Download presentation

Presentation is loading. Please wait.

Published byAnnalise Millard Modified over 2 years ago

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 Design**

1 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

Similar presentations

OK

Models Physical: Scale, Analog Symbolic: Drawings Computer Programs Mathematical: Analytical (Deduction) Experimental (Induction)

Models Physical: Scale, Analog Symbolic: Drawings Computer Programs Mathematical: Analytical (Deduction) Experimental (Induction)

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on phonetic transcription to english Ppt on blood stain pattern analysis cases Ppt on the periodic table of elements Ppt on thank you Free ppt on human circulatory system Converter word para ppt online Ppt on 2nd world war american Ppt on cross site scripting definition Ppt on aerobics exercise Ppt on 7 wonders of india