In network coding based multicast, coding operations are expected to be minimized as they not only incur additional computational cost at corresponding nodes in network but also increase data transmission delay. On the other hand, delay constraint must be concerned particularly in delay sensitive applications, e.g. video conferencing. In this paper, we study the problem of minimizing the amount of coding operations required while meeting the end-to-end delay constraint in network coding based multicast. A population based incremental learning (PBIL) algorithm is developed, where a group of best so far individuals, rather than a single one, is maintained and used to update the probability vector, which enhances the global search capability of the algorithm. Simulation results demonstrate the effectiveness of our PBIL.