外文翻譯-用蟻群算法在刀庫索引位置的優(yōu)化配置

1、<p>　　Optimal allocation of index positions on tool magazines using an ant colony algorithm</p><p>　　Abstract Generation of optimal index positions of cutting tools is an important task to reduce the

2、non-machining time of CNC machines and for achievement of optimal process plans. The present work proposes an application of an ant colony algorithm, as a global search technique, for a quick identification of optimal or

3、 near optimal index positions of cutting tools to be used on the tool magazines of CNC machines for executing a certain set of manufacturing operations. Minimisation of total inde</p><p>　　Keywords Indexing

4、 time . Automatic tool change .CNC machine . Optimization . Ant colony algorithm</p><p>　　1 Introduction</p><p>　　In today’s manufacturing environment, several industries are adapting flexible m

5、anufacturing systems (FMS) to meet the ever-changing competitive market requirements. CNC machines are widely used in FMS due to their high flexibility in processing a wide range of operations of various parts and compat

6、ibility to be operated under a computer controlled system. The overall efficiency of the system increases when CNC machines are utilized to their maximum extent. So to improve the utilization, there i</p><p>

7、;　　The cutting tools on CNC machines can be changed or positioned automatically when the cutting tools are called within the part program. To do this turrets are used in CNC lathe machines and automatic tool changers (AT

8、C) in CNC milling machines. The present model can be used either for the ATC magazines or turrets on CNC machines.</p><p>　　The indexing time is defined as the time elapsed in which a turret magazine/ATC mov

9、es between the two neighbouring tool stations or pockets. Bi-directional indexing of the tool magazine is always preferred over uni-directional indexing to reduce the non-machining time of the machine. In this the magazi

10、ne rotates in both directions to select automatically the nearer path between the current station and target station. The present work considers bi-directional movement of the magazine. In bidirect</p><p>　　

11、Dereli et al. [1] formulated the present problem as a “traveling salesman problem” (TSP), which is NP complete. They applied genetic algorithms (GA) to solve the problem. Dorigo et al. [2, 3] introduced the ant colony al

12、gorithm (ACA) for solving the NP-complete problems. ACA can find the superior solution to other methods such as genetic algorithms, simulated annealing and evolutionary programming for large-sized NP-complete problems wi

13、th minimum computational time. So, ACA has been extended to </p><p>　　2 Methodology</p><p>　　Determination of the optimal sequence of manufacturing operations is a prerequisite for the present p

14、roblem. This sequence is usually determined based on minimum total set-up cost. The authors [4] suggested an application of ACA to find the optimal sequence of operations. Once the sequence of operations is determined, t

15、he following approach can be used to get the optimal arrangement of the tools on the magazine.</p><p>　　Step 1 Initially a set of cutting tools required to execute the fixed (optimal) sequence of the manufac

16、turing operations is assigned. Each operation is assigned a single cutting tool. Each tool is characterized by a certain number. For example, let the sequence of manufacturing operations{M1-M4-M3-M2-M6-M8-M9-M5-M7-M10} b

17、e assigned to the set of cutting tools {T8-T1-T6-T4-T3-T7-T8-T2-T6-T5}. The set of tools can be decoded as {8-1-6-4-3-7-8-2-6-5}. Here the manufacturing operation M1 requires cu</p><p>　　Step 2 ACA is applie

18、d as the optimization tool to find the best tool sequence that corresponds to the minimum total indexing time. For every sequence that is generated by the algorithm the same sequence of index positions (numbers) is assig

19、ned. For example, let the sequence of tools {4-6-7-8-2-5-3-1} be generated and hence assigned to the indexing positions {1-2-3-4-5-6-7-8} in the sequential order, i.e. tool 4 is assigned to the 1st position, tool 6 to th

20、e 2nd position and so on.</p><p>　　Step 3 The differences between the index numbers of subsequent cutting tools are calculated and then totaled to determine the total number of unit rotations for each seque

21、nce of cutting tools. Absolute differences are to be taken while calculating the number of unit rotations required from current tool to target tool. This following section describes an example in detail.</p><p

22、>　　The first two operations M1 and M4 in the pre-assumed fixed sequence of operations require the cutting tools 8 and 1, respectively. The tool sequence generated by the algorithm is {4-6-7-8-2-5-3-1}. In this sequenc

23、e tools 8 and 1 are placed in the 4th and 8th indexing positions of the turret/ ATC. Hence the total number of unit rotations required to reach from current tool 8 to target tool 1 is | 4-8 |= 4. Similarly the total numb

