This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed.
A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective.
Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature.
Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases.
[1]
A. Steinberg,et al.
A Strip-Packing Algorithm with Absolute Performance Bound 2
,
1997,
SIAM J. Comput..
[2]
Guochuan Zhang,et al.
A 3-approximation algorithm for two-dimensional bin packing
,
2005,
Oper. Res. Lett..
[3]
Zafer Bingul,et al.
Hybrid genetic algorithm and simulated annealing for two-dimensional non-guillotine rectangular packing problems
,
2006,
Eng. Appl. Artif. Intell..
[4]
Rob van Stee,et al.
An approximation algorithm for square packing
,
2004,
Oper. Res. Lett..
[5]
Daniel Dominic Sleator,et al.
A 2.5 Times Optimal Algorithm for Packing in Two Dimensions
,
1980,
Inf. Process. Lett..