Dimensional Packing Problem Research Articles

Object-Oriented Class Library for Resource Allocation Problems

The object-oriented class library designed for solving various optimization problems of resource allocation, including problems of cutting materials and any dimensional packing problems, is described in this paper. The class library enables obtaining of suboptimal solutions of NP-completed resource allocation problems using standard evolutionary and modified heuristic optimization algorithms. The developed class library can be used in creation of an applied software for a wide class of optimization problems, including problems of resource allocation in storage systems and logistics, problems of cutting materials on machine tools with numerical control, scheduling problems and a large set of other practical problems.

Two dimensional packing problem using a hybrid constructive algorithm of variable neighborhood search and simulated annealing

Two dimensional packing problem using a hybrid constructive algorithm of variable neighborhood search and simulated annealing

О построении расписаний выполнения параллельных задач на группах кластеров с различной производительностью

A classical problem of scheduling the set of tasks optimizing load balancing for a set of given processors was considered in theory in 1966. Graham's algorithm sending each task to a least loaded machine (processor) was the first example of approximate algorithm with guaranteed constant approximation quality. But all tasks and processors (machines) in Graham's example were simple (only one processor was sufficient for each task). On the other hand Graham's algorithm was an on-line one that is each task was sended to processor without knowing future tasks. With wide use of computational clusters very actual became the problem of scheduling parallel tasks on the set of parallel clusters in the class of on-line algorithms.. This problem has very close relation to a two dimensional packing problem, socalled multiple strip packing problem. Few years ago the author proposed an on-line algorithm for this problem and proved that for arbitrary set of parallel tasks (rectangles) the obtained schedule (packing) is within 2e of the optimal. In this paper the author generalized his on-line algorithm for the case of related parallel machines when all clusters have different speeds of processors in different clusters. An on-line algorithm for scheduling parallel tasks on a group of clusters with different speeds of processors is presented and it was proved that its approximation ratio is 2e for any set of parallel tasks. This result is non-trivial because even the case of one-processor related machines was intensively investigated and some algorithms with constant approximation ratio were presented.

TAM/wrapper Co-optimization And Test Scheduling For SOCs Based On Hybrid Genetic Algorithm

In this paper, a new method is presented for TAM/wrapper co-optimization based on hybrid genetic algorithm and two- dimensional packing problem. In this method, core test is represented by rectangles, and a hybrid genetic algorithm that provides highly optimal solution for two-dimensional packing problem is introduced for TAM allocation and test scheduling. During the scheduling, the TAM width assigned to cores could be adjusted to an appropriate size to minimize the idle time. This HGA based method was implemented in C and applied to ITC’02 SOC Test Benchmark. Experimental results show that lower testing time was obtained by this new method compared to other methods [1,4,5].

Comparison of Deterministic Heuristics and Simulated Annealing for the Rotational Placement Problem over Containers with Fixed Dimensions

Two dimensional packing problem arises in the industry whenever one must place multiple items inside a container such that there is no collision between the items, while either minimizing the size of the container or maximizing the area occupied by the items. High material utilization is of particular interest to mass production industries since small improvements of the layout can result in large savings of material and considerably reduce production cost. In this work the Simulated Annealing is combined with deterministic heuristics (larger first (LF), bottom left (BL) and translations only (Tr)) and compared. The rotational generic approach has discrete (sequence of placement) and continuous (angle and position) parameters. It is very important to notice that the cost function (non occupied space) has only discrete values.

Near-Optimal Solutions to Two-Dimensional Bin Packing With 90 Degree Rotations

We consider a multidimensional generalization of the bin packing problem, namely, packing 2−dimensional rectangles into the minimum number of unit squares, where 90 degree rotations are allowed. Our main contribution is a polynomial time algorithm for packing rectangles into at most OPT bins whose sides have length (1+ɛ), for any ɛ>0. Additionally, we show how this result can be used to obtain near optimal packing results for a variety of two and three dimensional packing problems in which 90 degree rotations are allowed. These include minimum rectangle packing, two dimensional strip packing, and the z-oriented 3-dimensional packing problem.

Heuristics Acquisition from Problem Solving Process and Knowledge Representation by State-Action Network. Application to Two-Dimensional Packing Problems.

This paper proposes a new model and method for knowledge acquisition for planning problems in manufacturing, such as production planning, packing problems, and so forth, based on a problem solving process of a planner. In our proposed model, knowledge used for solving the objective problem is obtained through construction of state action network. A state action network consists of states describing some phases of the problem solving process and planner's actions in each phase. Moreover, reinforcement learning is used to refine the obtained state action network and to evaluate the problem solving process. We apply the proposed method to two dimensional packing problems and demonstrate its applicability and effectiveness through some computational experiments.

Modeling of packing problems

In this paper the modeling of packing problems (cutting and allocation problems) is investigated. Especially, linear mixed-integer models are proposed for two-dimensional packing problems of convex and non-convex polygons. The models are based on the so-called (outer) hodograph and the inner hodograph. Rotations of the polygons are not allowed. The principles of modeling in the two-dimensional case can be applied alsofor three- and higher dimensional packing problems