[Tex/LaTex] tikz trees : how to modify some edges style

Question

I want to draw a flowchart using tikz trees.

I would like to change the style of some of my edges.
I want the edges from W to GI2 and GI4 to be curved.

I try to use child from parent path={... but it doesn't work (problem with \tikzparentnode ?).

Could you explain me how to do that ?
Thanks !

Here is my code

\documentclass{article}

\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{positioning,shadows,arrows,shapes,shapes.arrows,trees}

\tikzset{
    wait/.style={circle, draw=black, text centered, anchor=north, text=black, font=\scriptsize},
    adopt/.style={single arrow, draw=black, minimum height=1cm, minimum width=0.8cm, single arrow head extend=.15cm, inner sep=0.1cm, text centered, anchor=north, text=black, font=\footnotesize},
    end/.style={draw=none, fill=none, text centered, anchor=north}
}

\begin{document}

\begin{figure}[h]
    \begin{tikzpicture}[level distance=0.3cm, growth parent anchor=south,sibling distance = 3.7cm, align=center]
        \node (start) [end] {Begin $P_{I0-1}$} [->]
        child{[level distance=0.5cm]
            node (adopt5) [adopt, label=0:{\textbf{label 1}}] {$G_{I1}$}
            child{[level distance=1cm, sibling distance=5cm]
                node (w) [wait] {$\mathcal{W}$}
                child{[level distance=0.6cm]
                    node (g1) [adopt, label=0:{\textbf{label 2}}] {$G_{I2}(f)$}
                    child{
                        node (bye1) [end] {}
                    }
                    edge from parent node[pos=0.2,left=0.6cm]  {label on edge 1}
                }
                child{[level distance=0.6cm]
                    node (g2) [adopt, label=0:{\textbf{label 3}}] {$G_{I3}(f)$}
                    child{
                        node (bye2) [end] {}
                    }
                    edge from parent node[pos=0.3]  {label on edge 2}
                }
                child{[level distance=0.6cm]
                    node (g3) [adopt, label=0:{\textbf{label 4}}] {$G_{I4}(f)$}
                    child{[-]
                        node (bye3) [end] {}
                    }
                    edge from parent node[pos=0.2,right=0.6cm]  {label on edge 3}
                }
            }
        };

        \draw [->] (bye3.north) --  (bye2.north) -- (bye1.north) -- (-6cm,-4.63cm) -- (-6cm,-1.6cm) -- (0cm,-1.6cm);
    \end{tikzpicture}
\end{figure}

\end{document}

Answer 1

Why do you want to use a tree?

\documentclass[tikz,border=2mm]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning,shadows,arrows,shapes,shapes.arrows,trees}

\tikzset{
    wait/.style={circle, draw=black, text centered, anchor=north, text=black, font=\scriptsize},
    adopt/.style={single arrow, draw=black, minimum height=1cm, minimum width=0.8cm, single arrow head extend=.15cm, inner sep=0.1cm, text centered, anchor=north, text=black, font=\footnotesize},
    end/.style={draw=none, fill=none, text centered, anchor=north}
}

\begin{document}

    \begin{tikzpicture}[]
        \node[end] (start) [end] {Begin $P_{I0-1}$};
        \node[adopt] (adopt5) [below=0.5 of start, label=0:{\textbf{label 1}}] {$G_{I1}$};
        \node[wait] (w) [below=1cm of adopt5] {$\mathcal{W}$};
        \node[adopt, below left=1cm and 3.7cm of w] (g1) [label=0:{\textbf{label 2}}] {$G_{I2}(f)$};
         \node[adopt, below right=1cm and 3.7cm of w] (g3) [label=0:{\textbf{label 4}}] {$G_{I4}(f)$};

        \node[adopt,anchor=center] (g2) [label=0:{\textbf{label 3}}] at (g1-|w) {$G_{I3}(f)$};


        \draw[->] (start)--(adopt5);
        \draw[->] (adopt5)-- coordinate (aux) (w);
        \draw[->] (w) to [out=185, in=90] node[above left]{label on edge 1} (g1.north);
        \draw[->] (w) -- node{label on edge 2} (g2.north);
        \draw[->] (w) to [out=-5, in=90] node[above right]{label on edge 3} (g3.north);
            \draw[->] (g1.south)--++(-90:1cm);
            \draw[->] (g2.south)--++(-90:1cm);
            \draw[->] (g3.south)|-([shift={(-1cm,-1cm)}]g1.south west)|-(aux);
    \end{tikzpicture}


\end{document}