Abstract
The bin-packing problem consists of determining the minimum number of bins needed to pack a given set of n items. It has been shown that the dual-feasible functions (DFF) proposed by Johnson and the data-dependent DFF (DDFF) proposed by the present authors can be used to obtain good lower bounds for bin-packing problems. In a recent paper we proposed fast bounds for the two-dimensional bin-packing problem using three (D)DFF. In this paper we discuss two new methods for generating (D)DFF, at a higher computational cost, to improve the results obtained. The first method consists of iteratively composing the three functions previously proposed. We show that the obtained set of functions contains a dominant set whose size is of O(n 2). The second method uses the enumerative method of Carlier and Néron to generate discrete DFF. We provide computational experiments to compare the effectiveness of the two methods against classical benchmarks derived from the literature.
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