Rateless codes are representative capacity achieving codes for the binary erasure channels. We consider a network where multiple noncooperative sources with arbitrarily correlated messages communicate with a single destination. The conventional distributed rateless coding scheme introduces a general And-or tree analysis and provides linear programming (LP) based solutions only for some special cases. However, in this paper, an optimization method applicable to all the cases is proposed. Based on the generalized analysis, we define a new objective and employ the sequential quadratic programming (SQP) algorithm to solve the problem. The obtained solution contains optimal degree distributions and symbol-selection weights. It is shown that the proposed scheme exhibits the reduced overhead at the higher symbol recovery rate region compared to the conventional schemes.