From e433c367985eeaf887e0b97fe244c06c8f80dc8b Mon Sep 17 00:00:00 2001 From: Austin Schaffer Date: Tue, 16 Jan 2024 18:52:34 -0500 Subject: [PATCH] Module 2 notes --- .../Module 02 - Simulated Annealing.md | 49 ++++++++++++++++++ .../images/Pasted image 20240116182506.png | Bin 0 -> 202566 bytes 2 files changed, 49 insertions(+) create mode 100644 OMSCS/Courses/AI/Module_02/Module 02 - Simulated Annealing.md create mode 100644 OMSCS/Courses/AI/Module_02/images/Pasted image 20240116182506.png diff --git a/OMSCS/Courses/AI/Module_02/Module 02 - Simulated Annealing.md b/OMSCS/Courses/AI/Module_02/Module 02 - Simulated Annealing.md new file mode 100644 index 0000000..5449006 --- /dev/null +++ b/OMSCS/Courses/AI/Module_02/Module 02 - Simulated Annealing.md @@ -0,0 +1,49 @@ +--- +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." + diff --git a/OMSCS/Courses/AI/Module_02/images/Pasted image 20240116182506.png b/OMSCS/Courses/AI/Module_02/images/Pasted image 20240116182506.png new file mode 100644 index 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