This paper describes a heuristic algorithm for the two-dimensional free-form bin packing (2DFBP) problem, which is also called the irregular cutting and packing, or nesting problem. Given a set of 2D free-form bins, which in practice may be plate materials, and a set of 2D free-form items, which in practice may be plate parts to be cut out of the materials, the 2D-FBP problem is to lay out item...

This thesis presents a programme of research which investigated a genetic programming hyper-heuristic methodology to automate the heuristic design process for one, two and three dimensional packing problems. Traditionally, heuristic search methodologies operate on a space of potential solutions to a problem. In contrast, a hyper-heuristic is a heuristic which searches a space of heuristics, rat...

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0,1], and reveal the conne...

We survey lower bounds for the variant of the two-dimensional bin packing problem where items cannot be rotated. We prove that the dominance relation claimed by Carlier et al.[5] between their lower bounds and those of Boschetti and Mingozzi [1] is not valid. We analyze the performance of lower bounds from the literature and we provide the results of a computational experiment.

We prove that Best Fit bin packing has linear waste on the discrete distributionU{j, k} (where items are drawn uniformly from the set {1/k, 2/k, · · · , j/k}) for sufficiently large k when j = αk and 0.66 ≤ α < 2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0, a], for 0.66 ≤ a < 2/3. This implies that the expected asymptotic performance ratio of ...

Bin packing problem is a traditional problem in combinatorial optimization and applied widely in modern society. This paper presents bin packing problem with uncertain volumes and capacities. First, two types of uncertain programming models are mathematically constructed for the uncertain bin packing problem, including expected value model and chance-constrained programming model. Next, the pro...

In this paper we address the two-dimensional knapsack problem with unloading constraints: we have a bin B, and a list L of n rectangular items, each item with a class value in {1, . . . , C}. The problem is to pack a subset of L into B, maximizing the total profit of packed items, where the packing must satisfy the unloading constraint: while removing one item a, items with higher class values ...

Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given O(1/ǫ) advice bits for each input item allows approximating the dual bin packing problem online to within a factor of 1 + ǫ. Renault asked about the advice complexity of dual bin packing in the tape-advice model of online algorithms. We make progress on this q...