Upper Bounds for Heuristic Approaches to the Strip Packing Problem

We study a new variant of the bin packing problem with a color constraint. Given a finite set of items, each item has a set of colors. Each bin has a color capacity, the total number of colors for a bin is the unification of colors for its items and cannot exceed the bin capacity. We need to pack all items into the minimal number of bins. For this NP-hard problem we present approximability results and design a hybrid matheuristic based on the column generation technique. A hybrid VNS heuristic is applied to the pricing problem. The column generation method provides a lower bound and a core subset of the most promising bin patterns. Fast heuristics and exact solution for this core produce upper bounds. Computational experiments for test instances with number of items up to 500 illustrate the efficiency of the approach.

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Constrained order packing: comparison of heuristic approaches for a new bin packing problem

Central European Journal of Operations Research ◽

10.1007/s10100-011-0228-1 ◽

2011 ◽

Vol 21 (1) ◽

pp. 237-264 ◽

Cited By ~ 2

Author(s):

Nikolaus Furian ◽

Siegfried Vössner

Keyword(s):

Bin Packing ◽

Packing Problem ◽

Heuristic Approaches ◽

Bin Packing Problem

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Robust mixed-integer linear programming models for the irregular strip packing problem

European Journal of Operational Research ◽

10.1016/j.ejor.2016.03.009 ◽

2016 ◽

Vol 253 (3) ◽

pp. 570-583 ◽

Cited By ~ 28

Author(s):

Luiz H. Cherri ◽

Leandro R. Mundim ◽

Marina Andretta ◽

Franklina M.B. Toledo ◽

José F. Oliveira ◽

...

Keyword(s):

Linear Programming ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Packing Problem ◽

Programming Models ◽

Mixed Integer ◽

Strip Packing

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A Reinforced Tabu Search Approach for 2D Strip Packing

Modeling, Analysis, and Applications in Metaheuristic Computing ◽

10.4018/978-1-4666-0270-0.ch011 ◽

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.

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