  In this paper, we consider a generalized longest common subsequence problem
with multiple substring inclusive constraints. For the two input sequences $X$
and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints
$P=\{P_1,\cdots,P_d\}$ of total length $r$, the problem is to find a common
subsequence $Z$ of $X$ and $Y$ including each of constraint string in $P$ as a
substring and the length of $Z$ is maximized. A new dynamic programming
solution to this problem is presented in this paper. The correctness of the new
algorithm is proved. The time complexity of our algorithm is $O(d2^dnmr)$. In
the case of the number of constraint strings is fixed, our new algorithm for
the generalized longest common subsequence problem with multiple substring
inclusive constraints requires $O(nmr)$ time and space.
