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Music-Inspired Optimization Algorithm Harmony Search

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

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Music-Inspired Optimization Algorithm Harmony Search

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  1. Music-Inspired Optimization AlgorithmHarmony 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 Mi, Fa, Sol Do, Re, Mi Sol, La, Si = Do = Mi = Sol f (100, 300, 500) 100mm 200mm 300mm 300mm 400mm 500mm 500mm 600mm 700mm = 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 forBenchmark Problems

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

  24. Multi-Modal Function

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

  26. HS Applications forReal-World Problems

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

  28. Music Composition – Medieval Organum

  29. Project Scheduling (TCTP)

  30. University Timetabling

  31. Internet Routing

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

  33. Truss Structure Design GA = 546.01, HS = 484.85

  34. 15 20 10 5 5 8 4 10 School 9 8 7 4 5 10 20 15 10 4 4 5 6 6 5 7 5 7 4 10 5 15 5 1 3 Depot 2 3 8 5 School Bus Routing Problem 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

  36. 1 1 15 2 15 2 14 3 14 3 4 13 4 13 19 5 12 18 5 6 12 17 18 6 7 11 7 11 8 19 8 10 20 9 21 20 9 10 16 16 17 Water Distribution Network Design • 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 = 401.3 (GO)

  39. I O Wedge Storage = K x (I - O) Prism Storage = K O O Hydrologic Parameter Calibration Mathematical = 143.60, 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 = 0.3808 W/K HS: Mass = 25.8 kg, Conductance = 0.3945 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 Shifta change in basic assumptions within the ruling theory of science

  50. Stochastic Partial Derivative of HS

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