We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin’s level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst...

Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items, into a minimum size rectangular bin, without overlapping. The restriction is that the items cannot be rotated. The current paper is comparing a greedy algor...

Packing a given sequence of items into as few bins as possible in an online fashion is a widely studied problem. We improve lower bounds for packing hypercubes into bins in two or more dimensions, once for general algorithms (in two dimensions) and once for an important subclass, so-called Harmonic-type algorithms (in two or more dimensions). Lastly, we show that two adaptions of the ideas from...

Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items, into a minimum size rectangular bin, without overlapping. The restriction is that the items cannot be rotated. The current paper is comparing a greedy algor...

The relative worst order ratio, a new measure for the quality of online algorithms, was defined in [3]. Classical bin packing algorithms such as First-Fit, Best-Fit, and Next-Fit were analyzed using this measure, giving results that are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but also giving new separations and ea...

This goal of this senior design project is to implement and analyze the effectiveness of different meta-heuristic algorithms on solving two constrained optimization problems: the Bin Packing Problem and the Generalized Assignment Problem. Specifically, we are most interested in applying a certain meta-heuristic technique, the Genetic Algorithm. Although genetic algorithms have been used to solv...