Information Technology Reference
In-Depth Information
DE
Continuous Space Optimization
DE
Permutative-based Combinatorial
Optimization DE
(i) Differential Evolution: A Practical
Approach to Global Optimization
(ii) Differential Evolution: A Handbook for
Global Permutative-based Optimization
Fig. 1.1.
DE framework (i) Existing topic (Price et al. 2005); (ii) Present topic
problems characterized by continuous parameters. This means that only a subset of
real-world problems could be solved by the original canonical DE. For quite some time,
this deficiency made DE not to be employed to a vast number of real-world problems
which characterized by permutative-based combinatorial parameters. Fig 1.1 shows the
framework into which the current topic fits, showing that there are two mainstreams of
philosophical schools that need to be considered in presenting DE for solving real-world
problems. This framework is important as it shows that the current topic compliments
the first topic on DE which only addresses one aspect: continuous parameters.
1.1.1
Continuous Space Optimization DE Problems
A typical continuous space optimization DE problem is the generalized Rosenbrock
function given as:
100
.
x
j
+1
−
1)
2
,
x
j
2
D
2
j
=0
−
f
(
x
)=
+(
x
j
−
(1.1)
−
30
≤
x
≤
30
,
j
= 0
,
1
,...,
D
−
1
,
D
>
1
,
f
(
x
∗
)=0
,
x
j
= 1
,
10
−
6
.
ε
= 1
.
0
×
The solution of this problem is shown in Fig 1.2.
1.1.2
Permutative
−
Based Combinatorial Optimization DE Problem
A typical permutative-based combinatorial optimization DE problem is the flow shop
scheduling five-job-four machine problem whose operation times are shown in
Table 1.1 The objective is to find the best sequence to realize the optimal completion
time (makespan). As we see, this problem is very different from the continuous space
problem because we are interested in sequence such as 1, 2, 3, 4, 5 which is permutative
in nature.
The minimization of completion time (makespan) for a flow shop schedule is equiv-
alent to minimizing the objective function
ℑ
:
n
j
=1
C
m
,
j
ℑ
=
(1.2)
Search WWH ::
Custom Search