#import "@preview/touying:0.6.1": *
#import themes.university: *

#show: university-theme.with(
  aspect-ratio: "16-9",
  config-info(
    title: [bioai - assignment 1],
    author: [fredrik robertsen],
    date: "09.02.2026",
    institution: [ntnu idi],
    logo: box(image("ntnu.png", height: 1em))
  ),
)

#title-slide(authors: [fredrik robertsen])

== problem 1 - binary knapsack

- there are many items, each with a value and weight
- the knapsack you are wearing can only carry so much weight
- you want the most bang for your buck
  - what's the best _combination_ of items to keep?
- combinatory problem, np hard
  - approximate using a genetic algorithm
- this is like optimizing your inventory in games like skyrim
  - do you want 400 spoons in your pocket, each worth a dime, or do you want that gold bar that weighs a ton?
- formally, you want to maximize $z = sum_(j=1)^n p_j x_j$ such that $sum_(j=1)^n w_j x_j <= c$ where $x_j in {0, 1}$
  - for item $j$: $p_j$ is the profit; $w_j$ the weight; $x_j$ whether to keep it

== problem 2 - feature selection

- similar to the binary knapsack problem
- this time you have many data points
  - each data point consists of _features_
- each data point has an associated _output_
- you wish to eliminate the features that are least influential in producing a given output
  - this is like choosing what items to keep in your knapsack
- this is like weather forecasting
  - hundreds of features in data
    - which are most relevant?
    - which are noise?

== general implementation

- generate a population of randomized chromosomes
- calculate their fitness values
- perform a _tournament selection_ to choose parent chromosomes
  - more fit individuals are more likely to be selected
  - introduces less diversity
- combine two parents to form two children via _single point crossover_
- mutate children randomly
- merge children into population, evicting the least fit individuals
  - this is the _elitism survivor selection_
- repeat

== specific implementation

- fitness function
  - used the sum mentioned earlier
  - used linear regression and rmse for feature selection

== optimizations

todo

== results

todo

== conclusion

todo