24、er of unit rotations required for the entire sequence is | 4-8 |+|</p><p>　　Step 4 Minimization of total indexing time is taken as the objective function. The value of the objective function is calculated by

25、 multiplying the total number of unit rotations with the catalogue value of turret/ATC index time. If an index time of 4 s is assumed then the total index time required for the tool sequence becomes 120 s.</p><

26、;p>　　Step 5 As the number of iterations increases ACA converges to the optimal solution.</p><p>　　3 Allocation policy</p><p>　　The following are the three cases where the total number of avai

27、lable positions can be related with the total number of cutting tools employed.</p><p>　　Case 1 The number of index positions is equal to the number of cutting tools</p><p>　　Case 2 The number o

28、f index positions is greater than the number of cutting tools (a) without duplication of tools, (b) with duplication tools</p><p>　　Case 3 The number of index positions is smaller than the number of cutting

29、tools</p><p>　　If the problem falls into case 1, duplication of cutting tools in the tooling set is not required as the second set-up always increases the non-machining time of the machine.</p><p&

30、gt;　　Table 1 List of features and their abbreviations</p><p>　　In case 2, the effect of duplication of cutting tools should be tested carefully. Most of the times the duplication of tooling is too expensive.

31、 Case 3 leads to finding the cutting tools to be used in the second set-up. However, other subphases are possible in cases 2(b) and 3. The duplicated tools may be used in such a way that no unloaded index is left o

32、n ATC or some indexing positions are left unloaded.</p><p>　　Table 2 Operations assigned to the features</p><p>　　4 Ant colony algorithm</p><p>　　The ant colony algorithm (ACA) is a

33、 population-based optimization approach that has been applied successfully to solve different combinatorial problems like traveling salesman problems [2, 3], quadratic assignment problems [5, 6], and job shop scheduling

34、problems [7]. This algorithm is inspired by the foraging behaviour of real life ant colonies in which individual ants deposit a substance called pheromone on the path while moving from one point to another. The paths wit

35、h higher pheromone would </p><p>　　It is assumed that there is ‘k’ number of ants and each ant corresponds to a particular node. The number of ants is taken as equal to the number of nodes required to execut

36、e the fixed set of manufacturing operations. The task of eachant is to generate a feasible solution by adding a new cutting\ tool at a time to the current one, till all operations are completed. An ant ‘k’ situated in st

37、ate ‘r’ moves to state ‘s’ using the following state transition rule:</p><p>　　Table 3 Cutting tools assigned to optimal sequence of operations</p><p>　　Where τ (r, s) is called a pheromone leve

38、l. τ (r, s)’s are changed at run time and are intended to indicate how useful it is to make move ‘s’ when in state ‘r’. η(r, s) is a heuristic function, which evaluates the utility</p><p>　　of move ‘s’ when

39、at ‘r’. In the present work, it is the inverse of the number of unit rotations required to move from ‘r’ to ‘s’.</p><p>　　Parameter ‘β’ weighs the relative importance of the heuristic function. ‘q’ is a valu

40、e chosen randomly with uniform probability in [0,1], and ‘q0’ e0 q0 1T is a parameter. The smaller the ‘q0’, the higher the probability to make a random choice. In short ‘q0’ determines the relative importance of explo

41、itation versus exploration in Eq. 1.</p><p>　　Jk(r) represents the number of states still to be visited by the ‘k’ ant when at ‘r’.S is a random variable selected according to the distribution</p><

42、;p>　　given by Eq. 2, which gives the probability with which an ant in operation ‘r’ chooses ‘s’ to move to.</p><p>　　This state transition rule will favour transitions towards nodes connected by short edg

43、es with high amount of trail.</p><p>　　4.1 Local updating rule</p><p>　　While building a solution, ants change their trails by applying the following local updating rule:</p><p>　　W

44、here τ0 represents the initial pheromone value.</p><p>　　4.2 Global updating rule</p><p>　　Global trail updating provides a higher amount of trail to shorter solutions. In a sense this is simila

45、r to a reinforcement learning scheme in which better solutions get a higher reinforcement.</p><p>　　Once all ants have completed their solutions, edges (r, s) belonging to the shortest solution made by an an

46、t have their trail changed by applying the following global updating rule.</p><p>　　Where Lbest-iter is the best solution obtained in an iteration that has the minimum total indexing time. ‘α’ is the pheromo

