Method of cutting metal ingot with changing direction of deformation

Abstract

The paper considers the priority problem of cutting an ingot with a changing direction of rolling which can be presented as a priority problem of packaging with incompatible categories and dynamically changing bin sizes. This problem is a NP-complete optimization problem which is often found in the production of metalwork. Priorities reflect the “importance” of manufacturing elements for production and incompatible categories show that elements of different thicknesses cannot be made from the same bin. In addition, we use guillotine restrictions to take into account the specifics of production. The problem of cutting the ingot is characterized by the fact that the bin sizes are not known in advance. Thus, the task is to find the optimal bin sizes, the sequence of actions and the placement of elements in these bins. We propose a sequential tree metaheuristic to solve this problem. It is a deterministic method. This method is based on sequential metaheuristic which was proposed by the authors earlier. The proposed method also has the ideas of dividing a set of elements into groups and subgroups by thickness and priorities, as well as their sequential packing. However, it differs from previous one in that it uses a tree to represent options for rolling operations. The best subtree from the point of view of any criterion, formed as a path from the root to one of the nodes, will be the solution. The ability to find several better solutions with the same value of the criterion is another advantage of the proposed method. Such a situation may arise, for example, for a square ingot. In this case, two solutions are possible with accuracy up to 90 degrees rotation of the workpieces. The priority heuristic is used as a heuristic to solve the packaging subproblem. The results of computational experiments are based on test cases which were compiled specially. Test instances differ in the number and characteristics of elements, categories, priorities. The results show that the metaheuristic proposed by the authors solves the problem effectively.