An improved typology of cutting and packing problems

Wäscher, Gerhard; Haußner, Heike; Schumann, Holger

doi:10.1016/j.ejor.2005.12.047

Cited by 1,225 publications

(714 citation statements)

References 118 publications

Supporting

Mentioning

602

Contrasting

Unclassified

Order By: Relevance

“…Beginning with an original solution for a problem, While ( making one step forward to final goal) { Use available strategies to find a solution } Get a final solution by combining all the solutions VLSI routing problem [3] and 2D packing problem [4] chooses different row cable and column cable will get different matrix connections. Travelling salesmen problem [5] has capacity restriction and mutual restriction.…”

Section: Improved Greedy Algorithm Based Matrix Cable Connection Optimentioning

confidence: 99%

Improved Greedy Algorithm Based Matrix Satellite Cable Connection Optimal Design

Wang

Zong

et al. 2017

MATEC Web Conf.

View full text Add to dashboard Cite

Abstract. An improved greedy algorithm based matrix satellite cable optimal design method is presented in this paper aim to overcome the difficulties including designing complexity, designing cycle and iterative designing process. An optimal algorithm model is built to help designer not only to accomplish design correctly and efficiently, but also to obtain better designing outcomes. Firstly, matrix cable designing model is pre-translated by turning electrical interface to equivalent digital model. Then the digital model is turned into computer language. At last, optimal design rules and method are extracted according to improved greedy algorithm. Real project data are used to prove the feasibility and validity of the proposed method.

show abstract

Section: Improved Greedy Algorithm Based Matrix Cable Connection Optimentioning

confidence: 99%

Improved Greedy Algorithm Based Matrix Satellite Cable Connection Optimal Design

Wang

Zong

et al. 2017

MATEC Web Conf.

View full text Add to dashboard Cite

show abstract

“…2D-SPP is a NP-hard combinatorial Contact author. 1 The guillotine constraint imposes a sequence of edge-to-edge cuts.…”

Section: Introductionmentioning

confidence: 99%

“…According to these notations, the 2D-SPP is then to determine the (x r i , y r i ) coordinates of the bottom-left corner of all r i ∈ R (i.e. the location of each r i in P ) so as to minimize the y r i + h r i value of the highest object in P , see (1). This can be formally stated as follows:…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

A Tabu Search Algorithm with Direct Representation for Strip Packing

Hamiez

Robet

Hao

2009

Evolutionary Computation in Combinatorial Optimization

View full text Add to dashboard Cite

Abstract. This paper introduces a new tabu search algorithm for a twodimensional (2D) Strip Packing Problem (2D-SPP). It integrates several key features: A direct representation of the problem, a satisfaction-based solving scheme, two different complementary neighborhoods, a diversification mechanism and a particular tabu structure. The representation allows inexpensive basic operations. The solving scheme considers the 2D-SPP as a succession of satisfaction problems. The goal of the combination of two neighborhoods is (to try) to reduce the height of the packing while avoiding solutions with (hard to fill) tall and thin wasted spaces. Diversification relies on a set of historically "interesting" packings. The tabu structure avoids visiting similar packings. To assess the proposed approach, experimental results are shown on a set of well-known benchmark instances and compared with previously reported tabu search algorithms as well as the best performing algorithms.

show abstract

“…There are sufficient standard size rectangular stock-sheets available to meet demand, where the stock sheet has length L and width W. Let P be the demand set of pieces, and each piece is considered to be unique. According to the typology proposed by Wäscher et al (2007), which improves the typology presented in Dyckhoff (1990Dyckhoff ( , 1985, this is a single bin size bin packing problem (SBSBPP). The further refinements are that all pieces are convex and usually irregular, pieces can be rotated continuously and reflected, and only guillotine cuts are allowed.…”

Section: Problem Descriptionmentioning

confidence: 99%

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

Martínez-Sykora

Álvarez-Valdés

Bennell

et al. 2015

Omega

View full text Add to dashboard Cite

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focused on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraints.

show abstract

An improved typology of cutting and packing problems

Cited by 1,225 publications

References 118 publications

Improved Greedy Algorithm Based Matrix Satellite Cable Connection Optimal Design

Improved Greedy Algorithm Based Matrix Satellite Cable Connection Optimal Design

A Tabu Search Algorithm with Direct Representation for Strip Packing

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

Contact Info

Product

Resources

About