الگوریتم ترکیبی هیوریستیک برای مسئله دو بعدی برش سیم پیچ فولاد

This paper is concerned with the problem of two-dimensional cutting of small rectangular items, each of which has its own deadline and size, from a large rectangular plate, whose length are more than one thousand times its width, so as to minimize the trim loss and the reduction of the times of clamping and changing speed are also concerned. This problem is different with the classical two-dimensional cutting problem. In view of the distinguishing features of the problem proposed, we put forward the definition of non-classical cutting, that is to say, put a series of items on the rectangular plates in their best layout, so as to enhance utility and efficiency at the same time. These objectives may be conflicting and a balance should be necessary, so we present a Hybrid Heuristic Algorithm (HHA), consisting of clustering, ordering, striping and integer programming etc. We demonstrate the efficiency of the proposed algorithm through the comparison with the algorithm we studied before.

The problem of Two-Dimensional Steel Coil Cutting (TDSCC) proposed in this paper is essentially Two-Dimensional Cutting problem (TDC). The TDC problem consists in cutting a rectangular plate into a number of smaller rectangular items, each with a given size, so that the item edges are always parallel or orthogonal to the rectangular plate edges (orthogonal cutting). The objective is to minimize the amount of waste produced. The constrained form of this problem imposes restrictions on number of items of each size required to be cut to order. The related problem of maximizing the total value of the items cut can be also converted into this problem by taking the value of item to be proportional to its area. Examples of two-dimensional orthogonal cutting problems can be found in cutting of steel or glass plates into smaller pieces, in the cutting of wood sheets to produce furniture, and so on (Baldacci & Boschetti, 2007). In an industrial setting, the problem could be to compute how many plates are needed and how they can be cut in order to produce all the items in the list of required ordered sizes. As such, the two-dimensional orthogonal cutting problem must be solved as part of a pattern generating process in a heuristic or exact method for a two-dimensional cutting stock problem of the Gilmore–Gomory type. TDC problems are NP-hard as shown in Garey and Johnson (1979). The TDSCC problem considered in this paper is the Two-Dimensional Guillotine Cutting (TDGC) problem but has something different between TDGC, where the aspect ratio of plate used to large to converse frequently between vertical cutting and horizontal cutting. We call plate as steel coil here since its size and it is usually rolled up for transportation, illustrated in Fig. 1.

In the steel manufacturing industry, the efficiency of the operational solutions is very important and may means large savings. Although the problem is very complex, the use of HHA used in this application provides good solutions for the TDSCC problem. The comparison between the solutions obtained by HHA with the algorithm in Ge et al. (2010) shows that efficiency of the algorithm. In additional, we develop a actual cutting system for TDSCC problem, and had been used in actual production. We will do further study in the parameter analysis concerning the balance of the two goals. Therefore, the following studies should be devoted to the Pareto Optimality in Layout with regard to the question.