Thesis-Introduction.lyx

#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\input{Thesis.sty}

\title{标题}
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\begin_body

\begin_layout Chapter
\begin_inset CommandInset label
LatexCommand label
name "chap:introduction"

\end_inset

绪论
\end_layout

\begin_layout Section
XXX概述
\end_layout

\begin_layout Standard
参考文献
\begin_inset CommandInset citation
LatexCommand cite
key "IEEEexample:article_typical"

\end_inset

，同时引用多个参考文献
\begin_inset CommandInset citation
LatexCommand cite
key "IEEEexample:articleetal,IEEEexample:articlelargepages,IEEEexample:babel"

\end_inset

建议用LyX 2.1或以上版本。
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\begin_inset Float figure
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status collapsed

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset Graphics
	filename Figures/DTLZ/dtlz1.pdf
	width 45line%

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
DTLZ1
\begin_inset CommandInset label
LatexCommand label
name "fig:dtlz1"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Float figure
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\begin_inset space \hfill{}
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\begin_inset Graphics
	filename Figures/DTLZ/dtlz2.pdf
	width 45line%

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
DTLZ 2---4
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset Float figure
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status collapsed

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset Graphics
	filename Figures/DTLZ/dtlz5.pdf
	width 45line%

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
DTLZ 5 & 6
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset Graphics
	filename Figures/DTLZ/dtlz7.pdf
	width 45line%

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
DTLZ7
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:dtlz"

\end_inset

DTLZ系列测试函数
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
引用Deb–Thiele–Laumanns–Zitzler系列测试函数（DTLZ
\begin_inset CommandInset nomenclature
LatexCommand nomenclature
symbol "DTLZ"
description "Deb–Thiele–Laumanns–Zitzler系列测试函数"

\end_inset

）的图表（
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:dtlz"

\end_inset

，
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:functions-for-dtlz"

\end_inset

），
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:dtlz1"

\end_inset

。
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:functions-for-dtlz"

\end_inset

DTLZ系列测试函数的基本组成部分
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
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\begin_inset Text

\begin_layout Plain Layout
类型
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
函数
\end_layout

\end_inset
</cell>
</row>
<row>
<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
距离函数
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $d1\left(\vec{x_{d}}\right)=100\left(\left|\vec{x_{d}}\right|+{\displaystyle \sum_{x_{\imath}\in\vec{x_{d}}}}\left(\left(x_{\imath}-0.5\right)^{2}-\cos\left(20\pi\left(x_{\imath}-0.5\right)\right)\right)\right)$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $d2\left(\vec{x_{d}}\right)={\displaystyle \sum_{x_{\imath}\in\vec{x_{d}}}}\left(x_{\imath}-0.5\right)^{2}$
\end_inset


\end_layout

\end_inset
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<row>
<cell multirow="4" alignment="center" valignment="top" usebox="none">
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\end_layout

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</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $d3\left(\vec{x_{d}}\right)={\displaystyle \sum_{x_{\imath}\in\vec{x_{d}}}x_{\imath}^{0.1}}$
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\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $d4\left(\vec{x_{d}}\right)=\frac{1}{\left|\vec{x_{d}}\right|}{\displaystyle \sum_{x_{\imath}\in\vec{x_{d}}}x_{\imath}}$
\end_inset


\end_layout

\end_inset
</cell>
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<row>
<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
形状函数
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $s1_{\imath}\left(\vec{x_{p}}\right)=\begin{cases}
{\displaystyle \prod_{\jmath=1}^{m-1}x_{\jmath}} & \imath=1\\
\left(1-x_{m-\imath+1}\right){\displaystyle \prod_{\jmath=1}^{m-\imath}x_{\jmath}} & \imath=2,3,\cdots,m
\end{cases}$
\end_inset


\end_layout

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<row>
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\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $s2_{\imath}\left(\vec{x_{p}}\right)=\begin{cases}
{\displaystyle \prod_{\jmath=1}^{m-1}\cos}\left(\frac{\pi}{2}x_{\jmath}\right) & \imath=1\\
\sin\left(\frac{\pi}{2}x_{m-\imath+1}\right){\displaystyle \prod_{\jmath=1}^{m-\imath}\cos}\left(\frac{\pi}{2}x_{\jmath}\right) & \imath=2,3,\cdots,m
\end{cases}$
\end_inset


\end_layout

\end_inset
</cell>
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<row>
<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $s3\left(\vec{x_{p}},d\right)=m-{\displaystyle \sum_{x_{\imath}\in\vec{x_{p}}}\left[\frac{x_{\imath}}{d}\left(1+\sin\left(3\pi x_{\imath}\right)\right)\right]}$
\end_inset


