Dealing with Nonregular Shapes Packing

Abstract

This paper addresses the irregular strip packing problem, a particular two-dimensional cutting and packing problem in which convex/nonconvex shapes (polygons) have to be packed onto a single rectangular object. We propose an approach that prescribes the integration of a metaheuristic engine (i.e., genetic algorithm) and a placement rule (i.e., greedy bottom-left). Moreover, a shrinking algorithm is encapsulated into the metaheuristic engine to improve good quality solutions. To accomplish this task, we propose a no-fit polygon based heuristic that shifts polygons closer to each other. Computational experiments performed on standard benchmark problems, as well as practical case studies developed in the ambit of a large textile industry, are also reported and discussed here in order to testify the potentialities of proposed approach.

A Parallel Biased Random‐Key Genetic Algorithm with Multiple Populations Applied to Irregular Strip Packing Problems

“…In the field of metaheuristics, Jakobs [16] exposed an approach that combines a genetic algorithm and a Bottom-Left (BL) strategy as a constructive heuristic for the positioning of items. The chromosome coding was mapped as an ordered sequence of parts, also applied by [17,18]. On the other hand, in [19], the authors used the same idea, but a raster representation for the pieces.…”

An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry

“…They integrate a greedy bottom-left as placement rule and a genetic algorithm as metaheuristic searching engine. They still utilized no-fit polygon to reduce geometric complexity [8]. However, the researches devoted to 2D irregular cutting stock problem have not received as much attention as SPP.…”

A fast and scalable bottom-left-fill algorithm to solve nesting problems using a semi-discrete representation

“…Many methods use a continuous representation of the pieces and the strip. We refer to the use of the no-fit polygon, see Amaro Junior, Pinheiro, Saraiva and Pinheiro (2014); Pinheiro, Amaro Junior and Saraiva (2016), or the use of 'direct trigonometry' as in Burke, Hellier, Kendall and Whitwell (2006). Several methods combine a continuous representation of the pieces with a discretized strip, as for example in Burke et al (2006) and in the dotted board model, see for example Toledo, Carravilla, Ribeiro, Oliveira and Gomes (2013).…”

“…Of course, the simple bottom-left-fill heuristic cannot achieve high quality solutions to the nesting problem, but many approaches in the literature use metaheuristics on top of this greedy heuristic, e.g. Gomes and Oliveira (2002); Burke et al (2006); Ma and Liu (2007); Akunuru and Babu (2013); Amaro Junior et al (2014); Pinheiro et al (2016); Sato et al (2019). These metaheuristics can be applied regardless of the representation of the pieces and the strip.…”