一個排版問題主要由兩個過程來完成，一是零件排列次序（permutation）之決定，另一是排放零件至基板的排置（placement）方法；這兩個過程就主宰了一次排版結果的優劣。如果次序對了，排置方法也滿足需求，這個時候我們就可以找到正解或最佳解；但是往往無法得知正確的排列次序，因此需要利用搜尋法則來尋找最佳解。但是如果排置的方法不佳，即使排列的次序對了，排版出來的結果也不盡完善。本研究針對具間隙零件的排版需求，開發創新的排置演算法（placement algorithm），結合模擬退火法（simulated annealing）之特點而來進行排版系統之最佳決策，找出最好的排版效果。二維排版問題最佳化的目的乃將特定數量的相同或不同工件（piece）排列於基材（sheet）上，期使基材使用率最高或浪費最少為目標，如此基板的使用率最高以減少物料成本。本研究更進一步將系統以自動化的方式來呈現，發展一模擬排版巨
集指令，將繁瑣的設定工作交由自動系統完成，簡化操作人員技術上的要求。

A nesting problem can be solved using two processes; one is determining the permutation for sequences of pieces, and the other is applying a placement algorithm to place the pieces onto the sheet. These two vital processes dominate the solutions to the nesting problem. If the sequence of permutation is available, and the placement rule meets the packing demand, then the exact or optimum solution can be determined. However, whether the sequence of permutation is adequate is unknown. Even if the sequence is appropriate for permutation, without a suitable placement
algorithm, the final results are unacceptable. Therefore, this study develops a new placement algorithm for pieces with gaps in nesting operations. Under this placement algorithm, the simulated annealing approach is adopted in the optimal decisions of hollow nesting systems. The objective of the two-dimensional optimal nesting system is to determine the most effective use of the stock sheet under different piece considerations, maximizing the material use rate and subsequently reducing
material costs. Additionally, a macro module is included in the system to support automatic operation.