47、ne decay parameter, which is a value in between 0 and 1. The parameter values [3] are set as β=2, q0=0.9, and..</p><p>　　4.3 Local search mechanism</p><p>　　Many ant systems are hybrid algorithm

48、s employing some kind of local optimization techniques such as 2-opt technique, tabu search, simulated annealing etc. Once each ant has constructed a solution, a local search mechanism is used to further improve the solu

49、tion to its local optimum and finally the pheromone levels are updated based on its solution. This integration significantly increases the effectiveness and efficiency of ant colony algorithms. In the present work, the 2

50、-opt technique is used </p><p>　　Fig. 3 Convergence of ACA</p><p>　　5 Case study</p><p>　　The example part taken for the present work is shown in Fig. 1. It contains 18 features. Th

51、e features and their abbreviations are listed in Table 1. The operations required to execute the features are exhibited in Table 2. The preassumed fixed sequence of operations and the assignment</p><p>　　of

52、a cutting tool to each operation are shown in Table 3. The maximum number of cutting tools and the indexing time of ATC are taken as 28 and 0.69 s, respectively. The objective lies in finding the positions of cutting<

53、/p><p>　　tools on the tool magazine for completing the sequence of operations: M1-M2-M3-M4-M5-M6-M7-M8-M9-M10-M11-M12-M13-M14-M15-M16-M17-M18-M19-M20-M21-M22-M23-M24-M25-M26-M27. The corresponding tools require

54、d to perform the above operations in the sequential order are T1-T1-T2-T3-T4-T2-T2-T2-T2-T5-T6-T5-T7-</p><p>　　T5-T5-T8-T9-T5-T10-T5-T11-T5-T12-T5-T13-T5-T14.The total number of different tools required here

55、 are 14and hence there are 14 (!) ways of sequencing the cutting tools.</p><p>　　The problem described here falls into case 2(a) where the total number of index positions is greater than the number of cuttin

56、g tools without duplication of tools. ACA is applied to get the set of positions of cutting tools that results in the minimum total indexing time to complete the above stated fixed sequence of operations.</p><

57、p>　　execution time has been reduced to 14 s. It is observed that ACA gets the optimal solution in quicker time than GA. Figure 3 exhibits the convergence of ACA. The best solution obtained in each iteration is plotted

58、 against the iteration number. The optimal solution is obtained in the 10th iteration. To ensure the optimal solution, the graph is extended for a maximum of 18 iterations.</p><p>　　7 Conclusion</p>&

59、lt;p>　　Since the present problem can be modeled as a traveling salesman problem, the present work deals with the development of an ACA-based system for the optimization of turret index positions of cutting tools to be

60、 used on the turret or ATC magazine of the CNC machine tools. Even a small saving in the total turret indexing time will cause a significant increase in machining time in high-volume production. This leads to increased u

61、tilization of CNC machine tools and hence the overall efficiency of th</p><p>　　References</p><p>　　1. Dereli T, Filiz H (2000) Allocating optimal index positions on</p><p>　　tool m

62、agazines using genetic algorithms. Robotics Auton Syst</p><p>　　33:155–167</p><p>　　2. Dorigo M, Maniezzo V, Colorni A (1996) The ant system:</p><p>　　optimisation by a colony of co

63、operating agents. IEEE Trans</p><p>　　Syst Man Cybern 26(1):29–41</p><p>　　3. Dorigo M, Gambardella LM (1997) Ant colony system: A cooperative</p><p>　　learning approach to the trav

64、eling salesman problem.</p><p>　　IEEE Trans Evol Comput 1(1)53–66</p><p>　　4. Krishna AG, Rao KM (2004) Optimisation of operations</p><p>　　sequence in CAPP using ant colony algorit

65、hm. Int J Adv Manuf</p><p>　　Technol (in press)</p><p>　　5. Gambardella LM, Taillard ED, Dorigo M (1999) Ant colonies</p><p>　　for the QAP. J Oper Res Soc 50:167–176</p><

66、p>　　6. Stutzle T, Dorigo M (1999) ACO algorithms for the quadratic</p><p>　　assignment problems. In: Corne D, Dorigo M, Glover F (eds)</p><p>　　New ideas in optimization. McGraw-Hill, New Yor

67、k</p><p>　　7. Colorni A, Dorigo M, Maniezzo V, Trubian M (1994) Ant</p><p>　　system for job-shop scheduling. Belg J Oper Res Stat Comput</p><p>　　Sci 34(1):39–53</p><p>

