How to customize the number in the caption of an algorithm in algorithm2e

You could just force the counter associated with that environment.

Note that, in typical LaTeX fashion, counters are incremented just before they're used. So, in order to force the algorithm to start as Algorithm 3 (say), one would set the associated counter to 2. The counter used by algorithm2e for the algorithm environment is algocf (named after the author, Christophe Fiorio, I presume). So, using

\setcounter{algocf}{2}

immediately before using the algorithm environment would set the following algorithm as Algorithm 3.

The following example is taken from the algorithm2e documentation:

\documentclass{article}
\usepackage[ruled]{algorithm2e}% http://ctan.org/pkg/algorithm2e
\begin{document}

\setcounter{algocf}{2}% Modify counter of algorithm

\begin{algorithm}
  \DontPrintSemicolon
  \KwData{$G=(X,U)$ such that $G^{tc}$ is an order.}
  \KwResult{$G’=(X,V)$ with $V\subseteq U$ such that $G’^{tc}$ is an
    interval order.}
  \Begin{
    $V \longleftarrow U$\;
    $S \longleftarrow \emptyset$\;
    \For{$x\in X$}{
      $NbSuccInS(x) \longleftarrow 0$\;
      $NbPredInMin(x) \longleftarrow 0$\;
      $NbPredNotInMin(x) \longleftarrow |ImPred(x)|$\;
    }
    \For{$x \in X$}{
      \If{$NbPredInMin(x) = 0$ {\bf and} $NbPredNotInMin(x) = 0$}{
        $AppendToMin(x)$}
      }
      \nl\While{$S \neq \emptyset$}{\label{InRes1}
      \nlset{REM} remove $x$ from the list of $T$ of maximal index\;\label{InResR}
      \lnl{InRes2}\While{$|S \cap ImSucc(x)| \neq |S|$}{
        \For{$ y \in S-ImSucc(x)$}{
          \{ remove from $V$ all the arcs $zy$ : \}\;
          \For{$z \in ImPred(y) \cap Min$}{
            remove the arc $zy$ from $V$\;
            $NbSuccInS(z) \longleftarrow NbSuccInS(z) - 1$\;
            move $z$ in $T$ to the list preceding its present list\;
            \{i.e. If $z \in T[k]$, move $z$ from $T[k]$ to
              $T[k-1]$\}\;
          }
          $NbPredInMin(y) \longleftarrow 0$\;
          $NbPredNotInMin(y) \longleftarrow 0$\;
          $S \longleftarrow S - \{y\}$\;
          $AppendToMin(y)$\;
        }
      }
      $RemoveFromMin(x)$\;
    }
  }
  \caption{IntervalRestriction\label{IR}}
\end{algorithm}

\end{document}