# Genetic Algorithms and Heuristic Rules for Solving the Nesting Problem in the Package Industry

• Roberto Selow
• Flávio NevesJr.
• Heitor S. Lopes
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 6)

The cutting/nesting problem in the packing industry can be stated as finding the maximum number of packages that can be arranged in a paper sheet of known size, in such a way as to minimize the loss of material. Figure 14.1 illustrates an example of six packages that will be drawn from a standard paper sheet and turned into a box. This problem is commonly found in many industrial areas that deal with cutting out shapes from raw stock, such as fabric, steel plate, paper, and so on.

An important factor in the search for the optimal solution for this problem is the number of parts that will be manipulated in the mounting settle. This is discussed later. There is a combinatorial explosion as the number of parts increases, leading to infeasible computational costs. For real-world problems, the number of parts is usually not larger than 20.

Genetic algorithms (GA) [10] have been used successfully in the last decades for several complex combinatorial problems and also for problems similar to the above-mentioned one [5, 12]. Therefore, the objective of this work is to propose a new method that uses genetic algorithms and heuristic rules to solve the problem.

## Keywords

Genetic Algorithm Search Space Search Region Heuristic Rule Paper Sheet
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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