An optimal algorithm for rectangle placement
Operations Research Letters
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In rail-vehicle manufacturing enterprises, material costs are main part of total costs, so nesting optimization and material quota is important for enterprise's cost control and supply chain management. Because most parts are rectangular, rectangular object layout is solved first in nesting optimization. Rectangular object layout is not a simple NP (nondeterministic polynomial) optimization problem because of the practical production rules, such as guillotine. Under certain situations, the guillotine is even more important than the pure using ratio of metal sheets. The purpose of this paper is to construct the model of genetic algorithm and design the genetic operators for a practical case. Combined with the lowest-horizontal-line search algorithm, Genetic algorithm model is applied into rectangular object layout optimization. Results show that the model can satisfy not only the practical production requirements of guillotine, but also the requirement for production convenience. In this way, users can get optimal layout results and a higher material using ratio for practical production effectively and quickly.