Presentation for CraftmansGuild on 15-Jan-2013. Genetic Algorithms, Simulated Annealing, Particle Swarm Optimization.

1. Evolving Solutions
Machine Learning
Programs that Search for Solutions
Searching Random Points
Recursive Descent / Ascent
Sub-Optimization
Faulty Analogies
Fitness
Genetic Algorithms
Particle Swarm Optimization
Simulated Annealing
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2. Basic Concepts
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3. Learning ==> Improvement
Some quality is being improved.
There is some measure of good / bad.
There is some way to move toward good.
Change position
Change behavior
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4. Learning ==>
Some quality is being improved.
Implies / Assumes:
There is consensus about good versus bad.
There is some way to measure good / bad.
Give that measure a name: “Fitness”
Analogy to nature and evolution concept.
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5. Searching for Better
Random Search
Randomize values in degrees of freedom.
Compare resulting fitness.
Pick the best results.
And then what?
Recursive Descent / Ascent
Assumes that solution space has a gradient.
Assumes there are minima / maxima.
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6. Seeker:
When do you quit searching?
Infinite Loop versus “Stopping Condition”
Eventually we run out of time / resource / energy.
Complications:
Sometimes “Best” is not well-defined.
The solution space is continuously changing.
The shape (gradient qualities) of space is unknown.
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7. Faulty
Analogs
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8. Evolution
There is some way to measure “fitness”
Fitness is a function of a set of objects
that can vary over individual instances.
Call the objects “genes” to use genetic analogy.
Mutation ==> Changing the values of “genes”.
Sexual Reproduction
==> Merging gene “sequences.”
Next Generation <== keep most fit, cull least fit.
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9. Genetic Algorithm
Define degrees of freedom ==> genes.
Produce first generation with randomized genes.
Evaluate fitness of each individual
Calculate / Run a simulation of environment.
Keep most fit <==> Cull least fit.
Populate the next generation. ( mutate and/or splice )
Repeat until “done”
Note: Real environments change over time.
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10. Main Loop In Smalltalk
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11. Next Generation
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12. Mutation
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13. Degrees Of Freedom
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14. See Also: Java Example
for
Traveling Salesman
http://code.google.com/p/java-traveling-salesman/
source/checkout
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15. Insect (Swarm) Behavior
Swarms search for “food” / Encounter “intruders”
-- mostly random search.
Insects communicate with their buddies.
Their buddies re-direct their paths to gather / fight.
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16. Particle Swarm Optimization
Mixed Analogy: Particle <==> Flying insect.
Particles have “position” in multi-dimensional space.
Assign each particle to a group “swarm” (at random).
After fitness is evaluated, particles move toward the
most fit particle in their swarm.
The most fit particle in the swarm
can stay where it is, ascend, or dither (random move).
Recursive ascent / descent may guide moves
if the space is believed to be reasonably continuous.
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17. http://vimeo.com/17407010
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18. Stopping Conditions
How good is good enough?
Genetic Algorithms and Particle Swarm Optimization
can provide multiple solutions.
Stop when best fitness is no longer improving.
Stop when move method is no longer moving anything.
Stop at some arbitrary limit:
Number of generations.
Time limit.
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19. Simulated Annealing
Concept: Temperature ==> Energy Available.
Energy ==> speed of movement.
Speed == How much change from step to step?
Annealing == Cooling at controlled rate ==>
The allowed change decreases from step to step.
Stopping Condition:
Temperature (Change/Step) goes to zero.
Other stopping conditions may also apply.
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20. Gotcha’s
Experts refuse to say “optimum / optimal / optimized”
No way to verify solution is best possible.
Parameters selected may not cover everything.
Say “sub-optimal” or “satisfices” (good enough)
Solution is only good inside your simulation.
Real world is certainly different.
Don’t over-train: Solution may lack flexibility.
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21. Visualization
How do you visualize position in hyperspace?
Assign each degree of freedom to some geometry.
3 degrees (x,y,z) ==> position
2 degrees (angle, angle) ==> orientation of “axis”
additional degrees ==> shape dimensions
Example: Torus (donut) Shape -- 9 shape dimensions
Radius, Eccentricity, Angle (?), r, e, a
frequency of: twist, wave, bulge
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22. http://megaswf.com/serve/
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23. Lessons Learned
I did not and do not expect this to work.
It is just something I always wanted to tinker.
Best fitness for 2007-2008: Stay out of the market!
“When-to-buy” was competing with “when-to-sell”
and producing counter-productive results.
==> Need more complex strategy ==> more parameters.
Very compute intensive (generation takes way too long)
==> Need faster data structure ==> Refactor database.
==> Squeak VM is single-thread ==> Port to Erlang ???
==> Potential GPU application.
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