ALGORITHM OF STEPS MINIMIZATION FOR ORTHOGONAL FIGURE CUTTING

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The problem of orthogonal cutting of complex figures defined by multi- ply connected orthogonal polygons is considered. The urgency of this task is due to its broad practical interpretation, as well as its belonging to the NP-hard class. As exact methods lose their effectiveness in solving NP-hard problems, because costs increase up to unacceptable values, various heuristic and hyper-heuristic algorithms are developed for solv- ing orthogonal figured cutting. The problem of figured cutting is often found in practice in resource-intensive industries, where the optimiza- tion of the process of raw materials consumption plays an important economic role. In particular, the problem of cutting multiply connected orthogonal polygons from a sheet resource has to be solved daily in the construction industry, at enterprises when cutting cardboard packages, and when making furniture. The complexity of the problem lies in the presence of the cut-off blanks internal voids, which often in practice are quite large and are able to accommodate other cut-off blanks. The desire to optimize the packaging process leads to the emergence of a new math- ematical model and specific limitations, while the algorithmization of any methods associated with the solution of the task is significantly complicated compared to the classical rectangular nesting. In this paper, a meaningful statement of the problem is described, its mathematical model is given. The review of algorithms described in the literature and developed earlier, allowing to obtain rational plans for cut- ting the material in the case of pattern cutting is made. The algorithm described in the article is based on a number of heuristic ideas, its main idea is to reduce the so-called gradation of the cutting map. The gradation here is defined as the amplitude of the height difference of the contour of the cutting pattern of the blanks. The computational time of the algorithm when using the selected heuristic ideas is acceptable for its use in practice when solving real problems of resource-intensive industries.