https://github.com/johannesbuchner/nobrain_optimization

A naive constrained continuous n-dimensional optimization algorithm
https://github.com/johannesbuchner/nobrain_optimization

Last synced: 7 months ago
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A naive constrained continuous n-dimensional optimization algorithm

• Host: GitHub
• URL: https://github.com/johannesbuchner/nobrain_optimization
• Owner: JohannesBuchner
• License: other
• Created: 2009-04-26T12:29:22.000Z (over 16 years ago)
• Default Branch: master
• Last Pushed: 2009-04-26T13:13:48.000Z (over 16 years ago)
• Last Synced: 2025-01-23T20:51:45.172Z (9 months ago)
• Language: C
• Homepage:
• Size: 97.7 KB
• Stars: 3
• Watchers: 4
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: readme
  • License: copying

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README

          
This algorithm allows you to solve any minimum/maximum finding problem within a n-dimensional box.

It is meant for functions that are costly to evaluate (hours).

Algorithm description:

You are in a valley and want to go atop a mountain. However, you are blind. But you have a height detector.

The detector needs some time to take the measurement, and you can not measure while walking.

So what you do is:

Setup: n ... number of dimensions you are in. i=0, scale = 0.5 the size of your world.

 0 take a measure where you are.

 1 go in direction $x[i] for $scale long

 2 take a measure

  3 if it is better than where you were, stay here

    otherwise, go back

    4 if you turned back twice in every direction, it is time to refine:

      set scale = scale * zoom_in_factor, with zoom_in_factor being 0.5 or 0.1

 5 i = i mod n

 repeat 1

This algorithm always finds the local maximum. It performs good if your expectations are low :-)

However, it performs very bad compared at Rosenbrocks valley compared to "real" optimization 

algorithms like CONDOR.

It is especially useful if you have a n-dimensional slope with one maximum. 

Example:

We want to determine the optimal starting_scale and zoom_in_factor for the algorithm:

 $ mkfifo /tmp/in; mkfifo /tmp/out

in one terminal we provide our testing object (a polynomial):

 $ cat /tmp/out | while read ZOOM_IN_FACTOR START_SCALE; do 

     rm example_climber.exe

     CCFLAGS="-DZOOM_IN_FACTOR=$ZOOM_IN_FACTOR -DSTART_SCALE=$START_SCALE" make example_climber.exe 1>&2 && 

     	./example_climber.exe 1e-6 |tail -n1|sed 's/ steps//g'|sed 's/^/-/g'

	# the line above removes the text " steps" and turns the value in a maximization problem (least steps)

   done | tee -a /tmp/in

on another terminal we run the algorithm to find the best values in this 2-dimensional maximization problem:

 $ ./generic_climber.exe 0.001 d 0.01 0.99 0.17 d 0.1 2.0 1.0 < /tmp/in |tee -a /tmp/out

What do these parameters mean?

Usage output of generic_climber.exe:

---

./generic_climber.exe: SYNOPSIS:  parameters...

	exactness: 	how detailled should we refine the search

	parameters:	each parameter is a quadrupel of type, min, max, start

		type: i for integer, d for double

		min : lower bound of parameter values

		max : upperbound of parameter values

		start : starting point (0..1)

example: ./generic_climber.exe 0.001 i -10 100 0 d 12.3 54 20

---

Turns out, in bad scenarios (Rosenbrocks valley), best is starting_scale=1.1 and zoom_in_factor=0.5.

In a general polynomial that is not very steep, we don't have to be that cautious: zoom_in_factor=0.1.

You can find more details on how to adapt to your programs at 

http://wiki.github.com/JohannesBuchner/condor_optimization/usage

This page discribes the usage with the CONDOR algorithm, however the

interface is the same as generic_climber.exe.

You can use any tool or programming language to plug in.

Have fun,

Johannes Buchner