Dense packings of congruent circles in a circle
Discrete Mathematics
Order Allocation for Stock Cutting in the Paper Industry
Operations Research
Approximate algorithms for constrained circular cutting problems
Computers and Operations Research
Reformulation descent applied to circle packing problems
Computers and Operations Research
New heuristics for packing unequal circles into a circular container
Computers and Operations Research
A beam search algorithm for the circular packing problem
Computers and Operations Research
An augmented beam search-based algorithm for the circular open dimension problem
Computers and Industrial Engineering
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In this paper, a constructive method is investigated for solving the circular open dimension problem (CODP), a problem of the Cutting and Packing family. CODP is a combinatorial optimization problem which is characterized by a set of circular pieces of known radii and a strip of fixed width W and unlimited length. The objective is to determine the smallest rectangle of dimensions (L, W), where L is the length of the rectangle, that will contain all the pieces such that there is no overlapping between the placed pieces and all the demand constraints are satisfied. The method combines the separate-beams search, look-ahead, and greedy procedures. A study concerning both restarting and look-ahead strategies is undertaken to determine the best tuning for the method. The performance of the method is computationally analyzed on a set of instances taken from the literature and for which optimal solutions are not known. Best-known solutions are obtained.