2 What is Optimization?Procedure to make a system or design as effective, especially the mathematical techniques involved. ( Meta-Heuristics)Finding Best SolutionMinimal Cost (Design)Minimal Error (Parameter Calibration)Maximal Profit (Management)Maximal Utility (Economics)
3 Types of Optimization Algorithms Mathematical AlgorithmsSimplex (LP), BFGS (NLP), B&B (DP)Drawbacks of Mathematical AlgorithmsLP: Too Ideal (All Linear Functions)NLP: Not for Discrete Var. or Complex Fn., Feasible Initial Vector, Local OptimaDP: Exhaustive Enumeration, Wrong DirectionMeta-Heuristic AlgorithmsGA, SA, TS, ACO, PSO, …
8 Analogy = Do = Mi = Sol = 100mm = 300mm = 500mm f (100, 300, 500) Mi, Fa, SolDo, Re, MiSol, La, Si= Do= Mi= Sol100mm200mm300mm300mm 400mm500mm500mm600mm700mmf (100, 300, 500)= 100mm= 300mm= 500mm
9 Comparison Factors Musical Inst. → Decision Var. Pitch Range → Value RangeHarmony → Solution VectorAesthetics → Objective FunctionPractice → IterationExperience → 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 ConsideringDissonance Considering
19 Parameter-Setting-Free HS Overcoming Existing DrawbacksSuitable for Discrete Variables; No need for Gradient Information or Feasible Initial Vector; Better Chance to Find Global OptimumDrawbacks of Meta-Heuristic AlgorithmsRequirement of Algorithm Parameters