Journal Article10.1287/IJOC.11.4.345
Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems
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TL;DR: A new heuristic algorithm for each problem in the class of problems arising from all combinations of the above requirements, and a unified tabu search approach that is adapted to a specific problem by simply changing the heuristic used to explore the neighborhood.
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Abstract: Two-dimensional bin packing problems consist of allocating, without overlapping, a given set of small rectangles (items) to a minimum number of large identical rectangles (bins), with the edges of the items parallel to those of the bins. According to the specific application, the items may either have a fixed orientation or they can be rotated by 90°. In addition, it may or not be imposed that the items are obtained through a sequence of edge-to-edge cuts parallel to the edges of the bin. In this article, we consider the class of problems arising from all combinations of the above requirements. We introduce a new heuristic algorithm for each problem in the class, and a unified tabu search approach that is adapted to a specific problem by simply changing the heuristic used to explore the neighborhood. The average performance of the single heuristics and of the tabu search are evaluated through extensive computational experiments.
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Citations
Two-dimensional packing problems: A survey
TL;DR: This work considers problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste by discussing mathematical models, lower bounds, classical approximation algorithms, recent heuristic and metaheuristic methods and exact enumerative approaches.
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Recent advances on two-dimensional bin packing problems
TL;DR: This work surveys recent advances obtained for the two-dimensional bin packing problem, with special emphasis on exact algorithms and effective heuristic and metaheuristic approaches.
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Volleyball Premier League Algorithm
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References
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Knapsack Problems: Algorithms and Computer Implementations
Silvano Martello,Paolo Toth +1 more
- 01 Nov 1990
TL;DR: This paper focuses on the part of the knapsack problem where the problem of bin packing is concerned and investigates the role of computer codes in the solution of this problem.
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Local Search in Combinatorial Optimization
Emile H. L. Aarts,Jan Karel Lenstra +1 more
- 01 Apr 1997
TL;DR: Local search is still the method of choice for NP-hard problems as it provides a robust approach for obtaining high-quality solutions to problems of a realistic size in a reasonable time.
A typology of cutting and packing problems
TL;DR: The paper develops a consistent and systematic approach for a comprehensive typology integrating the various kinds of problems, founded on the basic logical structure of cutting and packing problems.
1.1K
An Algorithm for Two-Dimensional Cutting Problems
TL;DR: A tree-search algorithm for two-dimensional cutting problems in which there is a constraint on the maximum number of each type of piece that is to be produced is presented.
Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms
TL;DR: This work analyzes several “level-oriented” algorithms for packing rectangles into a unit-width, infinite-height bin and gives more refined bounds for special cases in which the widths of the given rectangles are restricted and in which only squares are to be packed.
554