Local search & optimization
- path to goal irrelevant, only goal state matters
- uses single current state → moves to neighbors
- Advantages:
- low memory use
- works in huge/infinite state spaces
- good for optimization problems
Example: N-Queens
- goal: place n queens with no conflicts
- state: configuration of queens
- solution: valid arrangement
Hill-climbing search
- moves to neighbour with best heuristic
- stops at local maxima (no better neighbours)
- doesn’t look ahead
graph TD Start[Initial state] --> A[Neighbor 1] Start --> B[Neighbor 2] A --> Peak1[Local maximum] B --> Peak2[Goal or Local max]
Variations:
- Stochastic: random among uphill moves
- First-choice: pick first better successor
- Random-restart: try multiple random states to avoid local maxima
Drawbacks of hill-climbing
- Local maxima: stuck at non-optimal peaks
- Ridges: difficult sequences for greedy search
- Plateaux: flat evaluation function → random walk
- success rate can be low (e.g., 86% stuck in 8-queens)
Genetic Algorithms
Darwinian Evolution 1: survival of the fittest
- all environments have finite resources (can only support a limited number of individuals)
- lifeforms have basic instinct/lifecycles geared towards reproduction
- some kind of selection is inevitable
- the individuals that compete for the resources most effectively have increased chance of reproduction
Note
skipped everything else lol?
Biological evolution
- genes are like parameters → control our development/adjust how the GA works
- evolution creates the genes and specifies the different values a gene can take (alleles)
- Reproduction with inheritance: individuals make copies of themselves
- copies should resemble their parents (not be duplicates)
- Variation: ensure that copies are not identical to parents
- mutations, crossover produces individuals with different traits
- Selection: need a method to ensure that some individuals make copies of themselves more than others
- fittest individuals (favourable traits) have more offspring than unfit individuals, and population therefore has those traits
- over time, changes will cause new species that can specialize for particular environments
- Evolution: reproduction with inheritance + variability + selection
Evolutionary computation
- very important ⇒ take notes on this
Note
up to slide 24