應用免疫演算法於印刷配置問題之研究

隨著市場環境快速的變遷，個人化的產品已在印刷市場中發展出另一個全新的契機，藉由少量多樣化的生產模式創造出更大的生產效益。對印刷產業而言，為了達到個人化生產之需求，需要考慮到諸多因素，例如印版之配置方式、印刷成本、印刷所需紙張數量、印版以及產品之尺寸等，在本研究中為了滿足不同消費者的訂購需求，將探討兩類印刷相關之問題，分別為封面印刷問題及標籤印刷問題，前者是屬於混合型整數規劃問題，後者則是屬於非線性整數規劃問題。由於這兩類印刷問題的求解範圍非常廣闊，產品配置之可能性並非單一，本研究在第一個問題中為了降低印刷所耗用的成本，將以免疫演算法搜尋其配置方式，並結合Lp_solve求解其印刷所耗用的紙張數量，以達到印刷所耗用成本最低之目標；而第二個問題是為了減少印刷所造成的浪費，本研究將以免疫演算來搜尋每款標籤之配置位置，並利用數值分析決定其每款標籤之配置數量以及每一塊印版的印刷數量，以達到印版充分利用並減少多餘的標籤印製之目標。在本研究中，我們利用免疫演算法測試過去文獻所提出之指標性問題，結果顯示均可求得其配置的位置以及印刷所需的印製數量，並且在最佳化的數值結果中可獲得多種組合。最後，我們將測試結果與過去所提出之相關文獻作比較，數值結果顯示，對於全部測試問題利用免疫演算法可獲得優於或相同於文獻的目前最佳解。

關鍵字

免疫演算法；封面印刷問題；標籤印刷問題；混合型整數規劃；非線性整數規劃

並列摘要

With the rapid changes of market, customized products have in the printing market and have earned more profits by using an efficient small size manufacturing. Many factors, such as the allocation of plates, printing costs, the number of printing copies and plates, as well as product size, are to be considered in printing industry so as to meet the individual needs of production In this study, we investigate two types of printing problems, including the cover printing problem and the label printing problem. The former is a mixed integer programming problem, while the latter is a nonlinear integer programming problem. The feasible regions of these two types of printing problems are pretty large. In this study, we propose an immune algorithm combined with Lp_solve to solve the cover printing problem with the objective of minimizing the printing cost. For the label printing problem, we propose an immune algorithm to solve for the number of labels and their allocations so as to minimize the redundance percentage of printing papers. Several benchmarks of test problems are solved by the proposed immune algorithm. Numerical results show that the proposed immune algorithm performs well for all test problems. Moreover, the proposed immune algorithm can obtain better solutions than those of well known best solutions in the literature.