We consider the optimal placement of hardware modules in space and time for FPGA architectures with reconfiguration capabilities, where modules are modeled as three-dimensional boxes in space and time. Using a graphtheoretic characterization of feasible packings, we are able to solve the following problems: (a) Find the minimal execution time of the given problem on an FPGA of fixed size, (b) Find the FPGA of minimal size to accomplish the tasks within a fixed time limit. Furthermore, our approach is perfectly suited for the treatment of precedence constraints for the sequence of tasks, which are present in virtually all practical instances. Additional mathematical structures are developed that lead to a powerful framework for computing optimal solutions. The usefulness is illustrated by computational results.

Recent generations of Field Programmable Gate Arrays (FPGA) allow the dynamic reconfiguration of cells on the chip during run-time. For a given problem consisting of a set of tasks with computation requirements modeled by rectangles of cells, several optimization problems such as finding the array of minimal size to accomplish the tasks within a given time limit are considered. Existing approaches based on ILP formulations to solve these problems as multi-dimensional packing problems turn out not to be applicable for problem sizes of interest. Here, a breakthrough is achieved in solving these problems to optimality by using the new notion of packing classes. It allows a significant reduction of the search space such that problems of the above type may be solved exactly using a special branch-and-bound technique. We validate the usefulness of our method by providing computational results.

More-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a two-level tree search algorithm for solving more-dimensional packing problems to optimality. Computational results are reported, including optimal solutions for all two-dimensional test problems from recent literature. This is the third in a series of three articles describing new approaches to more-dimensional packing.

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a two-level tree search algorithm for solving higher-dimensional packing problems to optimality. Computational results are reported, including optimal solutions for all two--dimensional test problems from recent literature.

The bin packing problem is one of the classical NP-hard optimization problems. Even though there are many excellent theoretical results, including polynomial approximation schemes, there is still a lack of methods that are able to solve practical instances optimally. In this paper, we present a fast and simple generic approach for obtaining new lower bounds, based on dual feasible functions. Worst case analysis as well as computational results show that one of our classes clearly outperforms the currently best known "economical" lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. This indicates the usefulness of our results in a branch and bound framework.

More-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for instances in two- or higher-dimensional space. We present a new approach for modeling packings, using a graph-theoretical characterization of feasible packings. Our characterization allows it to deal with classes of packings that share a certain combinatorial structure, instead of having to consider one packing at a time. In addition, we can make use of elegant algorithmic properties of certain classes of graphs. This allows it to make it the basis for a successful branch-and-bound framework. This is the first in a series of three articles describing new approaches to more-dimensional packing.

More-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is of crucial importance to have good and easy bounds for an optimal solution. Previous efforts have produced a number of special classes of such bounds. Unfortunately, some of these bounds are somewhat complicated and hard to generalize. We present a new approach for obtaining classes of lower bounds for more-dimensional packing problems; our bounds improve and simplify several well-known bounds from previous literature. In addition, our approach provides an easy framework for proving correctness of new bounds. This is the second in a series of three articles describing new approaches to more-dimensional packing.

In this paper, we consider the two-dimensional rectangular strip packing problem. A standard simple heutistic, Bottom-Left-Decreasing (BLD), has been shown to perform quite well in practice. We introduce and demonstrate the effectiveness of BLD, a stochastic search variation of BLD. While BLD places the rectangles in decreasing order of heigh, width, area and perimeter, BLD successively tries random orderings, chosen from a distribution determined by their Kendall-tau distance from one of these fixed orderings. Our experiments on benchmark problems show that BLD produces significantly better packings than BLD after only 1 minute of computation. Furthermore, we show that BLD outperforms recently reported methaheuristics. Furthermore, we observe that people seem able to reason about packing problems extremely well. We incorporate our new algorithms in an interactive system that combines the advantages of computer speed and human reasoning. Using the interactive system, we are able to quickly produce signiticantly better solutions than BLD by itself

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a dichotomous algorithm and a branch and price method. The three methods were carried out and compared on literature instances.

We study the problem of allocating berth space for vessels in container terminals, which is referred to as the berth allocation planning problem. We solve the static berth allocation planning problem as a rectangle packing problem with release time constraints, using a local search algorithm that employs the concept of sequence pair to define the neighborhood structure. We embed this approach in a real time scheduling system to address the berth allocation planning problem in a dynamic environment. We address the issues of vessel allocation to the terminal (thus affecting the overall berth utilization), choice of planning time window (how long to plan ahead in the dynamic environment), and the choice of objective used in the berthing algorithm (e.g., should we focus on minimizing vessels ’ waiting time or maximizing berth utilization?). In a moderate load setting, extensive simulation results show that the proposed berthing system is able to allocate space to most of the calling vessels upon arrival, with the majority of them allocated the preferred berthing location. In a heavy load setting, we need to balance the concerns of throughput with acceptable waiting time experienced by vessels. We show that, surprisingly, these can be handled by deliberately delaying berthing of vessels in order to achieve higher throughput in the berthing system. 1