1. Music-Inspired Optimization Algorithm Harmony Search
Zong Woo Geem

2. What is Optimization?
Procedure to make a system or design as effective, especially the mathematical techniques involved. ( Meta-Heuristics)
Finding Best Solution
Minimal Cost (Design)
Minimal Error (Parameter Calibration)
Maximal Profit (Management)
Maximal Utility (Economics)

3. Types of Optimization Algorithms
Mathematical Algorithms
Simplex (LP), BFGS (NLP), B&B (DP)
Drawbacks of Mathematical Algorithms
LP: Too Ideal (All Linear Functions)
NLP: Not for Discrete Var. or Complex Fn., Feasible Initial Vector, Local Optima
DP: Exhaustive Enumeration, Wrong Direction
Meta-Heuristic Algorithms
GA, SA, TS, ACO, PSO, …

4. Existing Nature-Inspired Algorithms

5. Existing Meta-Heuristic Algorithms
Definition & Synonym
Evolutionary, Soft computing, Stochastic
Evolutionary Algorithm (Evolution)
Simulated Annealing (Metal Annealing)
Tabu Search (Animal’s Brain)
Ant Algorithm (Ant’s Behavior)
Particle Swarm (Flock Migration)
Mimicking Natural or Behavioral Phenomena → Music Performance

6. Algorithm from Music Phenomenon

7. Algorithm from Jazz Improvisation
Click Below

8. Analogy = Do = Mi = Sol = 100mm = 300mm = 500mm f (100, 300, 500)
Mi, Fa, Sol
Do, Re, Mi
Sol, La, Si
= Do
= Mi
= Sol
100mm
200mm
300mm
300mm 400mm
500mm
500mm
600mm
700mm
f (100, 300, 500)
= 100mm
= 300mm
= 500mm

9. Comparison Factors Musical Inst. → Decision Var.
Pitch Range → Value Range
Harmony → Solution Vector
Aesthetics → Objective Function
Practice → Iteration
Experience → Memory Matrix

10. Good Harmony & Bad Harmony
An Algorithm which Keeps Better Harmonies!

11. Procedures of Harmony Search
Step 0. Prepare a Harmony Memory.
Step 1. Improvise a new Harmony with Experience (HM) or Randomness (rather than Gradient).
Step 2. If the new Harmony is better, include it in Harmony Memory.
Step 3. Repeat Step 1 and Step 2.

12. HS Operators Random Playing Memory Considering Pitch Adjusting
Ensemble Considering
Dissonance Considering

13. Random Playing
x ∈ Playable Range = {E3, F3, G3, A3, B3, C4, D4, E4, F4, G4, A4, B4, C5, D6, E6, F6, G6, A6, B6, C7}

14. Memory Considering
x ∈ Preferred Note = {C4, E4, C4, G4, C4}

15. Pitch Adjusting
x+ or x-, x ∈ Preferred Note

16. Ensemble Considering

17. Rule Violation (Parallel 5th)

18. Example of Harmony Search

19. Initial Harmony Memory

20. Next Harmony Memory

21. With Three Operators
{1, 2, 3, 4, 5} +1 f
= 6 1 4 2

22. HS Applications for Benchmark Problems

23. Six-Hump Camel Back Function
f*( , ) = (Exact)
f ( , ) = (HS)

24. Multi-Modal Function

25. Artificial Neural Network - XOR
   
          T F
Bias
Sum of Errors in BP = 0.010
Sum of Errors in HS = 0.003

26. HS Applications for Real-World Problems

27. Sudoku Puzzle 6 1 4 2 5 3 8 7 9

28. Music Composition – Medieval Organum
Interval
Rank
Fourth 1
Fifth 2
Unison 3
Octave
Third 4
Sixth
Second 5
Seventh

29. Project Scheduling (TCTP)

30. University Timetabling

31. Internet Routing

32. Web-Based Parameter Calibration
RMSE: (Powell), (GA), (HS)

33. Truss Structure Design
GA = , HS =

34. School Bus Routing Problem
Depot
School 1 2 3 4 5 6 7 8 9 10 15 20
Min C1 (# of Buses) + C2 (Travel Time)
s.t. Time Window & Bus Capacity
GA = $409,597, HS = $399,870

35. Generalized Orienteering Problem
Max. Multi-Objectives
1. Natural Beauty
2. Historical Significance
3. Cultural Attraction
4. Business Opportunity
Case1
Case2
Case3
Case4
Case5
ANN
12.38
13.05
12.51
12.78
12.36 HS
13.08
12.56
12.40

36. Water Distribution Network Design1 2 3 4 5 6 7 8 9 15 14 11 18 12 13 17 10 19 16 20 21
MP: $78.09M
GA: $38.64M (800,000)
SA: $38.80M (Unknown)
TS: $37.13M (Unknown)
Ant: $38.64M (7,014)
SFLA: $38.80M (21,569)
CE: $38.64M (70,000)
HS: $38.64M (3,373)
5 times out of 20 runs

37. Large-Scale Water Network Design
Huge Variables
(454 Pipes)
GA = 2.3M Euro
HS = 1.9M Euro

38. Multiple Dam Operation
Max. Benefit (Power, Irrigation)
GA = 400.5, HS = (GO)

39. Hydrologic Parameter Calibration
Wedge Storage
= K x (I - O)
Prism Storage
= K O O I
Mathematical = , GA = 38.23, HS = 36.78

40. Ecological Conservation
With 24 Sites, SA = 425, HS = 426

41. Satellite Heat Pipe Design

42. Satellite Heat Pipe Design
BFGS HS
Minimize Mass
Maximize Conductance
BFGS: Mass =25.9 kg, Conductance = W/K
HS: Mass = 25.8 kg, Conductance = W/K

43. Oceanic Oil Structure Mooring

44. RNA Structure Prediction

45. Medical Imaging

46. Radiation Oncology

47. Astronomical Data Analysis

48. All that Jazz Robotics Visual Tracking Internet Searching
Management Science
Et Cetera

49. Paradigm Shift a change in basic assumptions within the ruling theory of science

50. Stochastic Partial Derivative of HS

51. Stochastic Co-Derivative of HS

52. Parameter-Setting-Free HS
Overcoming Existing Drawbacks
Suitable for Discrete Variables
No Need for Gradient Information
No Need for Feasible Initial Vector
Better Chance to Find Global Optimum
Drawbacks of Meta-Heuristic Algorithms
Requirement of Algorithm Parameters

54. Wikipedia (Web Encyclopedia)

55. Books on Harmony Search

56. Visitor Clustering (As of Nov. 2010)

57. Citations in Major Literature in tantum ut si priora tua fuerint parva, et novissima tua multiplicentur nimis. Iob 8:7

58. What is Your Contribution?

59. Question for Harmony Search?
Visit the Website
HarmonySearch.info