Using a footnote multiple times in tabular* environment with desired symbols

Question

I have the following table, which I still keep filling. I would like to add footnotes to several places. For instance, for rows 2 (207.09) and 3 (300.00) of the Nonlinear column, I want to add the same footnote (say note1), and for rows 4 (600.00) and 5 (600.00) of the same column, I want another footnote (say note2). Also, I would prefer customizable footnote symbols like *, +, etc.

I tried several methods that were readily given as answers. Some solutions include threeparttable and scrextend packages. I also tried others, but they did not work (got errors) probably because of tabular*.

\documentclass[review]{elsarticle}
\usepackage[colorlinks]{hyperref}
\usepackage{xcolor}
\usepackage{lineno}
\usepackage{amsmath,amsthm,amssymb,enumitem,nccmath}
\usepackage{graphicx,geometry,tabularx,tabulary}
\usepackage{booktabs,mathtools,multirow,relsize,subfig,mwe}
\usepackage{newtxmath}
\usepackage[ruled,vlined]{algorithm2e}
\usepackage{threeparttable}
\begin{table}
    \caption{Solution statistics for computational experiments.}\label[tab]{comp_res}
    {\begin{tabular*}{\textwidth}{c @{\extracolsep{\fill}} cccccccc}
    \toprule 
    \multirow{2}{*}{$|\setI|$} & \multirow{2}{*}{$|\setK|$} & \multirow{2}{*}{Instances} & \multicolumn{3}{c}{Average Gap}  & \multicolumn{3}{c}{Average Time (s)} \\ \cline{4-9}
    & & & \multicolumn{1}{c}{Cut} & \multicolumn{1}{c}{User cut} & \multicolumn{1}{c}{Nonlinear} & \multicolumn{1}{c}{Cut} & \multicolumn{1}{c}{User cut} & \multicolumn{1}{c}{Nonlinear} \\
    \midrule
    \multirow{6}{*}{40} & 5 & 50 & $3.7\times 10^{-5}$ & $2.0\times 10^{-5}$ & $3.4\times 10^{-5}$ & 15.06 & 14.04 & 23.87 \\
    & 10 & 25 & $8.8\times 10^{-5}$ & $5.9\times 10^{-5}$ & $2.5\times 10^{-2}$ & 19.10 & 26.04 & 207.09 \\
    & 15 & 10 & $9.4\times 10^{-5}$ & $6.5\times 10^{-5}$ & $7.6\times 10^{-2}$ & 28.35 & 74.89 & 300.00 \\
    & 20 & 5 & $1.1\times 10^{-4}$ & $2.2\times 10^{-5}$ & $11.9\times 10^{-2}$ & 112.9 & 464.6 & 600.00 \\
    & 25 & 5 & $2.2\times 10^{-4}$ & $9.1\times 10^{-5}$ & $11.2\times 10^{-2}$ & 123.7 & 314.6 & 600.00 \\
    \bottomrule
    \end{tabular*}}
\end{table}
\end{document}

Answer 1

In the following example, I have used \tnote and the tablenotes environment for the table notes, added siunitx in order to improve the input and alignment of numbers in the table, replaced the \cline command with two \cmidrule commands in order to improve the visual separation between the two blocks of three columns.

In addition, I removed the optional argument of the \label command since this caused "tab]{comp_res}" to be printed above the table in the resulting pdf file. I also placed the hyperref package at the end of the preamble since this package should (with a few exceptions) be the lat package you load. Lastly, I also had to replace \setK and \setI since the definitions of there commands was not given in the original example code.

\documentclass[review]{elsarticle}
\usepackage{xcolor}
\usepackage{lineno}
\usepackage{amsmath,amsthm,amssymb,enumitem,nccmath}
\usepackage{graphicx,geometry,tabularx,tabulary}
\usepackage{booktabs,mathtools,multirow,relsize,subfig,mwe}
\usepackage{newtxmath}
\usepackage[ruled,vlined]{algorithm2e}
\usepackage{threeparttable}
\usepackage{siunitx}
\usepackage[colorlinks]{hyperref} % Should be the last package in the preamble (with a few exceptions)
\begin{document}
\begin{table}
\begin{threeparttable}
    \caption{Solution statistics for computational experiments.}\label[tabl]{compres}
    \begin{tabular}{\textwidth}{c @{\extracolsep{\fill}} 
                                 c
                                 S[table-format=2]
                                 S[table-format=1.1e-1]
                                 S[table-format=1.1e-1]
                                 S[table-format=2.1e-1]
                                 S[table-format=3.2]
                                 S[table-format=3.2]
                                 S[table-format=3.2,table-space-text-post=\tnote{+}]
                                 }
    \toprule 
    \multirow{2}{}{$|I|$} 
      & \multirow{2}{}{$|K|$} 
        & {\multirow{2}{}{Instances}} 
          & \multicolumn{3}{c}{Average Gap} 
             & \multicolumn{3}{c}{Average Time (s)} \ 
     \cmidrule(r){4-6} \cmidrule(l){7-9}
      & & 
        & \multicolumn{1}{c}{Cut} 
          & \multicolumn{1}{c}{User cut} 
            & \multicolumn{1}{c}{Nonlinear} 
              & \multicolumn{1}{c}{Cut} 
                & \multicolumn{1}{c}{User cut} 
                  & \multicolumn{1}{c}{Nonlinear} \
    \midrule
    \multirow{5}{}{40} & 5  & 50 & 3.7 E-5 & 2.0 E-5 &  3.4 E-5 & 15.06 & 14.04 & 23.87 \
                        & 10 & 25 & 8.8 E-5 & 5.9 E-5 &  2.5 E-2 & 19.10 & 26.04 & 207.09\tnote{} \
                        & 15 & 10 & 9.4 E-5 & 6.5 E-5 &  7.6 E-2 & 28.35 & 74.89 & 300.00\tnote{} \
                        & 20 & 5  & 1.1 E-4 & 2.2 E-5 & 11.9 E-2 & 112.9 & 464.6 & 600.00\tnote{+} \
                        & 25 & 5  & 2.2 E-4 & 9.1 E-5 & 11.2 E-2 & 123.7 & 314.6 & 600.00\tnote{+} \
    \bottomrule
    \end{tabular}
    \begin{tablenotes}
    \item[*] text 
    \item[+] other text
    \end{tablenotes}
\end{threeparttable}
\end{table}
\end{document}