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Stabilized branch-and-price algorithms for vector packing problems
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DOI：10.1016/j.ejor.2018.04.047.png)
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摘要
En 中文
This paper considers packing and cutting problems in which a packing/cutting pattern is constrained independently in two or more dimensions. Examples are restrictions with respect to weight, length, and value. We present branch-and-price algorithms to solve these vector packing problems (VPPs) exactly. The underlying column-generation procedure uses an extended master program that is stabilized by (deep) dual-optimal inequalities. While some inequalities are added to the master program right from the beginning (static version), other violated dual-optimal inequalities are added dynamically. The column generation subproblem is a multidimensional knapsack problem, either binary, bounded, or unbounded depending on the specific master problem formulation. Its fast resolution is decisive for the overall performance of the branch-and-price algorithm. In order to provide a generic but still efficient solution approach for the subproblem, we formulate it as a shortest path problem with resource constraints (SPPRC), yielding the following advantages: (i) Violated dual-optimal inequalities can be identified as a by-product of the SPPRC labeling approach and thus be added dynamically; (ii) branching decisions can be implemented into the subproblem without deteriorating its resolution process; and (iii) larger instances of higher-dimensional VPPs can be tackled with branch-and-price for the first time. Extensive computational results show that our branch-and-price algorithms are capable of solving VPP benchmark instances effectively. (C) 2018 Elsevier B.V. All rights reserved.
Keyword:
Cutting
Vector packing
Shortest path problem with resource constraints
Dual-optimal inequalities
Stabilization
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期刊
IF:
6
论文数:
2.2W
被引数:
6.4W
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