\end_layout

\end_inset
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<row>
<cell multirow="3" alignment="left" valignment="middle" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
转换函数
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $t1_{\imath}\left(\vec{x_{p}},\alpha\right)=x_{\imath}^{\alpha}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell multirow="4" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $t2_{\imath}\left(\vec{x_{p}},d,k\right)=\begin{cases}
x_{\imath} & \imath=1,2,\cdots,k\\
\frac{0.5+x_{\jmath}d}{1+d} & \imath=k+1,k+2,\cdots,\left|\vec{x_{p}}\right|
\end{cases}$
\end_inset

, 
\begin_inset Formula $k\geq1$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
NSGA-II的环境选择如
\begin_inset CommandInset ref
LatexCommand ref
reference "alg:nsga_ii-environmental-selection"

\end_inset

所示。
\begin_inset CommandInset ref
LatexCommand ref
reference "alg:nondominate-sort"

\end_inset

为非支配排序。
\end_layout

\begin_layout Standard
\begin_inset Float algorithm
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
begin{algorithmic}[1]
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Require{
\end_layout

\end_inset

种群
\begin_inset Formula $R=\left\{ x_{1},x_{2},\cdots,x_{l}\right\} $
\end_inset

，输出种群大小
\begin_inset Formula $n$
\end_inset

（
\begin_inset Formula $n\leq l$
\end_inset

）
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Ensure{
\end_layout

\end_inset

种群
\begin_inset Formula $P=\left\{ x_{1},x_{2},\cdots,x_{n}\right\} $
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
State
\end_layout

\end_inset


\begin_inset Formula $P=\emptyset$
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
State
\end_layout

\end_inset


\begin_inset Formula $\mathscr{F}=NondominateSort\left(R\right)=\left\{ F_{1},F_{2},\cdots\right\} $
\end_inset


\begin_inset CommandInset label
LatexCommand label
name "alg:nondominate-sort"

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ForAll{
\end_layout

\end_inset


\begin_inset Formula $F_{\imath}\in\mathscr{F}\wedge\left|P\right|<n$
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
If{
\end_layout

\end_inset


\begin_inset Formula $\left|P\right|+\left|F_{\imath}\right|\leq n$
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
State
\end_layout

\end_inset


\begin_inset Formula $P=P\cup F_{\imath}$
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Else
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
State
\end_layout

\end_inset


\begin_inset Formula $P=P\cup CriticalSelection\left(F_{\imath},n-\left|P\right|\right)$
\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
EndIf
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
EndFor
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
end{algorithmic}
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "alg:nsga_ii-environmental-selection"

\end_inset

NSGA-II的环境选择
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
GD定义如
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:indicator-gd"

\end_inset

所示。
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
GD\left(P\right)=\frac{\sqrt{{\displaystyle \sum_{x\in P}d\left(x,P^{*}\right)}^{2}}}{\left|P\right|}\label{eq:indicator-gd}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
noindent
\end_layout

\end_inset


\begin_inset Box Frameless
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
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width "100col%"
special "none"
height "1in"
height_special "totalheight"
status collapsed

\begin_layout Plain Layout
\begin_inset listings
lstparams "language={C++}"
inline false
status open

\begin_layout Plain Layout

\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "lis:otl-dtlz"

\end_inset

利用NSGA-II求解DTLZ2（实数编码）测试函数的C++代码
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

typedef std::mt19937 _TRandom;
\end_layout

\begin_layout Plain Layout

typedef double _TReal;(*@
\backslash
label{lis:otl-dtlz:TReal}@*)
\end_layout

\begin_layout Plain Layout

typedef otl::problem::dtlz::DTLZ2<_TReal> _TProblem;(*@
\backslash
label{lis:otl-dtlz:TProblem}@*)
\end_layout

\begin_layout Plain Layout

typedef otl::crossover::SimulatedBinaryCrossover<_TReal, _TRandom &> _TCrossover
;(*@
\backslash
label{lis:otl-dtlz:TCrossover}@*)
\end_layout

\begin_layout Plain Layout

typedef otl::mutation::PolynomialMutation<_TReal, _TRandom &> _TMutation;(*@
\backslash
label{lis:otl-dtlz:TMutation}@*)
\end_layout

\begin_layout Plain Layout

typedef _TProblem::TDecision _TDecision; // real-coded MOP: std::vector<_TReal>(
*@
\backslash
label{lis:otl-dtlz:TDecision}@*)
\end_layout

\begin_layout Plain Layout

typedef otl::optimizer::nsga_ii::NSGA_II<_TReal, _TDecision, _TRandom &>
 _TOptimizer;(*@
\backslash
label{lis:otl-dtlz:TOptimizer}@*)
\end_layout

