Nesting of two-dimensional parts in multiple plates using hybrid algorithm

Hybrid heuristic algorithms are proposed for the nesting of two-dimensional rectangular parts in multiple plates. The nesting algorithm of Babu and Babu is first modified and a new heuristic nesting algorithm, IBH, is proposed to utilize the material plate further. IBH is then combined in a meta-heuristic approach, simulated annealing. The proposed hybrid algorithms can then be extended to solve the nesting problem involving irregular parts by embedding irregular parts to rectangles. One problem arises in this ‘irregular-to-rectangular’ process, i.e. conversion of demands of the original irregular parts into demands of the embedding rectangles. A greedy heuristic rule is therefore presented to determine the number of embedding rectangles of different types to be used in order to maximize the utilization of the material plate given that the demand of each irregular part must be satisfied. Promising computational results are obtained and reported by running examples from the literature and data relevant to the footwear industry.