I present some of my favorite algorithms including: * Fuzzy Logic * Eval * General Problem Solvers * Simulated Annealing

1. Algorithms for More
Intelligent Apps
Frank A. Krueger
for Future Decoded
London
November 2, 2016

2. Frank A. Krueger
* @praeclarum on Twitter
* Independent mobile app developer (8 years!)
specializing in .NET and Xamarin
- iCircuit, Calca, Continuous
* Open Source Contributor: SQLite-net,
NGraphics, Netjs, …
* Co-host of Merge Conflict podcast with
James Montemagno (http://mergeconflict.fm)

3. #microsoft

4. Hiring Manager: Do this thing with a
linked list.
Me: What’s a linked list? 😰

5. #books

6. AGENDA
* Linked List Traversal----------------------- NO
* Fuzzy Logic
* Eval
* General Problem Solvers
* Simulated Annealing
(in no particular order)

9. if temp < desiredTemp
then
setFan(100%)
else
setFan(0%)
“Chatter”
These
can’t be
right

10. “Chatter” occurs when the fan jumps
from 100% to 0%
when it’s near desiredTemp
0% 100% 0% 100% 0% 100% 0%
temp
desiredTemp
fan

11. let error = desiredTemp -
temp
if error < 0° then
setFan(0%)
elif error < 10° then
setFan(10%)
elif error < 25° then
setFan(50%)
else
setFan(100%)
More Granularity Fixes All Problems
FUZZY
LOGIC

12. let error = desiredTemp -
temp
if error < 0° then
setFan(0%)
elif error < 10° then
setFan(10%)
elif error < 25° then
setFan(50%)
else
setFan(100%)
Input Classes
Outputs

13. Build a Table of Inputs and Outputs
Input | Output
(Error) | (Fan)
============+=========
TooHot | 0%
AlmostThere | 10%
AWaysToGo | 50%
JustStarted | 100%
Input Classes
Output per Class

14. “Classifiers” are functions
that measure how well an
input matches a class

15. Trapezoids are good classifiers
True
Input
False
“Fuzzy”
Error = 0 2° 8° 12° 18°
AlmostThere
Classifier

16. Lots of Classifiers
TooHot
AlmostThere
AWaysToGo
JustStarted

17. All Inputs are Classified

18. Some Inputs Have Multiple Classes

19. Blend The Outputs for Multi-class
Error = 16.5°
Input | Output
============+=========
TooHot | 0%
AlmostThere | 10%
AWaysToGo | 50%
JustStarted | 100%
Fan = 0.25 * 10% +
0.75 * 50%
= 40%
TooHot = 0
AlmostThere = 0.25
AWaysToGo = 0.75
JustStarted = 0

20. FUZZY LOGIC
* Formalizes a common pattern
* Simplifies problem with classes
- Doesn’t require mathematical models
- Your intuition is usually enough
* Smooth output thanks to blending
* Scales to many inputs and many outputs

21. A COURSE IN FUZZY SYSTEMS
AND CONTROL by Li Xin-Wang

22. FUZZY LOGIC LIBRARIES
GameplayKit
GKRuleSystem
Accord.Fuzzy
InferenceSystem
“Fuzzy”
4+ Packages

24. Eval is an algorithm
for computing anything.
(It’s a virtual computer!)

25. Program
{}
Eval
...
Value
42°
Abstract Syntax Tree
from Source Code
Pretty Much
Anything

26. type Syntax =
| Number of float
| Assign of string * Syntax
| Variable of string
| Invoke of Syntax * Syntax[]
| Program of Syntax[]
distance = 101390
velocity = 1000
G = 9.81
angle = 0.5 * asin(G*distance/velocity^2)
Source Code
Syntax Tree

27. ValueSyntax
Eval is a function that takes
Syntax and produces a Value

28. NumberNumber
Eval value;
Environment.Set value
Assign
Eval each lineProgram
Variable Environment.Lookup
Friend :-)
Invoke
Eval arguments;
Environment.Set arguments;
Eval body

29. Eval condition; if true
Eval true syntax, else Eval
false syntax
Conditional
Adding more Syntax is fun & easy
Eval initial; Assign variable;
Eval body; Increment variable;
Check condition; Loop
Loop
Return Closure object
containing Environment and
the function Syntax
Lambda

30. Recursive Functions of Symbolic Expressions
John McCarthy, 1960

31. Calca
Frank A. Krueger, 2013

32. Continuous
Frank A. Krueger, 2016

33. Why Learn Eval?
* Let users type math when entering numbers
* Add scripting to your app with full sandboxing
* Write Domain Specific Languages
* Write compilers in your spare time

34. SICP by Abelson & Sussmans

35. LIBRARIES
System.Linq.Expressions
Expression
Microsoft.CodeAnalysis
“Roslyn”, ISyntax
“Interpreter”
50+ Packages

37. I have a problem…
* I know roughly what the solution looks
like
* I know how to determine the quality of
a potential solution
* I don’t know how to find the solution
(or it takes too long)

38. * Layout Circuit Boards
- Know: Components & connections
- Want: Optimal layout
* Plan an Epic Trip
- Know: Cities you want to visit
- Want: Flight & hotel bookings

39. An algorithm to solve problems:
1. Guess at the solution
2. Randomly change the solution a bit
3. Measure the change in quality
4. If it is better, then accept it
Else, reject it
5. Good enough? DONE
6. GOTO 2

40. * Greedily looks for a “good” solution,
not the best
- Local minima, not global
“Goodish”
* General purpose
* Intuitive and simple to implement
* A bit slow because it has no knowledge
of the domain

41. An algorithm to solve problems:
1. Guess at the solution
2. Randomly change the solution a bit
3. Measure the change in quality
4. If it is better, then accept it
Else, reject it
5. Good enough? DONE
6. GOTO 2
Insight: let’s accept
bad changes!

