An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem

Abstract

The irregular strip packing problem is a combinatorial optimization problem that requires to place a given set of 2-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container. We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components into an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results.

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

“…Gomes and Oliveira [9] results and comparisons were then used as the basis for the subsequent literature comparisons. Such comparisons are reported in Egeblad et al [31], Bennell and Song [16], Imamichi et al [10] and Umetani et al [11]. Also Burke et al [7] introduced 10 new data sets, in addition to considering almost all Hopper's data sets in their reported comparison.…”

“…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].…”

“…The first approach utilizes an optimization technique to find the packing sequence of items that would lead to the best possible pattern when employed under a certain placement method (Babu and Babu [4], Fischer and Dagli [5], Takahara et al [6], and Burke et al [7]). While the second approach heuristically builds an initial pattern that may not be a feasible one, and an optimization technique is directly applied to the items positions seeking the best possible feasible pattern (Bennell and Dowsland [8], Gomes and Oliveira [9], Immamichi et al [10], and Umetani et al [11]). …”

Dotted-Board Model Dan Extended Local Search Untuk Optimalisasi Tata Letak Pola Busana Pada Bahan Bermotif Dengan Mempertimbangkan Aturan Keserasian Motif

“…Salah satu aplikasi Irregular SPP ditemukan pada industri busana. Tujuan dari Irregular SPP adalah untuk meminimalkan panjang kontainer dengan mengoptimalkan tata letak objek yang ada di dalamnya dengan syarat tidak ada objek yang saling tumpang tindih [6]. Pada pembuatan busana, perlu dipertimbangkan keserasian motif pada penjahitan (penyambungan) potongan-potongan pola busana, terutama pada busana bagian depan.…”

Collision free region determination by modified polygonal Boolean operations

“…Lee et al [4] used direct trigonometry to determine the interference among items and the container. Recently, the nofit polygon (NFP) has been used by several researchers [5][6][7][8][9] to ensure feasible layouts.…”