Abstract
This article deals with the packing problem of irregular items allocated into a rectangular sheet to minimize the waste. Conventional solution is not visual during the packing process. It obtains a reasonable and relatively satisfactory solution between the nesting time and nesting solution. This article adopts a physical method that uses rubber band packing algorithm to simulate a rubber band wrapping those packing irregular items. The simulation shows a visual and fast packing process. The resultant rubber band force is applied in the packing items to translate, rotate, and slide them to make the area decrease and obtain a high packing density. An improved analogy QuickHull algorithm is presented to obtain extreme points of rubber band convex hull. An adaptive module could set a variable rubber band force and a variable time step to make a proper convergence and no intersection. A quick convex decomposition method is used to solve the problem of concave polygon. A plural vector expression approach is adopted to calculate the resultant vector of the rubber band force. Several cases are compared with the benchmark problems to prove rubber band packing algorithm performance.
Highlights
In several industrial applications, one is required to allocate a set of rectangular or irregular items to larger rectangular standardized stock units to minimize the waste, such as shipbuilding, textile, wood, plastic, sheet metal, and leather manufacturing.The irregular packing problem is more complex than the rectangular one which has been shown to be nondeterministic polynomial time (NP) complete.[1]
This article is organized as follows: A brief review of previous work in the field is presented in section ‘‘Related works’’; section ‘‘New approach for the nesting system’’ states the rubber band packing algorithm (RBPA) including its definition and flow diagram; in section ‘‘Some key problems of the NestRB system,’’ the key problems of the proposed system are described in detail; section ‘‘Experimental results’’ presents experimental results on benchmark problems from the literature that demonstrates the capabilities of the proposed system; and section ‘‘Conclusion’’ draws a conclusion
NestRB system is tested based on the nesting problem of sheet metal cutting
Summary
One is required to allocate a set of rectangular or irregular items to larger rectangular standardized stock units to minimize the waste, such as shipbuilding, textile, wood, plastic, sheet metal, and leather manufacturing. A detailed survey by Bennell and Oliveira[2] presents a tutorial of current methods used by researchers in cutting and packing of irregular shapes. These heuristics, metaheuristics, and hybrid algorithms have been impressively applied to this problem as powerful optimization tools. An irregular stock cutting system (NestRB) based on rubber band packing algorithm (RBPA) is College of Mechanical Engineering, Guangxi University, Nanning, China. Unlike many existing packing algorithms, packing course of the present system is visual for user every step, showing perceptual intuition This is especially important for industrial applications to show the result of the layout design. This article is organized as follows: A brief review of previous work in the field is presented in section ‘‘Related works’’; section ‘‘New approach for the nesting system’’ states the RBPA including its definition and flow diagram; in section ‘‘Some key problems of the NestRB system,’’ the key problems of the proposed system are described in detail; section ‘‘Experimental results’’ presents experimental results on benchmark problems from the literature that demonstrates the capabilities of the proposed system; and section ‘‘Conclusion’’ draws a conclusion
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