68、;　　用蟻群算法在刀庫索引位置的優(yōu)化配置</p><p>　　摘要:生成最優(yōu)的索引位置切割工具是一個重要的任務(wù)，以減少非加工時間數(shù)控機(jī)床和成就的最佳工藝計劃.目前的工作提出了螞蟻的應(yīng)用蟻群算法，作為一個全球性的搜索技術(shù)，為迅速確定的最優(yōu)或接近最優(yōu)的索引位置刀具上使用數(shù)控刀庫機(jī)器執(zhí)行一組特定的制造業(yè)務(wù)。最小化的總的索引時間被當(dāng)作目標(biāo)函數(shù).</p><p>　　關(guān)鍵字:索引的時間 自動換刀 數(shù)

69、控機(jī)床 優(yōu)化 蟻群算法</p><p><b>　　1 引言</b></p><p>　　在當(dāng)今的制造環(huán)境中，幾個行業(yè)適應(yīng)柔性制造系統(tǒng)（FMS），以滿足不斷變化的競爭市場需求。 CNC機(jī)廣泛應(yīng)用于FMS中，由于其高的靈活性在加工范圍廣泛的各種操作下一個計算機(jī)控制的操作部件和兼容性系統(tǒng)。該系統(tǒng)的整體效率增加數(shù)控機(jī)床是其最大的利用程度。因此，為了提高利用率，有一個需要分配

70、優(yōu)化刀具的位置的刀庫。</p><p>　　數(shù)控機(jī)床的切削工具，可以改變或自動定位切割工具被稱為時內(nèi)的部分程序。要做到這刀塔采用數(shù)控車床，CNC自動換刀裝置（ATC）在銑床。本模型可以使用，也可以用于ATC刀庫或刀塔數(shù)控機(jī)床。</p><p>　　索引的時間被定義為經(jīng)過這兩者之間的時間的刀塔刀庫/ ATC移動鄰近的工具站或口袋。雙向刀庫的索引總是優(yōu)于單方向的索引，以減少非加工時間的機(jī)器。在

71、此刀庫在兩個方向上旋轉(zhuǎn)自動選擇較近的路徑之間的當(dāng)前的測站和目標(biāo)站。本工作考慮雙向運(yùn)動的刀庫。在雙向索引，索引之間的差異當(dāng)前站和目標(biāo)站的數(shù)目來計算在這樣一種方式，它的值是小于或等于一半的彈匣容量。</p><p>　　Dereli等制定本問題作為“旅行商問題 ”（TSP），這是NP完全的。他們采用遺傳算法（GA）來解決問題，多里戈等。 [2，3]介紹了蟻群算法（ACA）用于解決NP完全問題。ACA可以找到其他方法優(yōu)

72、越的解決方案，如遺傳算法，模擬退火和進(jìn)化編程大型NP完全問題以最小的計算時間。因此，ACA一直延伸到解決目前的問題。</p><p><b>　　2 方法</b></p><p>　　現(xiàn)在的問題是制造的最優(yōu)序列測定操作的前提條件。這通常是確定的基礎(chǔ)上最低的總序列設(shè)置成本。文獻(xiàn)[4]提出了應(yīng)用ACA找到最佳的操作順序。一旦的操作順序來確定，下面的方法可以使用，以獲得最佳

73、的安排刀庫上的工具。</p><p>　　步驟1 首先需要執(zhí)行的一組刀具制造業(yè)務(wù)的固定序列（最佳）被分配。每個操作都被分配了一個單一的切割工具。每個工具的特征在于由一定數(shù)目。為例如，讓我們制造業(yè)務(wù)的序列M1-M4-M3-M2-M6-M8-M9-M5-M7-M10}分配一套刀具{T8-T1-T6-T4-T3-T7-T8-T2-T6-T5}。工具集可以被解碼為{8-1-6-4-3-7-8-2- 6-5}。這里經(jīng)營生產(chǎn)

74、的M1要求切削刀具8，M4要求1，依此類推。總共有八個不同的工具，從而8階乘方式工具序列可能在刀庫。</p><p>　　步驟2 ACA優(yōu)化工具找到最好的工具的序列，該序列對應(yīng)于最小的總索引的時間。對于每一個所產(chǎn)生的序列，該序列算法相同順序的索引位置（數(shù)字）被分配。例如，讓我們的工具4-6-7的順序 - 8-2-5-3-1}來生成，因此分配給索引的位置{1-2-3-4-5-6-7-8}的順序，即工具4被分配到第

