我创建了一个有 4 列的表格:
\begin{table}
\centering
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{1}{|l|}{Test function} & \multicolumn{1}{l|}{Study domain} & \multicolumn{1}{l|}{Formula} & \multicolumn{1}{l|}{Global minimum} \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{} Rastrigin\\\textasciitilde{}( dim = n ) \end{tabular} & $-5.12 \leq x_i \leq 5.12$ & $f(x_1 \cdots x_n) = 10n + \sum_{i=1}^n (x_i^2 -10cos(2\pi x_i))$ & $ \text{minimum at }f(0, \cdots, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{}Ackley\\\textasciitilde{}( dim = 2 ) \end{tabular} & \multicolumn{1}{l|}{$-5 \leq x_i \leq 5$ } & \multicolumn{1}{l|}{\textasciitilde{}$f(x_0 \cdots x_2) = -20 exp(-0.2 \sqrt{\frac{1}{2} \sum_{i=1}^2 x_i^2}) - exp(\frac{1}{2} \sum_{i=1}^n cos(2\pi x_i)) + 20 + e$ } & \multicolumn{1}{l|}{$\text{minimum at }f(0, 0) = 0$ } \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{} Rosenbrock\\( dim=n ) \end{tabular} & \multicolumn{1}{l|}{$ \mathbb{R}^{N}$ } & \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}\\$f(x_1 \cdots x_n) = \sum_{i=1}^{n-1} (100(x_i^2 - x_{i+1})^2 + (1-x_i)^2)$ \end{tabular}} & \multicolumn{1}{l|}{$ \text{minimum at }f(1, 1, \cdots, 1) = 0 $ } \\
\hline
\begin{tabular}[c]{@{}c@{}}Sphere\\(dim = n ) \end{tabular} & \multicolumn{1}{l|}{$ \mathbb{R}^{N}$ } & \multicolumn{1}{l|}{$f(x_1 \cdots x_n) = \sum_{i=1}^n x_i^2$ } & \multicolumn{1}{l|}{$\text{minimum at }f(0, \cdots, 0) = 0$ } \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{}Beale\\( dim = 2 ) \end{tabular} & $-4.5 \leq x_i \leq 4.5$ & $( 1-x+x.y)^{2} + ( 2.25-x+x. y^{2} )^{2} +( 2.625-x+x. y^{2} )^{2} $ & $\text{minimum at }f(3, 0.5) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Alpine\\( dim = n) \end{tabular} & $0 \leq x_i \leq 10$ & $ \sum_{i=1}^n \mid x_{i}.sin( x_{i} )+0.1.x_{i} \mid $ & $\text{minimum at }f(0, \cdots, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Brown\\( dim = n) \end{tabular} & \multicolumn{1}{l|}{$-1 \leq x_i \leq 4$ } & \multicolumn{1}{l|}{$ \sum_{i=1}^{n-1}[(x_{i}^{2})^{(x_{i+1}^{2}+1)} + (x_{i+1}^{2})^{(x_{i}^{2}+1)} ]$ } & \multicolumn{1}{l|}{$\text{minimum at }f(0, \cdots, 0) = 0$ } \\
\hline
\begin{tabular}[c]{@{}c@{}}Schaffer\\( dim = 2 ) \end{tabular} & $-100 \leq x_i \leq 100$ & $f(x,y)=0.5+\frac{sin({x^2 - y^2})-0.5}{[1+0.001 \cdot (x^2 + y^2)]^2}$ & $\text{minimum at }f(0, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Colville\\( dim = 4) \end{tabular} & $-10 \leq x_i \leq 10$ & $100( x_{1}^{2} - x_{2} )^{2} + ( x_{1}-1 )^{2} + ( x_{3}-1 )^{2} +90( x_{3}^{2} - x_{4} )^{2}+19.8(x_{2}-1 ).(x_{4}-1 )+10.1(( x_{2} - 1)^{2})+( x_{4} - 1)^{2}))$ & $\text{minimum at }f(1,1,1,1) = 0$ \\
\hline
Himmelblau’s & $-6 \leq x_i \leq 6$ & $ ( x^{2} +y-11)^{2} + (x+ y^{2} -7)^{2} $ & \begin{tabular}[c]{@{}c@{}}$\text{minimum at }f(3,2) = 0$\\$\text{minimum at }f(-2.805...,3.131) = 0$\\$\text{minimum at }f(-3.779...,-3.283) = 0$\\\\$\text{minimum at }f(3.584...,-1.848) = 0$ \end{tabular} \\
