Finding an alternative with the most cost effective or highest achievable performance under the given constraints, by maximizing desired factors and minimizing undesired ones. It also mean that it make best use of a situation or resource. In comparison, maximization means trying to attain the highest or maximum result or outcome without regard to cost or expense. Practice of optimization is restricted by the lack of full information, and the lack of time to evaluate what information is available (see bounded reality for details). In computer simulation (modeling) of business problems, optimization is achieved usually by using linear programming techniques of operations research.

1. MUSIC-INSPIRED OPTIMIZATION
ALGORITHM
HARMONY SEARCH

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. Principle of harmony search
 HS mimics the improvisation process of
musicians during which each musician plays
a note for finding a best harmony all
together.
 When applied to optimization problems,
the musicians typically represent the
decision variables of the cost function.
 And HS acts as a meta-heuristic algorithm
which attempts to find a solution vector that
optimizes this function.

4. 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

5. Algorithm from Music Phenomenon

6. 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.

7. HS OPERATORS
1. Random Playing
2. Memory Considering
3. Pitch Adjusting
4. Ensemble Considering

8. 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}

9. MEMORY CONSIDERING
x ∈ Preferred Note = {C4, E4, C4, G4, C4}

10. PITCH ADJUSTING
x+ or x-, x ∈ Preferred Note

11. ENSEMBLE
CONSIDERING
    ji
j
ji xxCorrMaxxfx ,,

12. HS Applications for
Real-World Problems

13. List Of Application For Real-
World Problem
 Sudoku Puzzle
 Music Composition - Medieval
Organum
 Project Scheduling (TCTP)
 UniversityTime-tabling
 Internet Routing
 Web-Based Parameter
Calibration
 Truss Structure Design
 School Bus Routing Problem
 GeneralizedOrienteering
Problem
 Water Distribution Network
Design
 Multiple Dam Operation
 Hydrologic Parameter
Calibration
 EcologicalConservation
 Satellite Heat Pipe Design
 Satellite Heat Pipe Design
 OceanicOil Structure Mooring
 RNA Structure Prediction
 Medical Imaging
 RadiationOncology
 Astronomical Data Analysis
 Large-ScaleWater Network
Design

14. 614253879
295784613
378196254
439627581
781549326
526318947
952461738
843972165
167835492
Sudoku Puzzle

15. Music Composition – Medieval Organum
Interval Rank Interval Rank
Fourth 1 Fifth 2
Unison 3 Octave 3
Third 4 Sixth 4
Second 5 Seventh 5

16. University Timetabling

17. Truss Structure Design
75 in.
100 in.
Y
X
Z
75 in.
75 in.
200 in.
200 in.
100 in.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(10)
(9)
1
4
2
3
5
89
67
11
10
13
12
17
16
14
15
21
19
20
18
25
24
22
23
GA = 546.01, HS = 484.85
ii
n
i
LAW 

1
)( A

18. 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
5 4 5
3
4 5 6
8
5 7 4
5 4
5
10 15 5
10 15 20 10
15 10 20
Min C1 (# of Buses) + C2 (Travel Time)
s.t. Time Window & Bus Capacity

19. Medical Imaging

20. Stochastic Partial Derivative
of HS
0.000
0.001
0.010
0.100
1.000
1 2 3 4 6 8 10 12 14 16 18 20 22 24
Pipe Diameter (inch)
Probability Random Selection Memory Consideration
Pitch Adjustment Total Gradient
Pipe 7
  PARHMCR
HMS
mkxn
PARHMCR
HMS
kxn
HMCR
Kx
f ii
ii




 )(
)1(
))((
)1(
1

21. 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

22. THANK YOU