add some more references

Author: danymukesha

README.Rmd

@@ -1,5 +1,6 @@
 ---
 output: github_document
+bibliography: references.bib
 ---
 
 <!-- README.md is generated from README.Rmd. Please edit that file -->
@@ -21,9 +22,9 @@ knitr::opts_chunk$set(
 
 <!-- badges: end -->
 
-Genetic algorithms (GAs) are metaheuristic optimization techniques inspired by the principles of natural selection and evolution. They operate on a population of potential solutions, applying genetic operators such as selection, crossover, and mutation to evolve better solutions over successive generations.
+Genetic algorithms (GAs) are metaheuristic optimization techniques inspired by the principles of natural selection and evolution. They operate on a population of potential solutions, applying genetic operators such as selection, crossover, and mutation to evolve better solutions over successive generations[@whitley1994].
 
-GAs are particularly useful for optimizing complex, non-linear functions with multiple local optima, where traditional gradient-based methods may fail.
+GAs are particularly useful for optimizing complex, non-linear functions with multiple local optima, where traditional gradient-based methods may fail[@holland1992; @goldberg1988].
 
 We come out with a simple example to explore how these components work together in our quadratic function optimization problem using `genetic.algo.optimizeR` package.
 
@@ -62,7 +63,55 @@ Here's a breakdown of the aim and the results:
 
 After multiple generations of repeating these steps, the genetic algorithm aims to converge towards an optimal or near-optimal solution. In this example, since it's simple and the solution space is small, we could expect the algorithm to converge relatively quickly towards the optimal solution $x = 2$, where $f(x) = 0$.
 
-[***Explaining Graph***](https://danymukesha.github.io/genetic.algo.optimizeR/articles/explaining_graph.html) ![Web capture_8-2-2024_233215_mermaid live](https://github.com/danymukesha/genetic.algo.optimizeR/assets/45208254/a9dc80bc-a464-4151-b9ff-9630310cdf9f)
+[***wikipedia***](https://en.wikipedia.org/wiki/Genetic_algorithm)
+
+```{r diagram_GAs, eval=FALSE, include=FALSE}
+library(DiagrammeR)
+
+grViz("
+  digraph genetic_algorithm {
+    rankdir=LR;
+    
+    A [label = 'Initialize Population'];
+    B [label = 'Evaluate Fitness'];
+    C [label = 'Selection'];
+    D [label = 'Termination Condition?'];
+    E [label = 'End'];
+    F [label = 'Crossover and Mutation'];
+    G [label = 'Replace Population'];
+    
+    X1 [label = 'Individual 1: x = 1', shape = ellipse];
+    X2 [label = 'Individual 2: x = 3', shape = ellipse];
+    X3 [label = 'Individual 3: x = 0', shape = ellipse];
+    
+    Y1 [label = 'Selected Parents: x = 1, x = 3', shape = ellipse];
+    
+    Z1 [label = 'Offspring 1: x = 1', shape = ellipse];
+    Z2 [label = 'Offspring 2: x = 3', shape = ellipse];
+    
+    A -> B;
+    B -> C;
+    C -> D;
+    D -> E [label = 'Yes'];
+    D -> F [label = 'No'];
+    F -> G;
+    G -> B;
+    
+    # Examples
+    B -> X1 [label = 'Example:'];
+    B -> X2;
+    B -> X3;
+    
+    C -> Y1 [label = 'Example:'];
+    
+    F -> Z1 [label = 'Example:'];
+    F -> Z2;
+  }
+")
+
+```
+
+![](https://github.com/danymukesha/genetic.algo.optimizeR/assets/45208254/a9dc80bc-a464-4151-b9ff-9630310cdf9f)
 
 ## Usage
 
@@ -121,7 +170,7 @@ The above example illustrates the process of a genetic algorithm, where individu
         (Note: the values are random and the population should be highly diversified)
     -   The space of x value is kept integer type and on range from 0 to 3,for simplification.
 
-    ```{r}
+    ```{r population}
     population <- c(1, 3, 0)
     population
     ```
@@ -144,7 +193,7 @@ $$
 
 In R, we write:
 
-```{r}
+```{r f_function}
 a <- 1
 b <- -4
 c <- 4
@@ -295,7 +344,7 @@ By understanding these fundamental concepts and their implementation, we can tak
 
 ### Multi-objective optimization
 
-While our example focuses on single-objective optimization, genetic algorithms are particularly powerful for multi-objective problems. In such cases, the concept of Pareto optimality is used to evaluate solutions, and techniques like NSGA-II (Non-dominated Sorting Genetic Algorithm II) can be employed.
+While our example focuses on single-objective optimization, genetic algorithms are particularly powerful for multi-objective problems. In such cases, the concept of Pareto optimality is used to evaluate solutions, and techniques like NSGA-II (Non-dominated Sorting Genetic Algorithm II) can be employed[@deb2002].
 
