A hybrid algorithm for the two‐dimensional layout problem: the cases of regular and irregular shapes

Abstract

The two-dimensional layout (TDL) optimization problem consists of finding the minimal length layout of a set of both regular and irregular two-dimensional shapes on a stock sheet of finite width but infinite length. The layout should not contain any overlap. In this paper, we solve the TDL problem by proposing two approximate algorithms. The first one is a new heuristic based on a constructive approach specifically designed for irregular shapes, but that works well with regular ones. The second is a hybrid method in which the constructive approach displays the layouts corresponding to the chromosomes yielded by the genetic algorithm. The resulting algorithm yields satisfactory results in relatively short computational times as shown by the extensive computational testing on problems from the literature.

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

“…Constructive Approach (CA). This heuristic is based on the work presented by (Hifi and M'Hallah 2003). The heuristic starts by placing the first piece at the bottom-left of the object.…”

A Particle Swarm Optimization Algorithm for a 2-D Irregular Strip Packing Problem

“…Others are not included as they contain holes and/or arcs in the shapes of their items. Furthermore, we extracted a single data set (Grinde) from Hifi and M'Hallah [18].…”

“…Pixel or Raster Method is an approximate method that is employed by Jain and Gea [17], Babu and Babu [4], and Fischer and Dagli [5]. Direct trigonometry techniques are used by Hifi and M'Hallah [18], Takahara et al [6], and Burke et al [7]. A more sophisticated technique is the no-fit polygon which is applied by Oliveira et al [15], Bennell and Song [16], and Imamichi et al [10].…”

“…Three main meta-heuristics are commonly used with irregular cutting and packing problems, they are; Genetic Algorithm (Jakobs [19], Hifi and M'Hallah [18], and Hu-yao and Yuan-jun [20]), Simulated Annealing (Oliveira and Ferreira [21], Han and Na [22], Heckmann and Lengauer [23], and Gomes and Oliveira [9]), and Tabu Search (Blazewicz et al [24], Bennell and Dowsland [8], and Burke et al [7]). …”

Rotational placement of irregular polygons over containers with fixed dimensions using simulated annealing and no-fit polygons

“…This bounding rectangle algorithm is not a good approach as the bounding rectangle usually contains wasted material. Hifi and Hallah (2003) proposed a hybrid algorithm to solve the irregular problem. The hybrid algorithm searches for an optimal ordering of the small items using a genetic algorithm and identifies the best packing using a constructive approach, which consists of sequentially positioning a set of ordered small items.…”