Information Technology Reference
In-Depth Information
effective optimization algorithm, which can quickly lead to the global design
optimum, is badly needed. Conventional numerical optimization algorithms
are based on explicitly formulated design models. No explicit formulations
are given and only implicit parametric models can be used [27]. Some intui-
tive design aspects, such as video quality measurements, can only be evalu-
ated human interventions and cannot be modeled in mathematics and are
incapable of handing an objective function with local optima. For search-
ing global optimum, two approaches are widely used: least squares method
(LSM) and simulated annealing (SA) [28]. These two methods do not require
gradient information but need tens and thousands of iterations to converge.
Due to the computation intensive nature of the curve fitting, the direct use of
these two global optimization methods becomes less feasible.
3.5.4 Least Squares Method
The method of least squares (LSM) is used to solve overdetermined systems.
Least squares is often applied in statistical contexts, particularly regression
analysis.
A plot of
x
,
y
,
z
against −1 (see below) shows that it cannot be modeled
by a straight line, so a regression is performed by modeling the data by a
parabola.
β
0
x
2
+ β
1
y
2
+ β
2
z
2
+ β
3
xy
+ β
4
xz
+ β
5
yz
+ β
6
x
+ β
7
y
+ β
8
z
+ β
9
xyz
= −1.
Where the dependent variable,
x
, is packet lost rate, the independent
variable,
y
, is frame lost rate, and the independent variable,
z
is PEVQ.
Place the coefficients,
x
i
2
,
y
i
2
,
z
i
2
,
x
i
y
i
,
x
i
z
i
, y
i
z
i
, x
i
, y
i
, z
i
and
x
i
y
i
z
i
of the
parameters for the
i
ith row of the matrix
S
.
The values of the parameters are found by solving the normal equations
)
ˆ
(
SS
β=− 1
…
S
[
] .
T
T
T
The matrix is well conditioned and positive definite, that is, it has full
rank, the normal equations can be solved directly by using the Cholesky
decomposition.
ˆ
β=−
(
SS S
)
[
11
…
]
.
T
−
1
T
T
3.5.5 Simulated annealing
SA is a generic probabilistic meta-algorithm for the global optimization
problem, namely locating a good approximation to the global minimum of a
given function in a large search space. It is often used when the search space
