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4. Ideal point method:
= is the optimal value of each branch objective
function. If the value of each branch objective function is as close as possible to the
corresponding ideal value, we can get better non-inferior solutions. The evaluation
function is as follows.
j fj
*
1, 2,...,
r
r
*2
f
() min[
X
=
f
()- )]
X
f
(4)
j
j
j
=1
3
3LM-CDE Algorithm
3LM-CDE algorithm which has a population space, a medium space and a belief
space is selected from our former work [16].The Pareto optimal set in section 2 is
search by this algorithm and basic differential evolution (DE) algorithm.
4
Numerical Experiments
To validate and compare the performance of the 3LM-CDE and the 4 multi-objective
optimization strategies, 6 test functions [15] (Appendix) are used and compared with
standard DE algorithm which has the same value of each related parameter.
Fig.1-Fig.4 shows the Pareto solution vectors of Main Objective, Linear Weighted,
Max-min, and Ideal Point methods of function g01 , Fig.5-Fig.8 of g02 , Fig.9-Fig.12
of g03 , Fig.13-Fig.16 of g04 , Fig.17-Fig.20 of g05 , and Fig.21-Fig.24 of g06 .
5
Optimal Operation for Texaco Coal-Water Slurry Gasfier
The input and output of Texaco water-coal slurry gasifier is shown in Fig.25. Under
the stable production situation, there are 3 control parameters can be operated, which
are the Total Oxygen feed flowrate (Fo) from the three-stream burner port on top of
the gasfier (the oxygen stream in the outer annular tube), the Central Oxygen feed
flowrate (Foc) from the tube of the three-stream burner port on the top of the gasfier
(the oxygen flow in the central tube), and the Quench Water feed flowrate (Fw).
Many types of factors influence the yield of the syngas and its effective components
(CO+H 2 ), and the relationships among them are very complicated which cannot be
formulated.
Based on the work of reference [17], 18 variables of 3 BP neural network soft
sensor models describing the relationship between the 15 inlet variables and 3 outlet
variables were selected. Via data preprocessing, 310 groups' historical data of 18
variables during one month were firstly collected and normalized. Then, 15 inlet
variables were reduced into 8 principal variables using principal component analysis.
Finally, three 3-layer BP neural networks (Fig.26) were established, each of which
had the same structure of 8 input nodes, 8 hidden nodes, and 1 output node. The outlet
flowrate of synthesis gas (Fg), the CO volume% in the outlet syngas, and the H 2
volume% in the outlet syngas are the three output node variables. The actual values
are gained via the denormalized process via equations (5).
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