| Cutting and packing optimization is an important method to utilize resources efficiently in production.The circle cutting problem is a process to arrange circles of different radius in a rectangle or circle container under certain requirements or constraints. The optimization goal is to find the optimal layout of circles in order to achieve maximum utilization of raw materials or the least waste. The optimal cutting and packing problem belongs to the NP-complete problems with tiptop calculation complexity, and is difficult to be solved.The main research contents are as follows:(1) A random search algorithm is proposed for solving the problem of circle packing into a rectangle. In this method, all the circles are firstly put into a large enough space randomly. Then define the bow shift area to be the searching space. Then random search algorithm is used to find the local optimal solution in the shift area. Finally by moving and turning method the global optimization in the whole area is achieved.(2) The greedy algorithm is improved based on the adaptive-length bow shift area and the disturbance method.(3) A simulated annealing approach is presented to resolve the problem of cutting circles in a circular container. In this method, we define the risk ring and generate the initial packing configuration by the redium of cycles in the risk ring. By defining the central shift area, symmetrical places and turning shift area based on the initial position of each cycles and the energy equations with the risk ring, a strategy for producing neighborhood solutions is formulated.The feasibility and effectiveness of the three new method have been verified by large number of benchmark examples.(4) A production management system for optimal cutting of circular parts of electric motors has been developed for small and medium-sized motor enterprises. The practical application of this system to two companies showed that the system can improve the utilization ratio of silicon steel sheets effectively. |
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