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In this paper, we propose three heuristics for the circular two-dimensional open dimension problem, also known as the circular strip cutting/packing problem. We first propose an open strip generation solution procedure that uses the best local position rule into the open strip. Second, we propose a simple augmented version of the first heuristic by introducing an exchange-order strategy. Third, we propose a hybrid heuristic that combines beam search and a series of target values belonging to a predetermined interval search. We evaluate the performance of these heuristics on several instances varying from small to large ones. Encouraging results have been obtained.

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Recently, we have developed two heuristics for the circle packing problem. The first one is called Maximum Hole Degree (MHD) and was used for packing unequal circles into a rectangular and a circular container. The second heuristic is called Minimum Damage (MinD) and is particularly adapted for packing equal circles into a circular container. MHD obtains good results when the instances contain very varied circles (different radii) but its performances decrease when there are more and more equal circles in the instances. In this paper, we propose a hybrid heurisctic named Null-Damage-MHD (NDMHD) used for packing unequal circles into a circular container. NDMHD combines MinD and MHD heuristics and we show that the obtained heuristic is adapted for every kind of circle instances.

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