Creating Worst-Case Instances for Upper and Lower Bounds of the Two-Dimensional Strip Packing Problem

2017 ◽  
pp. 55-61
Author(s):  
Torsten Buchwald ◽  
Guntram Scheithauer
Keyword(s):  
Lower Bounds ◽  
Packing Problem ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Strip Packing ◽  
Worst Case

scholarly journals A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

2010 ◽  
Vol 102 (3-4) ◽  
pp. 467-487 ◽  
Author(s):  
Takehide Soh ◽  
Katsumi Inoue ◽  
Naoyuki Tamura ◽  
Mutsunori Banbara ◽  
Hidetomo Nabeshima
Keyword(s):  
Packing Problem ◽  
Two Dimensional ◽  
Strip Packing

A Reinforced Tabu Search Approach for 2D Strip Packing

2012 ◽  
pp. 171-188
Author(s):  
Giglia Gómez-Villouta ◽  
Jean-Philippe Hamiez ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Fitness Function ◽  
Packing Problem ◽  
Two Dimensional ◽  
Strip Packing ◽  
Benchmark Instances ◽  
Finite Set ◽  
Infinite Height ◽  
Search Approach

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

Improved metaheuristics for the two-dimensional strip packing problem

2020 ◽  
Vol 92 ◽  
pp. 106268 ◽  
Author(s):  
Rosephine G. Rakotonirainy ◽  
Jan H. van Vuuren
Keyword(s):  
Packing Problem ◽  
Two Dimensional ◽  
Strip Packing

Exact algorithms for the two-dimensional strip packing problem with and without rotations

2009 ◽  
Vol 198 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Mitsutoshi Kenmochi ◽  
Takashi Imamichi ◽  
Koji Nonobe ◽  
Mutsunori Yagiura ◽  
Hiroshi Nagamochi
Keyword(s):  
Packing Problem ◽  
Exact Algorithms ◽  
Two Dimensional ◽  
Strip Packing

scholarly journals Provable Guarantees on the Robustness of Decision Rules to Causal Interventions

2021 ◽  
Author(s):  
Benjie Wang ◽  
Clare Lyle ◽  
Marta Kwiatkowska
Keyword(s):  
Decision Making ◽  
Bayesian Networks ◽  
Lower Bounds ◽  
Decision Rules ◽  
Experimental Results ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Data Generating Process ◽  
Causal Bayesian Networks ◽  
Novel Model

Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes to parameters and/or causal influences. By relying on a tractable representation of Bayesian networks as arithmetic circuits, we provide efficient algorithms for computing guaranteed upper and lower bounds on the interventional robustness probabilities. Experimental results demonstrate that the methods yield useful and interpretable bounds for a range of practical networks, paving the way towards provably causally robust decision-making systems.

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