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
34 School Bus Routing Problem DepotSchool123456789101520Min C1 (# of Buses) + C2 (Travel Time)s.t. Time Window & Bus CapacityGA = $409,597, HS = $399,870
35 Generalized Orienteering Problem Max. Multi-Objectives1. Natural Beauty2. Historical Significance3. Cultural Attraction4. Business OpportunityCase1Case2Case3Case4Case5ANN12.3813.0512.5112.7812.36HS13.0812.5612.40
36 Water Distribution Network Design 123456789151411181213171019162021MP: $78.09MGA: $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 EuroHS = 1.9M Euro
52 Parameter-Setting-Free HS Overcoming Existing DrawbacksSuitable for Discrete VariablesNo Need for Gradient InformationNo Need for Feasible Initial VectorBetter Chance to Find Global OptimumDrawbacks of Meta-Heuristic AlgorithmsRequirement of Algorithm Parameters