Recent advances on two-dimensional bin packing problems

Lodi, Andrea; Martello, Silvano; Vigo, Daniele

doi:10.1016/s0166-218x(01)00347-x

Cited by 265 publications

(120 citation statements)

References 44 publications

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“…This body of work includes dynamic split and merge scheme for large scale wireless multicast. Present research is based on the scheme given in [6,7] and we model and analyze it. Previous research address mainly reducing number of existing servers and has considered neither a dynamic split and merge scheme nor the comparison between FFD and LL algorithms.…”

Section: Methodsmentioning

confidence: 99%

“…In order to handle key management efficiently and reduce the join/leave latency a dynamic split and merge scheme is suggested [5,7] . If the number of users in a server is greater than ∅ max , the server is split into several logical servers for which the number of users in each server is as close as possible to the optimal group size ρ/m* .…”

Section: Introductionmentioning

confidence: 99%

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Server Optimization Using Heuristic Algorithms for Dynamic-Split-and-Merge Scheme in Wireless Multicast

Sukumar¹,

Vasudevan²

2009

J. of Computer Science

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Problem statement:In order to minimize the overall network traffic in a multiserver system, the number of users served by each server (and hence the group size) should remain constant. As the underlying traffic fluctuates, a split and merge scheme is implemented in a physical server to achieve load balancing. Approach: Minimizing the number of servers during the merge operation is NP hard and to achieve these two algorithms namely FFD bin packing algorithm and LL algorithm were proposed to find the near optimal values of destination servers. Results: The performance of these algorithms were analyzed and compared based on several parameters. Conclusion: Results showed that LL algorithm outperforms FFD algorithm.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Server Optimization Using Heuristic Algorithms for Dynamic-Split-and-Merge Scheme in Wireless Multicast

Sukumar¹,

Vasudevan²

2009

J. of Computer Science

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“…Bortfeldt and Lesh and Mitzenmacher are unaware of each other's work so we compare their results. Lodi et al (2002) present an overview of two-dimensional packing. For 2D-SPP, they describe the layer-based heuristics next-fit decreasing, first-fit decreasing, and best-fit decreasing.…”

Section: W ∈ Rmentioning

confidence: 99%

One-dimensional heuristics adapted for two-dimensional rectangular strip packing

Belov

Scheithauer

Mukhacheva

2008

Journal of the Operational Research Society

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We consider two-dimensional rectangular strip packing without rotation of items and without the guillotine cutting constraint. We propose a single-pass heuristic which fills every free space in a onedimensional knapsack fashion, i.e. considering only item widths. It appears especially important to assign suitable heuristic "pseudo-values" as profits in this knapsack problem. This simple heuristic improves the results for most of the test classes from the literature, compared to the results of Bortfeldt (2004) and . Moreover, we describe a simple modification of the Bottom-Left heuristic and call it Bottom-Left-Right. Executing it iteratively with different input sequences generated by the randomized framework BubbleSearch of , we obtain the best results in some classes with smaller number of items (20, 40). For larger instances, the pseudo-value-based algorithm is the best one in most cases.

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“…A recent survey on 2D packing problems is given in Lodi et al [5]. Among the algorithms for exactly solving the general 2BP problem are the branch and bound algorithm of Martello and Vigo [7] and the hybrid Branch and Price / Constraint Programming algorithm presented by Pisinger and Sigurd [8].…”

Section: Introductionmentioning

confidence: 99%

An Evolutionary Algorithm for Column Generation in Integer Programming: An Effective Approach for 2D Bin Packing

Puchinger¹,

Raidl²

2004

Lecture Notes in Computer Science

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Abstract. We consider the 3-stage two-dimensional bin packing problem, which occurs in real-world problems such as glass cutting. For it, we present a new integer linear programming formulation and a branch and price algorithm. Column generation is performed by applying either a greedy heuristic or an Evolutionary Algorithm (EA). Computational experiments show the benefits of the EA-based approach. The higher computational effort of the EA pays off in terms of better final solutions; furthermore more instances can be solved to provable optimality.

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Recent advances on two-dimensional bin packing problems

Cited by 265 publications

References 44 publications

Server Optimization Using Heuristic Algorithms for Dynamic-Split-and-Merge Scheme in Wireless Multicast

Server Optimization Using Heuristic Algorithms for Dynamic-Split-and-Merge Scheme in Wireless Multicast

One-dimensional heuristics adapted for two-dimensional rectangular strip packing

An Evolutionary Algorithm for Column Generation in Integer Programming: An Effective Approach for 2D Bin Packing

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