\hline
\end{tabular}
\end{table}
问题是编译后最后一列没有显示。
提前感谢您的帮助。
答案1
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\begin{table}
\centering
\begin{tabular}{|0c|0c|0l|0l|}
\hline
Test function & Study domain & Formula & Global minimum at \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{} Rastrigin\\\textasciitilde{}( dim = n ) \end{tabular} & $-5.12 \leq x_i \leq 5.12$ & $\begin{aligned}f(x_1 \cdots x_n) = 10n + \sum_{i=1}^n (x_i^2 -10cos(2\pi x_i))\end{aligned}$ & $f(0, \cdots, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{}Ackley\\\textasciitilde{}( dim = 2 ) \end{tabular} & $-5 \leq x_i \leq 5$ & $\begin{aligned}f(x_0 \cdots x_2) = &-20 exp(-0.2 \sqrt{\frac{1}{2} \sum_{i=1}^2 x_i^2}) \\&- exp(\frac{1}{2} \sum_{i=1}^n cos(2\pi x_i)) + 20 + e\end{aligned}$ & $f(0, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{} Rosenbrock\\( dim=n ) \end{tabular} & $ \mathbb{R}^{N}$ & $\begin{aligned}f(x_1 \cdots x_n) = \sum_{i=1}^{n-1} (100(x_i^2 - x_{i+1})^2 + (1-x_i)^2)\end{aligned}$ & $ f(1, 1, \cdots, 1) = 0 $ \\
\hline
\begin{tabular}[c]{@{}c@{}}Sphere\\(dim = n ) \end{tabular} & $ \mathbb{R}^{N}$ & $\begin{aligned}f(x_1 \cdots x_n) = \sum_{i=1}^n x_i^2\end{aligned}$ & $f(0, \cdots, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}\textasciitilde{}Beale\\( dim = 2 ) \end{tabular} & $-4.5 \leq x_i \leq 4.5$ & $\begin{aligned} ( 1-x+x.y)^{2} &+ ( 2.25-x+x. y^{2} )^{2} \\&+( 2.625-x+x. y^{2} )^{2} \end{aligned}$ & $f(3, 0.5) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Alpine\\( dim = n) \end{tabular} & $\phantom{-1}0 \leq x_i \leq 10$ & $ \sum_{i=1}^n \mid x_{i}.sin( x_{i} )+0.1.x_{i} \mid $ & $f(0, \cdots, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Brown\\( dim = n) \end{tabular} & $-1 \leq x_i \leq 4$ & $\begin{aligned} \sum_{i=1}^{n-1}[(x_{i}^{2})^{(x_{i+1}^{2}+1)} + (x_{i+1}^{2})^{(x_{i}^{2}+1)} ]\end{aligned}$ & $f(0, \cdots, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Schaffer\\( dim = 2 ) \end{tabular} & $-100 \leq x_i \leq 100$ & $\begin{aligned}f(x,y)=0.5+\frac{sin({x^2 - y^2})-0.5}{[1+0.001 \cdot (x^2 + y^2)]^2}\end{aligned}$ & $f(0, 0) = 0$ \\
\hline
\begin{tabular}[c]{@{}c@{}}Colville\\( dim = 4) \end{tabular} & $-10 \leq x_i \leq 10$ & $\begin{aligned} 100( x_{1}^{2} &- x_{2} )^{2} + ( x_{1}-1 )^{2} + ( x_{3}-1 )^{2} \\&+90( x_{3}^{2} - x_{4} )^{2}+19.8(x_{2}-1 ).(x_{4}-1 )\\&+10.1(( x_{2} - 1)^{2})+( x_{4} - 1)^{2}))\end{aligned}$ & $f(1,1,1,1) = 0$ \\
\hline
Himmelblau’s & $-6 \leq x_i \leq 6$ & $ \begin{aligned}( x^{2} +y-11)^{2} + (x+ y^{2} -7)^{2} \end{aligned}$ & \begin{tabular}[c]{@{}l@{}}$f(3,2) = 0$\\$f(-2.805...,3.131) = 0$\\$f(-3.779...,-3.283) = 0$\\$f(3.584...,-1.848) = 0$ \end{tabular} \\
\hline
\end{tabular}
\end{table}
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