An Area-Decomposition Method for a Nesting System

Nesting is primarily composed of two processes: One is the determination of permutation; another is the placement for the pieces unto the sheet. These two processes determine the quality for nesting. If the permutation is right and placement also can satisfy the requirements, then we can locate the proper solution  or the optimum one; but most of the time, there is no way to know the correct permutation beforehand, therefore the search algorithm is needed to locate the optimum solution instead. Nonetheless, if the placement is not good enough, even the permutation is correct; still, the nesting result would not be perfect. Hence this research is to target the nesting requirement for pieces with gaps in between and develop the placement algorithm of innovation which integrates the simulated annealing characteristics so as to proceed to the optimum solution for nesting system with the best possible nesting results. The purpose of optimizing two-dimensional problem is to place the same or different number of pieces onto the sheet, enabling the usage ratio for sheet reaching the highest possible or cutting down the waste in the end, thus, with the high usage ratio of the sheet would result with cutting down the cost for materials.