovering images from a few pixels using [compressed sensing](https://www.youtube.com/watch?v=SbU1pahbbkc) (L1-norm minimization)
-- visalizing complex networks using quadratic optimization
-- ...
-
-## Research projects ⚗️
-
-Experiment and learn. Reproduce the results of a paper (in simplified form). Show me something exciting about optimization! Use [visuals](https://www.youtube.com/watch?v=gvck7ssg9dE) to tell a story.
-
-- [fitting a neural network by optimizing one weigth at a time](http://arxiv.org/abs/2005.05955)
-- search paths of Hill Climbing: an exhaustive search
-- [convex restrictions in physical design](https://stanford.edu/~boyd/papers/pdf/cvx_restrictions_physical_design.pdf)
-- non-covergence as a regularization mechanism in machine learning
-- improving gradient descent or learning using [gradient startvation](https://mohammadpz.github.io/GradientStarvation.html)
-- improving the convergence of evolutionary algorithms by varying the objective function
-- the optimization landscape of ANNs
-- comparision of optimizers for deep learning
-- Newton methods for lazy bums: is the diagonal sufficient?
-- utilitarian ethics: optimization for the Good Place?
-- [Maze solver using bacteria](https://www.technologyreview.com/2021/11/09/1039107/e-coli-maze-solving-biocomputer/?s=03) (simulation of an experiment)
-- ...
diff --git a/src/STMOZOO.jl b/src/STMOZOO.jl
deleted file mode 100644
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-module STMOZOO
-
-
-# execute your source file and export the module you made
-include("example.jl")
-export Example
-
-end # module
diff --git a/src/example.jl b/src/example.jl
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-# Michiel Stock
-# Example of a source code file implementing a module.
-
-
-# all your code is part of the module you are implementing
-module Example
-
-# you have to import everything you need for your module to work
-# if you use a new package, don't forget to add it in the package manager
-using LinearAlgebra
-
-# export all functions that are relevant for the user
-export solve_quadratic_system, quadratic_function
-
-"""
- solve_quadratic_system(P, q, r=0; testPD=false)
-
-Find the minimizer of a canonical quadratic system:
-
-``f(x) = 0.5xᵀ P x + x ⋅ q + r``
-
-with `P` a positive scalar or a positive-definite n x n matrix and `q` a scalar or
-a n x n vector. The intercept `r` can optionally be given but does not influence
-the minimizer. One can use the keyword argument `testPD` to test if `P` is positive definite,
-though this comes at a computational cost.
-
-## Examples
-
-Scalar case:
-
-```julia-repl
-julia> solve_quadratic_system(8, -4, 3)
-0.5
-```
-
-Vector case:
-
-```julia-repl
-julia> P = [3 1; 1 2];
-
-julia> q = [0.5, -2];
-
-julia> solve_quadratic_system(P, q)
-2-element Array{Float64,1}:
- -0.6
- 1.2999999999999998
-```
-"""
-function solve_quadratic_system(P, q, r=0; testPD=false)
- testPD && @assert isposdef(P) "Provided P is not positive definite"
- return - P \ q
-end
-
-"""
- quadratic_function(P, q, r)
-
-Give the paramters of a canonical quatratic function and returns a function.
-"""
-quadratic_function(P, q, r) = x -> 0.5x' * P * x + q ⋅ x + r
-
-end
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diff --git a/test/example.jl b/test/example.jl
deleted file mode 100644
index d554036c..00000000
--- a/test/example.jl
+++ /dev/null
@@ -1,51 +0,0 @@
-# example of a unit test in Julia
-# runs a test for a certain module
-# to run the tests, first open the package manager (`]` in REPL),
-# activate the project if not done so and then enter `test`
-
-# wrap all your tests and subgroups in a `@testset` block
-@testset "Example" begin
- using STMOZOO.Example # load YOUR module
-
- @testset "solve quadratic" begin
- # test some cases
- @test solve_quadratic_system(8.0, -2.0, 3.0) == 0.25
-
- # test for type
- @test solve_quadratic_system(7.0, 27.4, 3.0) isa Number
-
- # test for type stability
- @test solve_quadratic_system(1//2 , -2//1, 3//1) isa Rational
-
- P = [10 1; 1 5]
- q = [100, -7]
-
- # test for a result
- # use ≈ (`\approx`) to check approximate equality
- # useful for rounding errors
- # NOTE: does NOT work on ≈ 0!
- @test solve_quadratic_system(P, q) ≈ - P \ q
- @test solve_quadratic_system(P, q, testPD=true) isa Vector
-
- # test if a certain error is thrown
- @test_throws AssertionError solve_quadratic_system(-P, q, testPD=true)
- end
-
- @testset " quadratic function" begin
- f_scalar = quadratic_function(3, 4, 8)
-
- @test f_scalar isa Function
- @test f_scalar(2) isa Number
- @test f_scalar(2) ≈ 0.5 * 3 * 2^2 + 4 * 2 + 8
-
- P = [9.0 -2; -2 3]
- q = [-3, -4]
- r = -π
- x = [-2.0, 2.8]
-
- f_vect = quadratic_function(P, q, r)
- @test f_vect isa Function
- @test f_vect(x) isa Number
- @test f_vect(x) ≈ 0.5x' * P * x + q' * x + r
- end
-end
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diff --git a/test/runtests.jl b/test/runtests.jl
deleted file mode 100644
index ff9b0f7e..00000000
--- a/test/runtests.jl
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@@ -1,4 +0,0 @@
-using Test
-
-include("example.jl")
-# add here the file with your unit tests
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