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.
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.
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}
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
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