Multilevel Linked Data Structure for the Multidimensional Orthogonal Packing Problem

The actual NP-completed orthogonal bin packing problem is considered in the article. In practice a solution of a large number of different practical problems, including problems in logistics and scheduling comes down to the bin packing problem. A decision of an any packing problem is represented as a placement string which contains a sequence of objects selected to pack. The article proposes a new multilevel linked data structure that improves the effectiveness of decoding of the placement string and as a consequence, increases the speed of packing generation. The new data structure is applicable for all multidimensional orthogonal bin packing problems.

Effective Data Structure for the Multidimensional Orthogonal Bin Packing Problems

The actual in industry multidimensional orthogonal packing problem is considered in the article. Solution of a large number of different practical optimization problems, including resources saving problem, optimization problems in logistics, scheduling and planning comes down to the orthogonal packing problem which is NP-hard in strong sense. One of the indicators characterizing the efficiency of packing constructing algorithm is the efficiency of the used data structure. In the article a multilevel linked data structure that increases the speed of constructing of a packing is proposed. The carried out computational experiments show the high efficiency of the new data structure. Multilevel linked data structure is applicable for multidimensional orthogonal bin packing problems any kind.

Improved Data Structure for the Orthogonal Packing Problem

In paper is considered the actual in industry and engineering orthogonal multidimensional packing problem. This problem is NP-hard in strong sense therefore an important role is played effectiveness of the used packing representation model. To increase the speed of placement of a given set of orthogonal objects into containers is offered a new data structure – multilevel linked data structure. The carried out computational experiments demonstrate high time efficiency of the proposed data structure compared to the ordered simple linked list.

Improved Packing Representation Model for the Orthogonal Packing Problem

The multidimensional NP-hard orthogonal bin packing problem is considered in the article. Usually the problem is solved using heuristic algorithms of discrete optimization which optimize a selection sequence of objects to be packed in containers. The quality and speed of getting the resulting packing for a given sequence of placing objects is determined by the used packing representation model. In the article presented a new packing representation model for constructing the orthogonal packing. The proposed model of potential containers describes all residual free spaces of containers in packing. The developed model is investigated on well-known standard benchmarks of three-dimensional orthogonal bin packing problem. The model can be used in development of applied software for the optimal allocation of orthogonal resources.