\begin_layout Plain Layout

_TRandom random(std::time(0));
\end_layout

\begin_layout Plain Layout

_TProblem problem(3); // 3-objective optimization
\end_layout

\begin_layout Plain Layout

_TCrossover _crossover(random, 1, problem.GetBoundary(), 20);
\end_layout

\begin_layout Plain Layout

otl::crossover::CoupleCoupleCrossoverAdapter<_TReal, _TDecision, _TRandom
 &> crossover(_crossover, random);
\end_layout

\begin_layout Plain Layout

_TMutation mutation(random, 1 / (_TReal)problem.GetBoundary().size(), problem.GetBo
undary(), 20);
\end_layout

\begin_layout Plain Layout

const std::vector<_TDecision> initial = otl::initial::PopulationUniformReal(rand
om, problem.GetBoundary(), 100); // 100 individuals
\end_layout

\begin_layout Plain Layout

_TOptimizer optimizer(random, problem, initial, crossover, mutation);(*@
\backslash
label{lis:otl-dtlz:optimizer}@*)
\end_layout

\begin_layout Plain Layout

for (size_t generation = 1; problem.GetNumberOfEvaluations() < 30000; ++generatio
n) // 300 generations
\end_layout

\begin_layout Plain Layout

{
\end_layout

\begin_layout Plain Layout

	std::cout << "generation=" << generation << std::endl;
\end_layout

\begin_layout Plain Layout

	optimizer();
\end_layout

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
OTL托管在GitHub页面上（
\begin_inset CommandInset href
LatexCommand href
target "github.com/O-T-L"

\end_inset

）
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
脚注
\end_layout

\end_inset

。
\begin_inset CommandInset ref
LatexCommand ref
reference "lis:otl-dtlz"

\end_inset

给出了一段C++程序，决策变量类型
\begin_inset Flex styCode
status collapsed

\begin_layout Plain Layout
TDecision
\end_layout

\end_inset

已经由优化问题指定（
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ref{lis:otl-dtlz:TDecision}
\end_layout

\end_inset

，DTLZ2内部定义了
\begin_inset Flex styCode
status collapsed

\begin_layout Plain Layout
TDecision
\end_layout

\end_inset

的类型）。
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:otl-time"

\end_inset

不同软件框架中NSGA-II在不同测试函数上运行时间（以秒为单位）的结果（均值和方差）。其中深色和浅色分别代表表现最好和次好的软件框架，
\begin_inset Formula $\dagger$
\end_inset

符号表示PyOTL与对应的软件框架之间的均值存在显著区别。
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset CommandInset include
LatexCommand input
filename "Tables/OTL/Time.lyx"

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
从
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:otl-time"

\end_inset

可以看出，运行速度最快的是OTL。
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:besbs-igd-dtlz1"

\end_inset

所有算法在DTLZ1测试函数上的IGD结果（均值和方差）。其中深色和浅色分别代表表现最好和次好的算法。
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
scriptsize
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset CommandInset include
LatexCommand input
filename "Tables/BESBS/DTLZ1/IGD-MeanSD.lyx"

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:besbs-igd-dtlz3"

\end_inset

所有算法在DTLZ3测试函数上的IGD结果（均值和方差）。其中深色和浅色分别代表表现最好和次好的算法。
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
scriptsize
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset CommandInset include
LatexCommand input
filename "Tables/BESBS/DTLZ3/IGD-MeanSD.lyx"

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:besbs-igd-dtlz1"

\end_inset

–
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:besbs-igd-dtlz3"

\end_inset

给出了所有算法的IGD数据。
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:besbs-igd-anova-dtlz1"

\end_inset

BESBS与其余算法在DTLZ1测试函数上IGD的方差分析结果（均值差与显著性）。其中灰色代表BESBS的均值好于对应的算法，并用删除线标记不显著的结果。
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
scriptsize
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset CommandInset include
LatexCommand input
filename "Tables/BESBS/DTLZ1/IGD-DiffSig.lyx"

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:besbs-igd-anova-dtlz3"

\end_inset

BESBS与其余算法在DTLZ3测试函数上IGD的方差分析结果（均值差与显著性）。其中灰色代表BESBS的均值好于对应的算法，并用删除线标记不显著的结果。
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
scriptsize
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset space \hfill{}
\end_inset


\begin_inset CommandInset include
LatexCommand input
filename "Tables/BESBS/DTLZ3/IGD-DiffSig.lyx"

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
最后分析
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:besbs-igd-anova-dtlz1"

\end_inset

–
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:besbs-igd-anova-dtlz3"

\end_inset

中的IGD对比结果。
\end_layout

\begin_layout Section
论文的组织结构
\end_layout

\begin_layout Standard
\begin_inset CommandInset ref
LatexCommand ref
reference "chap:introduction"

\end_inset

：简述绪论。
\end_layout

\begin_layout Standard
\begin_inset CommandInset ref
LatexCommand ref
reference "chap:conclusion"

\end_inset

：总结全文。
\end_layout

\end_body
\end_document