In this paper, a genetic and heuristic approach is proposed for nesting of multiple, two-dimensional (2D)-shaped parts in 2D-shaped sheet with the aim of minimizing the wastage of sheet material. It presents a new method that can represent the geometry of sheet and part in a fast and effective way using the concepts of analytical geometry and semi-discrete form of representation. The method proposed to obtain an optimal sequence of parts is a modified genetic algorithm that chooses pre-determined sequence of parts as initial population instead of randomly generated sequence of parts as initial population. The effect of initial population on final optimal sequence and the effectiveness of the proposed scheme of representation are examined by comparing the results obtained to those obtained with the approach proposed by Babu and Babu (2001). Both utilized semi-discrete representation scheme proposed by Ma and Liu (2007). © 2012 World Scientific Publishing Company.