Weibull-Based Benchmarks for Bin Packing

Castiñeiras, Ignacio; Cauwer, Milan De; O’Sullivan, Barry

doi:10.1007/978-3-642-33558-7_17

Cited by 9 publications

(9 citation statements)

References 19 publications

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“…We select two classic BPP benchmarks from the literature [14,32], and generate new instances similar to the ones proposed in [5]. This results in a total of 1, 922 instances organized as follows:…”

Section: Methodsmentioning

confidence: 99%

Constraint propagation on GPU: A case study for the AllDifferent constraint

Tardivo

Dovier

Formisano

et al. 2023

Journal of Logic and Computation

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The AllDifferent constraint is a fundamental tool in Constraint Programming. It naturally arises in many problems, from puzzles to scheduling and routing applications. Such popularity has prompted an extensive literature on filtering and propagation for this constraint. This paper investigates the use of General Processing Units (GPUs) to accelerate filtering and propagation. In particular, the paper presents an efficient parallelization of the AllDifferent constraint on GPU, along with an analysis of different design and implementation choices and evaluation of the performance of the resulting system on several benchmarks.

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Section: Methodsmentioning

confidence: 99%

Constraint propagation on GPU: A case study for the AllDifferent constraint

Tardivo

Dovier

Formisano

et al. 2023

Journal of Logic and Computation

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“…Several benchmarks have been used in previous work on exact and approximation algorithms for (offline) bin packing (see [12] for a list of related work). Many of these benchmarks typically use item sizes that are generated using either uniform or normal distributions.…”

Section: Benchmarksmentioning

confidence: 99%

“…We evaluate our algorithms on two types of benchmarks. The first type is based on the Weibull distribution, and was first studied in [12] as a model of several real-world applications of bin packing, e.g., the 2012 ROADEF/EURO Challenge on a data center problem provided by Google and several examination timetabling problems. The Weibull distribution is specified by two parameters: the shape parameter sh and the scale parameter sc (with sh, sc > 0).…”

Section: Benchmarksmentioning

confidence: 99%

“…This is because values outside this range result in trivial sequences with items that are generally too small (hence easy to pack) or too large (for which any online algorithm tends to open a new bin). The scale parameter is not critical, since we scale items to the bin capacity, as discussed later; we thus set sc = 1000, in accordance with [12].…”

Section: Benchmarksmentioning

confidence: 99%

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Online Bin Packing with Predictions

Angelopoulos¹,

Kamali²,

Shadkami³

2021

Preprint

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Bin packing is a classic optimization problem with a wide range of applications from load balancing in networks to supply chain management. In this work we study the online variant of the problem, in which a sequence of items of various sizes must be placed into a minimum number of bins of uniform capacity. The online algorithm is enhanced with a (potentially erroneous) prediction concerning the frequency of item sizes in the sequence. We design and analyze online algorithms with efficient tradeoffs between their consistency (i.e., the competitive ratio assuming no prediction error) and their robustness (i.e., the competitive ratio under adversarial error), and whose performance degrades gently as a function of the error. Previous work on this problem has only addressed the extreme cases with respect to the prediction error, and has relied on overly powerful and error-free prediction oracles.

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“…• Weibull Distribution (WD sequences): In [5], it is shown that Weibull distribution can be used to model real-world bin packing benchmarks. The values considered for the shape parameter k are among the ones suggested in [5]. The scale parameter of the distribution is set to be proportional to E.…”

Section: Experimental Evaluationmentioning

confidence: 99%

All-Around Near-Optimal Solutions for the Online Bin Packing Problem

Kamali

López-Ortíz

2015

Algorithms and Computation

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In this paper we present the first algorithm with optimal average-case and close-to-best known worstcase performance for the classic on-line problem of bin packing. It has long been observed that known bin packing algorithms with optimal average-case performance were not optimal in the worst-case sense. In particular First Fit and Best Fit had optimal average-case ratio of 1 but a worst-case competitive ratio of 1.7. The wasted space of First Fit and Best Fit for a uniform random sequence of length n is expected to be Θ(n 2/3 ) and Θ( √ n log 3/4 n), respectively. The competitive ratio can be improved to 1.691 using the Harmonic algorithm; further variations of this algorithm can push down the competitive ratio to 1.588. However, Harmonic and its variations have poor performance on average; in particular, Harmonic has average-case ratio of around 1.27. In this paper, first we introduce a simple algorithm which we term Harmonic Match. This algorithm performs as well as Best Fit on average, i.e., it has an average-case ratio of 1 and expected wasted space of Θ( √ n log 3/4 n). Moreover, the competitive ratio of the algorithm is as good as Harmonic, i.e., it converges to 1.691 which is an improvement over 1.7 of Best Fit and First Fit. We also introduce a different algorithm, termed as Refined Harmonic Match, which achieves an improved competitive ratio of 1.636 while maintaining the good average-case performance of Harmonic Match and Best Fit. Finally, our extensive experimental evaluation of the studied bin packing algorithms shows that our proposed algorithms have comparable average-case performance with Best Fit and First Fit, and this holds also for sequences that follow distributions other than the uniform distribution.

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Weibull-Based Benchmarks for Bin Packing

Cited by 9 publications

References 19 publications

Constraint propagation on GPU: A case study for the AllDifferent constraint

Constraint propagation on GPU: A case study for the AllDifferent constraint

Online Bin Packing with Predictions

All-Around Near-Optimal Solutions for the Online Bin Packing Problem

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