 ### Adaptive parameter control
 
@@ -319,7 +368,3 @@ I would encourage the users to experiment with different parameter settings and
 
 ## References
 
-1.  Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley.
-2.  Holland, J. H. (1992). Adaptation in Natural and Artificial Systems. MIT Press.
-3.  Whitley, D. (1994). A genetic algorithm tutorial. Statistics and Computing, 4(2), 65-85
-4.  Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197.

README.md

@@ -78,10 +78,15 @@ In this example, since it’s simple and the solution space is small, we
 could expect the algorithm to converge relatively quickly towards the
 optimal solution $x = 2$, where $f(x) = 0$.
 
-[***Explaining
-Graph***](https://danymukesha.github.io/genetic.algo.optimizeR/articles/explaining_graph.html)
-![Web capture_8-2-2024_233215_mermaid
-live](https://github.com/danymukesha/genetic.algo.optimizeR/assets/45208254/a9dc80bc-a464-4151-b9ff-9630310cdf9f)
+[***wikipedia***](https://en.wikipedia.org/wiki/Genetic_algorithm)
+
+<figure>
+<img
+src="https://github.com/danymukesha/genetic.algo.optimizeR/assets/45208254/a9dc80bc-a464-4151-b9ff-9630310cdf9f"
+alt="Web capture_8-2-2024_233215_mermaid live" />
+<figcaption aria-hidden="true">Web capture_8-2-2024_233215_mermaid
+live</figcaption>
+</figure>
 
 ## Usage
 
@@ -93,7 +98,7 @@ population <- initialize_population(population_size = 3, min = 0, max = 3)
 print("Initial Population:")
 #> [1] "Initial Population:"
 print(population)
-#> [1] 2 0 1
+#> [1] 3 2 1
 
 generation <- 0 # Initialize generation/reputation counter
 
@@ -128,17 +133,17 @@ while (TRUE) {
     print(population)
 }
 #> [1] "Evaluation:"
-#> [1] 0 4 1
+#> [1] 1 0 1
 #> [1] "Selection:"
-#> [1] 2 1
+#> [1] 2 3
 #> [1] "Crossover and Mutation:"
-#> [1] 2 2
+#> [1] 3 3
 #> [1] "Replacement:"
-#> [1] 2 0 2
+#> [1] 3 2 3
 #> [1] "Evaluation:"
-#> [1] 0 4 0
+#> [1] 1 0 1
 #> [1] "Selection:"
-#> [1] 2 2
+#> [1] 2 3
 #> [1] "Crossover and Mutation:"
 #> [1] 2 2
 #> [1] "Replacement:"
@@ -386,9 +391,9 @@ versions of selection, crossover, and mutation operations can
 significantly reduce computation time for large-scale optimization
 problems.
 
-## Wrap-Up
+## Wrap-up
 
-Currrently only the fundamental concepts and implementation of genetic
+Currently only the fundamental concepts and implementation of genetic
 algorithms are used in the `genetic.algo.optimizeR` package. By
 following these steps and understanding the underlying principles, users
 can apply this powerful optimization technique to a wide range of

inst/tutorials/theory/.gitignore inst/tutorials/theoretical_background/.gitignore

@@ -1,5 +1,5 @@
 ---
-title: "Theory background"
+title: "Tutorial on GAs"
 output: learnr::tutorial
 runtime: shiny_prerendered
 ---
@@ -11,7 +11,28 @@ library(dplyr)
 knitr::opts_chunk$set(echo = FALSE)
 ```
 
-## 1.  Initialize Population:
+## Theoretical Background
+
+Genetic algorithms (GAs) are metaheuristic optimization techniques inspired by the principles of natural selection and evolution. They operate on a population of potential solutions, applying genetic operators such as selection, crossover, and mutation to evolve better solutions over successive generations.
+
+The key components of a genetic algorithm include:
+
+1. **Encoding**: Representing potential solutions as "chromosomes"
+2. **Fitness Function**: Evaluating the quality of solutions
+3. **Selection**: Choosing individuals for reproduction based on fitness
+4. **Crossover**: Combining genetic information from parents to create offspring
+5. **Mutation**: Introducing random changes to maintain genetic diversity
+6. **Replacement**: Updating the population with new individuals
+
+GAs are particularly useful for optimizing complex, non-linear functions with multiple local optima, where traditional gradient-based methods may fail.
+
+## Aim
+
+Our primary objective is to optimize the quadratic function \( f(x) = x^2 - 4x + 4 \) to find the value of \( x \) that minimizes the function. This function has a global minimum at \( x = 2 \), which we aim to discover using our genetic algorithm implementation.
+
+## Method
+
+### 1.  Initialize Population:
 
   -   Start with a population of individuals: X1(x=1), X2(x=3), X3(x=0).\
   (Note: the values are random and the population should be highly diversified)
@@ -21,7 +42,7 @@ knitr::opts_chunk$set(echo = FALSE)
 population <- c(1, 3, 0)
 ```
 
