A Simulated Annealing Heuristic Approach to Irregular Shapes Packing Cutting Problem 徐德興、吳泰熙
E-mail: 8919784@mail.dyu.edu.tw
ABSTRACT
Packing and cutting problems arise in many industries such as clothing, furniture, steel, shipbuilding, and footwear. Hence any savings in the utilization rate of material used can result in a big reduction in the production cost. Lots of research in the literature is, thus, devoted in finding the optimal way of cutting or packing patterns in the given plates. Since it is almost impossible to find the real optimum for the packing/cutting problems, developing heuristic approach for the problems is therefore more appropriate than exact methods. In this study, we propose a simulated annealing (SA) approach for packing patterns with irregular shapes. Extensive efforts have been spent in finding the best clustering policy among parts. Several parameters controlling the mechanism of SA are also validated through some experiments to accelerate the convergence of the SA algorithm. An empirical data from a footwear company in Taiwan is adopted to test the effectiveness of the proposed algorithm.
Keywords : simulated annealing ; SA ; cutting ; packing ; irregular pattern Table of Contents
封面內頁 簽名頁 授權書 iii 中文摘要 iv 英文摘要 v 誌謝 vi 目錄 vii 圖目錄 x 表目錄 xii 第一章 緒論 1 1.1 研究背景與動機 1 1.2 研究目的 3 1.3 研究假設 3 1.4 研究架構 5 1.5 研究方法 6 第二章 文獻探討 9 2.1 物件分類與排列 9 2.2 規則方形物件 13 2.2.1規則方形物件排列問題 13 2.2.2 規則方形物件之確切解法 13 2.3 非規則形狀物件 14 2.3.1 不規則物件排列問題 14 2.3.2 圓形物件之排列問題 15 第三章 模擬退火演算法 16 3.1 模擬退火演算法 16 3.2 模擬退火演算法原理 18 3.2.1 Metropolis演算 法 18 3.2.2 退火程序（Annealing Procedure） 19 第四章 不規則物件排列/切割問題之演算法設計 21 4.1起始解及預處理 23 4.1.1 起始解 24 4.1.2 預處理作業 25 4.2 移步之種類及選取方式 29 4.2.1 隨機移動 30 4.2.2 物件旋轉 31 4.2.3 物件交換 35 4.3 目標函數 36 4.4退火程序（冷卻率、起始溫度） 37 4.5熱平衡狀態（馬可夫鍊長度） 38 4.6終止條件（停止準則） 38 第五 章 演算結果及演算法參數推估 39 5.1 各參數推估過程 39 5.1.1 馬可夫鍊長度（MCL） 39 5.1.2 起始溫度 50 5.1.3 退火程序
（冷卻率） 52 5.1.4 停止準則（終止條件） 54 5.1.5 實驗設計 54 5.2 演算範例說明及結果 57 5.2.1演算範例說明 58 5.2.2演 算範例結果 62 5.2.2.1 範例1至範例8 62 5.2.2.2 範例9 65 5.2.2.3 範例10 70 5.2.2.4 範例11 71 5.2.2.5 範例12 75 5.2.2.6 範例13 77 5.2.2.7 總範例結果彙整 83 第六章 結論及建議 85 6.1 結論 85 6.2 建議 86 參考文獻 88
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