42. Simulated Annealing
StartWarmHot!Quench!Slowly cool…
Annealed because we gave it time
to try some “bad” configurations

43. Boltzmann’s Distribution
Even at low
temperatures, high
energy states can exist

44. An algorithm to solve problems:
1. Guess at the solution
2. Randomly change the solution a bit
3. Measure the change in quality
4. If it is better, then accept it
Else, reject it
5. GOTO 2

45. Simulated Annealing:
1. Guess at the solution
2. Start with a high temperature
3. Randomly change the solution a bit
4. Measure the change in quality (“energy”)
5. If it is better, then accept it
Else, calculate the change in energy
and the probability of that change
given the temperature
and accept if randomly chosen
6. If it’s been “awhile”, decrease temperature
7. GOTO 3

46. I want to visit London, Barcelona, Russia, and Japan:
Guess: Tokyo – Moscow – London – Barcelona
Random Change: Barcelona – Moscow – London – Tokyo
Energy = 900 ΔE = -100
Energy = 1000
Random Change: Barcelona – Moscow – London – Tokyo
Energy = 900 ΔE = -100
Random Change: Moscow – Barcelona – London – Tokyo
Energy = 1500 ΔE = 600
Random Change: Moscow – Barcelona – London – Tokyo
Energy = 1500 ΔE = 600
Boltzmann Probability (ΔE, T) = 0.1
*Roll the dice*

47. NUMERICAL RECIPES in C++ by
Press, et el.

48. LIBRARIES
LibOptimization
Optimization.clsOptSimulatedAnnealing

50. How to Solve Problems, Generally
State of the World is a collection of “truths”
Sunny
Outside
Watching a
Presentation
Bags
Unpacked
Happy
Curious
about
Twitter
Hungry

51. How to Solve Problems, Generally
Action: Pack My Bags
Remove: Bags Unpacked
Add: Bags Packed
Require: In Hotel Room
&& Bags Unpacked
Actions Remove Truths and Add New Ones

52. How to Solve Problems, Generally
Want: Bags Packed && Checked
into Flight
Problems are described by stating which truths
you want to be true
GPS
Current World State
All Possible Actions
Action 1
Action 2
Action 3
Action 4
Action …
New World State

53. General Problem Solvers Algorithm
1. Look for an Action that adds the needed state
to the world with all its requirements met
2. If one found, add it to the solution;
DONE!
3. Else, look for an Action that adds the needed
state to the world (requirements not met).
4. If one found, Solve the Sub-problem of meeting
that action’s Requirements. GOTO 1.
5. FAIL! :-(
Recursive

54. GPS Variations
1. First solution or best solution?
2. What do you mean best?

55. GPS Criticisms
1. Solution time grows exponentially
2. “Good at solving puzzles”
Looks good to me!

56. GPS as an Architecture

57. Where does the data come from?
Make Tile
Street Data
Building Data
Terrain Data
Vector
Data
Terrain
Server
Vector
Server
Route Car
Show Address

58. async Task<Tile> MakeTile ()
{
var terrain = await GetTerrain();
var vectors = await GetVectors();
var roads = GetRoads(vectors);
var buildings = GetBuildings(vectors);
return ReallyMakeTile(terrain, roads, buildings);
}
How do you handle network errors?

59. async Task<Tile> TryHarderToMakeTile ()
{
for (var i = 0; i < NumRetries; i++) {
try {
return await MakeTile();
}
catch (NetworkError e) {
// Keep trying after a little wait
await Task.Delay(1000);
}
catch {
throw;
}
}
}
I’m not impressed…

60. GPS as an Architecture
Possible Truths of the World
Vector
Terrain Network
Streets
Buildings

61. Define Single Problem Solver Actions
Action: Load Terrain
Add: Terrain
Require: Network

62. Define Single Problem Solver Actions
Action: Load Streets
Add: Streets
Require: Vector

63. Define Single Problem Solver Actions
Action: Load Vector
Add: Vector
Require: Network

64. GPS as an Architecture (Example 1)
Want: Streets && Buildings &&
Terrain
GPS
Network
All Actions
Load Vector
Load Streets
Load Buildings
Load Terrain

65. GPS as an Architecture (Example 2)
Want: Streets && Buildings &&
Terrain
GPS
Terrain && Vector
All Actions
Load Streets
Load Buildings

66. GPS as an Architecture (Example 3)
Want: Streets && Buildings &&
Terrain
GPS
Terrain
All Actions
FAIL
(No Network)

67. GPS Benefits
1. Standardized way of looking at problems
– helps you think!
2. Actions become very specialized doing
one thing very well.
3. Restartable – unlike async methods,
partially solved problems can be
continued.
4. Even the dumbest version of GPS can
help us write better software.

68. Paradigms of AI Programming
by Norvig

69. LIBRARIES
“Solver”
0 Packages :-(

70. Thank you!
* @praeclarum on Twitter and GitHub