-## 2.  Evaluate Fitness:
+### 2.  Evaluate Fitness:
 
   -   Calculate fitness(`f(x)`) for each individual:
 
@@ -85,7 +106,7 @@ ggplot2::ggplot(df, aes(x = x, y = y)) +
     theme_minimal()
 ```
 
-## 3.  Selection:
+### 3.  Selection:
 
   -   Select parents for crossover:
 
@@ -101,17 +122,17 @@ ggplot(df, aes(x = x, y = y)) +
     theme_minimal() # Use a minimal theme
 ```
 
-## 4.  Crossover and Mutation:
+### 4.  Crossover and Mutation:
 
   -   Generate offspring through crossover and mutation:
       -   Z1(x=1), Z2(x=3) (no mutation in this example)
 
-## 5.  Replacement:
+### 5.  Replacement:
 
   -   Replace individuals in the population:
       -   Replace X3 with Z1, maintaining the population size.
 
-## 6.  Repeat Steps 2-5 for multiple generations until a termination condition is met.
+### 6.  Repeat Steps 2-5 for multiple generations until a termination condition is met.
 
 The optimal/fitting individuals *F* of a quadratic equation, in this case the lowest point on the graph of f(x), is: 
 

inst/tutorials/theory/theory.Rmd inst/tutorials/theoretical_background/theory.Rmd

@@ -0,0 +1,51 @@
+
+@article{holland1992,
+	title = {Adaptation in Natural and Artificial Systems},
+	author = {Holland, John H.},
+	year = {1992},
+	month = {04},
+	date = {1992-04-29},
+	doi = {10.7551/mitpress/1090.001.0001},
+	url = {http://dx.doi.org/10.7551/mitpress/1090.001.0001},
+	langid = {en}
+}
+
+@article{goldberg1988,
+	author = {Goldberg, David E. and Holland, John H.},
+	year = {1988},
+	date = {1988},
+	journal = {Machine Learning},
+	pages = {95--99},
+	volume = {3},
+	number = {2/3},
+	doi = {10.1023/a:1022602019183},
+	url = {http://dx.doi.org/10.1023/A:1022602019183}
+}
+
+@article{whitley1994,
+	title = {A genetic algorithm tutorial},
+	author = {Whitley, Darrell},
+	year = {1994},
+	month = {06},
+	date = {1994-06},
+	journal = {Statistics and Computing},
+	volume = {4},
+	number = {2},
+	doi = {10.1007/bf00175354},
+	url = {http://dx.doi.org/10.1007/BF00175354},
+	langid = {en}
+}
+
+@article{deb2002,
+	title = {A fast and elitist multiobjective genetic algorithm: NSGA-II},
+	author = {Deb, K. and Pratap, A. and Agarwal, S. and Meyarivan, T.},
+	year = {2002},
+	month = {04},
+	date = {2002-04},
+	journal = {IEEE Transactions on Evolutionary Computation},
+	pages = {182--197},
+	volume = {6},
+	number = {2},
+	doi = {10.1109/4235.996017},
+	url = {http://dx.doi.org/10.1109/4235.996017}
+}

references.bib

@@ -24,7 +24,7 @@ The application of genetic algorithms (GAs) offers a powerful approach to optimi
 
 Genetic algorithms are inspired by the principles of natural selection and genetics. They are widely utilized in optimization problems where traditional methods may falter due to the complexity of the search space. We will illustrate the step-by-step implementation of a genetic algorithm to minimize the quadratic function \( f(x) = x^2 - 4x + 4 \). The objective is to identify the value of \( x \) that yields the minimum value of the function, thereby providing insights into the capabilities and workings of GAs.
 
-## Theory
+## Demonstration
 
 ### Initialization of population