Irregular shape nesting and placing with evolutionary approach

Abstract

The purpose of this paper is to propose an evolutionary method to solve a garment shape nesting and placing problem. The structure used by the evolutionary algorithm is organised into a hierarchical tree which is similar to representation used in genetic programming. The first level deals with the basic nesting operation in which a reduced 'comb code' is used. The higher level makes use of trees organised in such a way that each of them represent a strip of layout.This representation can efficiently cope with the combinatorial aspect of the shape placing. Simulations have been implemented in a Smalltalk environment. Results compared to those of tree search show that the evolutionary method is a suitable tool for finding several good solutions and deterministic search comes as a complementary tool for focusing the search on a specific region.

PacCAM

“…Request permissions from permissions@acm.org. algorithms [4,7] (NP-hard) for packing 2D shapes, there are certain cases that automatic methods can not handle. For instance, source materials that contain graphics or have spatially varying quality require complicated trade-offs between function, aesthetics and efficient material use.…”

Solving the two-dimensional irregular objects allocation problems by using a two-stage packing approach

“…In comparison with the literature on the famous concept of ''nofit polygons" Gomes & Oliveira, 2002;Li & Milenkovic, 1995;Oliveira, Gomes, & Ferreira, 2000;Stoyan, Novozhilova, & Kartashov, 1996), methods of bottom-left (BL) placement strategy (Dowsland & Dowsland, 1995;Oliveira et al, 2000) and approaches based on linear programming compaction methods Li & Milenkovic, 1995;Stoyan et al, 1996), some meta-heuristic algorithms have been considered as an alternative to avoid local optimal solutions. These approaches include simulated annealing (Burke, 1999;Gomes & Oliveira, 1999, 2006Heckmann & Lengauer, 1995;Oliveira & Ferreira, 1993), tabu search (Bennell & Dowsland, 1999Blazewicz, Hawryluk, & Walkowiak, 1993), neural network (Han & Na, 1996), and genetic algorithms (GA) (Bounsaythip et al, 1997;Bounsaythip, Maouche, & Neus, 1995;Fujita, Akagji, & Kirokawa, 1993;Hifi & Hallah, 2003;Hopper, 2000;Ismail & Hon, 1995;Jain & Chang, 1998;Jakobs, 1996). Amidst these approaches, genetic algorithms are the most popular technique to solve the irregular objects packing problems (Hifi & Hallah, 2003).…”

“…Jakobs (1996) also used an order-based genetic algorithm to solve polygon packing problems. Bounsaythip et al (1997) provided a binary tree approach for the packing problems in the textile industry. In their approach, the polygons were circumscribed by using their bounding rectangles.…”

An effective heuristic for the two-dimensional irregular bin packing problem

“…Several metaheuristic approaches have been applied to the strip packing problems, for example, tabu search (Bennell and Dowsland 2001), evolutionary computation (Bounsaythip and Maouche 1997) and ant algorithms (Burke and Kendall 1999a). Metaheuristic techniques are often very effective; however, there can be some reluctance to use them for money-critical problems.…”