New approaches to nesting rectangular patterns

Abstract

In this study, two approaches are explored for the solution of the rectangular stock cutting problem: neuro-optimization, which integrates artificial neural networks and optimization methods; and genetic neuro-nesting, which combines artificial neural networks and genetic algorithms. In the first approach, an artificial neural network architecture is used to generate rectangular pattern configurations, to be used by the optimization model, with an acceptable scrap. Rectangular patterns of different sizes are selected as input to the network to generate the location and rotation of each pattern after they are combined. A mathematical programming model is used to determine the nesting of different sizes of rectangular patterns to meet the demand for rectangular blanks for a given planning horizon. The test data used in this study is generated randomly from a specific normal distribution. The average scrap percentage obtained is within acceptable limits. In the second approach, a genetic algorithm is used to generate sequences of the input patterns to be allocated on a finite width with infinite-length material. Each gene represents the sequence in which the patterns are to be allocated using the allocation algorithm developed. The scrap percentage of each allocation is used as an evaluation criterion for each gene for determining the best allocation while considering successive generations. The allocation algorithm uses the sliding method integrated with an artificial neural network based on the adaptive resonance theory (ART1) paradigm to allocate the patterns according to the sequence generated by the genetic algorithm. It slides an incoming pattern next to the allocated ones and keeps all scrap areas produced, which can be utilized in allocating a new pattern through the ART1 network. If there is a possible match with an incoming pattern and one of the scrap areas, the neural network selects the best match area and assigns the pattern. Both approaches gave satisfactory results. The second approach generated nests having packing densities in the range 95–97%. Improvement in packing densities was possible at the expense of excessive computational time. Parallel implementation of this unconventional approach could well bring a quick and satisfactory solution to this classical problem.