Module 2 notes

OMSCS/Courses/AI/Module_02/Module 02 - Simulated Annealing.md

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+---
+tags:
+  - OMSCS
+  - AI
+---
+# Module 02 - Simulated Annealing
+
+> Do the stupid thing first, then add intelligence until you solve the problem.
+
+This module goes over the N-Queens problem a lot. On small boards, you can arrange the queens randomly, then move the queen with the most number of queens that it can attack to a space which minimizes that number. This works pretty well on some inputs, but stops working as N increases.
+
+This is effectively a hill climbing approach, in which the solution can get stuck in a local minimum. Options for improving this:
+
+- Randomly restart from another state. Keep track of the best solution.
+- Simulated annealing. Start with a large step size, but decrease it over time.
+
+Other issues with hill climbing:
+- step size too small
+	- Hitting "shoulders"
+	- Taking too long to reach a maximum
+- Step size too large
+	- Skipping over the local/global maximum
+- only searching immediate surrounding pixels
+
+## Simulated Annealing
+![[Pasted image 20240116182506.png]]
+
+## Local Beam Search
+- "Keep track of $K$ particles"
+- Randomly generate $K$ particles
+- Iterate
+	- Randomly generate $N$ neighbors of each particle
+	- Keep the $K$ best particles of the $K \times N$ existing particles
+- Stochastic beam search works the same, except $K$ "best" is determined probabilistically. Sometimes you pick a bad one just for fun.
+
+## Genetic Algorithms
+- simulating evolution and mating
+	- Randomly generate starting members of the population.
+	- Define a fitness function
+	- Define a method for selecting parents based on fitness
+	- Define a method for producing offspring from 2+ parents plus fitness
+	- Define a method for randomly mutating offspring to introduce new information.
+	- Carry over the best $N$ parents from the past generation for the next iteration so you don't lose useful information.
+- super cool in principle
+- super fun to implement
+- probably not a super pragmatic method for most optimization problems
+- "It's a fancy version of stochastic beam search which makes a nice analogy to biology."
+- "Some people call genetic algorithms the 2nd-best solution to any problem."
+