From 3538efa66e59dc118ec2609016b2cdb3177f2ca2 Mon Sep 17 00:00:00 2001 From: Peter Vacho Date: Sun, 16 Mar 2025 22:10:12 +0100 Subject: [PATCH] Add results --- PROTOCOL.md | 114 +++++++++++++++++++++++++++++++++ imgs/1_config.png | Bin 0 -> 21500 bytes imgs/1_ls.png | Bin 0 -> 31647 bytes imgs/1_shc.png | Bin 0 -> 31703 bytes imgs/2_config.png | Bin 0 -> 22087 bytes imgs/2_ls.png | Bin 0 -> 35973 bytes imgs/2_ls_iterations-1000.png | Bin 0 -> 33423 bytes imgs/2_ls_neighbors-100.png | Bin 0 -> 33661 bytes imgs/2_ls_stddev-30.png | Bin 0 -> 37448 bytes imgs/2_shc.png | Bin 0 -> 36362 bytes imgs/2_shc_iterations-1000.png | Bin 0 -> 33442 bytes imgs/2_shc_neighbors-100.png | Bin 0 -> 33264 bytes imgs/2_shc_stddev-30.png | Bin 0 -> 38301 bytes 13 files changed, 114 insertions(+) create mode 100644 PROTOCOL.md create mode 100644 imgs/1_config.png create mode 100644 imgs/1_ls.png create mode 100644 imgs/1_shc.png create mode 100644 imgs/2_config.png create mode 100644 imgs/2_ls.png create mode 100644 imgs/2_ls_iterations-1000.png create mode 100644 imgs/2_ls_neighbors-100.png create mode 100644 imgs/2_ls_stddev-30.png create mode 100644 imgs/2_shc.png create mode 100644 imgs/2_shc_iterations-1000.png create mode 100644 imgs/2_shc_neighbors-100.png create mode 100644 imgs/2_shc_stddev-30.png diff --git a/PROTOCOL.md b/PROTOCOL.md new file mode 100644 index 0000000..44982f6 --- /dev/null +++ b/PROTOCOL.md @@ -0,0 +1,114 @@ + + +# Protocol + +In this task, we were supposed to implement two optimization algorithms in an effort to find the minimum value of the +functions that we've worked with in the last task. The two algorithms were Local Search (LS) and Stochastic Hill +Climbing (SHC). Both of these are pretty similar, the only difference between them is that the LS algorithm includes the +center point when determining the minimum, while the SHC algorithm only considers the new points. + +From my testing, the SHC algorithm usually performed worse with the same amount of iterations, because LS was more +focused on exploring the lowest point of the minimum, while SHC often didn't and instead jumped elsewhere. + +That said, because of this fact, SHC actually performed better in cases where LS got stuck in a local minimum, as LS +can't recover from this, while SHC can. + +## Output (graphs) + +Below are a few examples of the runs I performed: + +### Sphere + +I first ran the algorithm on the sphere function, with the following settings: + +![img](./imgs/1_config.png) + +For Local Search, this was the resulting graph: + +![img](./imgs/1_ls.png) + +For Stochastic Hill Climbing, the result was this graph: + +![img](./imgs/1_shc.png) + +### Rosenbrock + +Next, I tried the Rosenbrock function, with the following settings: + +![img](./imgs/2_config.png) + +For LS, I got: + +![img](./imgs/2_ls.png) + +For SHC, I got: + +![img](./imgs/2_shc.png) + +### Further experimenting with Rosenbrock + +I also tried adjusting some of the settings with the Rosenbrock function, to compare how they affect the LS and SHC +algorithms. Each time, I only modified a single settings, with the rest matching the original Rosenbrock configuration +(already shown above). + +#### 1000 iterations + +I first tried increasing the number of iterations to 1000 (from 30). + +For LS, I got: + +![img](./imgs/2_ls_iterations-1000.png) + +for SHC, I got: + +![img](./imgs/2_shc_iterations-1000.png) + +#### 100 neighbors + +I then tried increasing the amount of neighbor points to 100 (from 3). + +For LS, I got: + +![img](./imgs/2_ls_neighbors-100.png) + +for SHC, I got: + +![img](./imgs/2_shc_neighbors-100.png) + +#### Standard deviation of 30 + +Finally, I tried increasing the standard deviation of the normal distribution to 30 (from 1.5). + +For LS, I got: + +![img](./imgs/2_ls_stddev-30.png) + +for SHC, I got: + +![img](./imgs/2_shc_stddev-30.png) + +### Summary + +I've tested a bunch more cases locally, however, I didn't want to clutter this report with a bunch of those images, +however, from this testing, I found out that in most cases: + +- The standard deviation should generally be fairly small, enough to allow precise searching around the minimum however, + not too small that the algorithm cannot explore enough of the search space in a single iteration. It's necessary to + find a number that balances this and works well. +- The number of iterations only matters up to a certain point. For LS, once a point close to a local minimum is found, + additional iterations may only refine the solution slightly, as the probability of finding a better point gets + progressively smaller. For SHC, increasing iterations generally improves the chances of escaping local minima and + potentially finding a better solution, especially when the standard deviation allows for exploration. +- The number of neighbors is a key factor in performance. Generally, increasing the number of neighbors allows the + algorithm to explore more options and find the optimal point faster. 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