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Music-Inspired Optimization Algorithm Harmony Search Zong Woo Geem.

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Presentation on theme: "Music-Inspired Optimization Algorithm Harmony Search Zong Woo Geem."— Presentation transcript:

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2 Music-Inspired Optimization Algorithm Harmony Search Zong Woo Geem

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

4 Types of Optimization Algorithms Mathematical Algorithms Mathematical Algorithms  Simplex (LP), BFGS (NLP), B&B (DP) Drawbacks of Mathematical Algorithms 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 Meta-Heuristic Algorithms  GA, SA, TS, ACO, PSO, …

5 Existing Nature-Inspired Algorithms

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

7 Algorithm from Music Phenomenon

8 Algorithm from Jazz Improvisation Click Below

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

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

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

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

13 HS Operators 1.Random Playing 2.Memory Considering 3.Pitch Adjusting 4.Ensemble Considering 5.Dissonance Considering

14 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}

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

16 Pitch Adjusting x+ or x-, x ∈ Preferred Note

17 Ensemble Considering

18 Rule Violation (Parallel 5 th )

19 Example of Harmony Search

20 Initial Harmony Memory

21 Next Harmony Memory

22 With Three Operators 14 +1 {1, 2, 3, 4, 5} 2 f= 6

23 HS Applications for Benchmark Problems

24 Six-Hump Camel Back Function f*(-0.08983, 0.7126) = -1.0316285 (Exact) f (-0.08975, 0.7127) = -1.0316285 (HS)

25 Multi-Modal Function

26 Artificial Neural Network - XOR Sum of Errors in BP = 0.010 Sum of Errors in HS = 0.003 TTF TFT FTT FFF Bias

27 HS Applications for Real-World Problems

28 Sudoku Puzzle 614253879 295784613 378196254 439627581 781549326 526318947 952461738 843972165 167835492

29 Music Composition – Medieval Organum IntervalRankIntervalRank Fourth1Fifth2 Unison3Octave3 Third4Sixth4 Second5Seventh5

30 Project Scheduling (TCTP)

31 University Timetabling

32 Internet Routing

33 Web-Based Parameter Calibration RMSE: 1.305 (Powell), 0.969 (GA), 0.948 (HS)

34 Truss Structure Design GA = 546.01, HS = 484.85

35 School Bus Routing Problem GA = $409,597, HS = $399,870 Depot School 1 2 3 4 5 6 7 8 9 10 7 5 8 54 5 3 456 8 5 7 4 5 4 5 155 10 15 20 10 15 10 20 Min C1 (# of Buses) + C2 (Travel Time) s.t. Time Window & Bus Capacity

36 Generalized Orienteering Problem Case1Case2Case3Case4Case5 ANN12.3813.0512.5112.7812.36 HS12.3813.0812.5612.7812.40 Max. Multi-Objectives 1. Natural Beauty 2. Historical Significance 3. Cultural Attraction 4. Business Opportunity

37 Water Distribution Network Design 1 2 3 4 5 6 7 8 9 15 14 11 1812 13 17 10 19 16 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2021  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

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

39 Multiple Dam Operation GA = 400.5, HS = 401.3 (GO) Max. Benefit (Power, Irrigation)

40 Hydrologic Parameter Calibration Mathematical = 143.60, GA = 38.23, HS = 36.78 Wedge Storage = K x (I - O) Prism Storage = K O O O I

41 Ecological Conservation With 24 Sites, SA = 425, HS = 426

42 Satellite Heat Pipe Design

43 Maximize Conductance Minimize Mass BFGS HS BFGS: Mass =25.9 kg, Conductance = 0.3808 W/K HS: Mass = 25.8 kg, Conductance = 0.3945 W/K

44 Oceanic Oil Structure Mooring

45 RNA Structure Prediction

46 Medical Imaging

47 Radiation Oncology

48 Astronomical Data Analysis

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

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

51 Stochastic Partial Derivative of HS

52 Stochastic Co-Derivative of HS

53 Parameter-Setting-Free HS Overcoming Existing Drawbacks 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 Drawbacks of Meta-Heuristic Algorithms  Requirement of Algorithm Parameters

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55 Wikipedia (Web Encyclopedia)

56 Books on Harmony Search

57 Visitor Clustering (As of Nov. 2010)

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

59 What is Your Contribution?

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


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