Create a table with two lines equations

Question

How create this table using latex.

The caption of the table should be in the left side and there is no space between the caption and the table. F2 and F3 should be in two lines. the contents of columns 1,3 and 4 are centered. I want it to be exactly like a table in the attached image.

This is my code

\documentclass{elsarticle}
\usepackage{booktabs}
\usepackage{amsmath}
\usepackage{siunitx}
\usepackage{booktabs, makecell, multirow}
\usepackage{caption}
\captionsetup[table]{format=plain,labelformat=simple,labelsep=period}%
\begin{document}
    \begin{table}[]
        \centering
        \caption{My caption}
        \label{my-label}
        \begin{tabular}{@{}llll@{}}
            \toprule
            F & Formula & f(x) & Search range \\ \midrule           
            1 & $\begin{array} {lcl} f(x) & = &  \sum_{i=1}^{n} \frac{x_i^{2}}{4000} - \prod_{i=1}^{n}cos(\frac{x_i}{\sqrt{i}}) + 1 \end{array}$       & 0    & [-100, 100]\\

            2 & $\begin{array} {lcl} f(x) & = & \frac{\pi}{n}10\sin (\pi {y_1}) 
            $+$ \sum_{i=1}^{n-1} {{( {{y_i} - 1})}^2}[{1 + 10{{\sin }^2}(\pi{y_{i + 1}})}] +(y_n -1)^{2}+\sum_{i=1}^{n}u(x_i,10,100,4)      \end{array}$    & 0    & [-100, 100]\\

            & $\begin{array} {lcl}
            u(x)
            u({x_i},a,k,m) =
            \begin{cases} 
              k{({x_i} - a)^m} & \,\,\,\,\,\,\,\,\,{x_i} > a\\
            0 & \,\,\,\,\,\,\,\,\,\, - a < {x_i} < a\\
            k{( - {x_i} - a)^m} &\,\,\,\,\,\,\,\,\, {x_i} <  - a

            \end{cases} & 

            \end{array}$ \\

            3 & $\begin{array} {lcl}   f\left( x \right) = 0.1\left\{ {{{\sin }^2}(3\pi {x_1}) + \mathop \sum \limits_{i = 1}^{n - 1} {{\left( {{x_i} - 1} \right)}^2}\left[ {1 + {{\sin }^2}(3\pi {x_i} + 1)} \right] + {{({x_n} - 1)}^2}\left[ {1 + {{\sin }^2}(2\pi {x_n})} \right]} \right\} + \sum\limits_{i = 1}^n {u({x_i},5,100,4)}     
            \end{array}$  & 0    & [-100, 100]\\
            \\ \bottomrule
        \end{tabular}
    \end{table} 
\end{document}

Answer 1

Something like this?

\documentclass{elsarticle}
\usepackage{booktabs,amsmath,caption,array}
\newcolumntype{C}[1]{>{\centering\arraybackslash}m{#1}}
\newlength\mylen
\newcommand\myrange{$[-100, 100]$}
\settowidth\mylen{\myrange}
\usepackage{newtxtext,newtxmath}
\captionsetup[table]{format=plain,
                     labelfont=bf,
                     labelsep=newline,
                     singlelinecheck=false,
                     skip=0pt}
\begin{document}
\begin{table}
\caption{Table caption here.}
\label{my-label}
$\begin{array}{@{} clcC{\mylen} @{}}
\toprule
\text{F} & \multicolumn{1}{c}{\text{Formula}} 
         & f_{\min} & \text{Search} \text{range} \\ 
\midrule           
\text{F1} & 
\begin{aligned} 
   &f(x) = \frac{1}{4000}\sum_{i=1}^{n} x_i^2 
         -\prod_{i=1}^n \cos\Bigl(\frac{x_i}{\sqrt{i}}\Bigr) + 1
\end{aligned}       
& 0 & \myrange\\
\cmidrule{1-4}
\text{F2} & 
\begin{aligned} 
   &f(x) = \Bigl\{ \frac{\pi}{n} 10\sin (\pi y_1) 
           + \sum_{i=1}^{n-1} (y_i - 1)^2 
           \bigl[ 1 + 10\sin^2(\pi y_{i+1}) \bigr] \\
   &\qquad\quad+(y_n -1)^2 \Bigr\} +\sum_{i=1}^n u(x_i,10,100,4)\\
   &y_i=1+\frac{x_i+1}{4} \\
   &u({x_i},a,k,m) =
      \begin{cases} 
            k(x_i - a)^m & x_i > a\\
            0            & - a < x_i < a\\
            k(-x_i- a)^m & x_i <  - a
      \end{cases}
\end{aligned} 
& 0 & \myrange\\
\cmidrule{1-4}
\text{F3} & 
\begin{aligned}
   &f(x) = 0.1\Bigl\{ \sin^2(3\pi x_1) + 
       \sum_{i=1}^{n-1}(x_i-1)^2
       \bigl[1 +\sin^2(3\pi x_i + 1) \bigr] \\
   &\qquad\quad+(x_n-1)^2\bigl[1 +\sin^2(2\pi x_n) 
       \bigr] \Bigr\}
       + \sum_{i=1}^n u(x_i,5,100,4)     
\end{aligned}  
& 0 & \myrange\\
\bottomrule
\end{array}$
\end{table} 
\end{document}

Some of the main changes I made were (i) use of an array environment instead of a tabular environment, as virtually all of the contents are in math mode; (ii) use of aligned environments to house the formulas in column 2; (iii) deletion of lots and lots of pairs of curly braces that do nothing except create code clutter, deletion of \,\,\,\,\,\,\,\,\,; (iv) no auto-sizing of the curly braces and square brackets, and (v) choice of different line breaks for the long formulas.