75、一位置，工具6的第二位置等。</p><p>　　步驟3 索引號之間的差異隨后的切削工具的計算，然后合計為確定的總數(shù)為每個單元的旋轉(zhuǎn)序列的切割工具。絕對差異是計算所需的單位轉(zhuǎn)數(shù)時拍攝從當(dāng)前工具目標(biāo)的工具。在此之前，本節(jié)中詳細(xì)描述的一個例子。前兩個操作在預(yù)先假設(shè)的M1和M4固定的操作順序要求刀具分別是8和1。由算法生成的刀具序列是{4-6-7-8-2-5-3-1}。在這個序列中的工具8和1被放置在轉(zhuǎn)臺/第4和第8的

76、分度位置ATC。因此，總的數(shù)量所需的單位轉(zhuǎn)從目前的工具達(dá)到8目標(biāo)工具1|4-8| = 4。同樣，所需的單元轉(zhuǎn)總數(shù)整個序列是|4-8|+|8-2|+|2-1| +|1-7|+|7-3| +|3-4|+ |4-5| +|5-2| +|2-6|= 30。</p><p>　　步驟4 最小化總的索引時間被當(dāng)作目標(biāo)函數(shù)。目標(biāo)函數(shù)的值是計算的總數(shù)乘以單位轉(zhuǎn)的目錄價值的刀塔/ ATC指數(shù)的時間。如果時間為4 s，假定指數(shù)總指數(shù)

77、時間所需的刀具序列變?yōu)?20秒。</p><p>　　步驟5 隨著迭代次數(shù)的增加ACA收斂到最優(yōu)解。</p><p><b>　　3 分配政策</b></p><p>　　以下是3個的情況下的總數(shù)目可利用的位置的總數(shù)可以與切削工具。</p><p>　　第1種情況 索引位置的數(shù)目等于數(shù)量的切削工具</p>

78、<p>　　第2種情況 的索引位置的數(shù)目是大于一些刀具（a）不重復(fù)的工具，（b）與復(fù)制工具</p><p>　　第3種情況 索引位置的數(shù)目是小于數(shù)量的切削工具</p><p>　　如果問題落入第1種情況，重復(fù)切割工具，在工具中不是必需的作為第二設(shè)置總是增加的機(jī)器的非加工時間。</p><p><b>　　圖1例部分</b></p

79、><p>　　表1列出的功能和它們的縮寫</p><p>　　在第2種情況中，重復(fù)切削工具的效果應(yīng)該仔細(xì)測試。大部分的時候，重復(fù)工裝是太貴了。第3種情況尋找切削刀具可以使用在所述第二設(shè)定。然而，其他的子階段可能在例2（b）和3。所復(fù)制的工具可能是以這樣的方式，沒有卸載指數(shù)被留在ATC或使用卸載留下一些索引位置。</p><p><b>　　表2 操作的特點(diǎn)&l

80、t;/b></p><p><b>　　4 蟻群算法</b></p><p>　　蟻群算法（ACA）是一個以人群為基礎(chǔ)的優(yōu)化方法，已被成功地應(yīng)用于解決不同的組合問題，如旅行商問題[2，3]，二次分配問題[5，6]，作業(yè)車間調(diào)度問題[7]。該算法是現(xiàn)實(shí)生活中螞蟻的覓食行為的啟發(fā)在單個螞蟻存入一個被稱為信息素的物質(zhì)的路徑上移動的同時從一個點(diǎn)到另一個。信息素具有較高的

81、路徑，將更有可能被選擇的其他的螞蟻造成進(jìn)一步放大目前的信息素。由于這種性質(zhì)，經(jīng)過一段時間后，螞蟻會選擇最短的路徑。算法適用于現(xiàn)在的問題是在下面的部分中。</p><p>　　它是假定存在數(shù)'k'螞蟻數(shù)量和每個螞蟻對應(yīng)于一個特定的節(jié)點(diǎn)。螞蟻的數(shù)量是執(zhí)行所需的節(jié)點(diǎn)的數(shù)目等于組固定的生產(chǎn)業(yè)務(wù)。每個螞蟻的任務(wù)是產(chǎn)生一個可行的解決方案，通過添加新的切割工具，在當(dāng)前的時間，直到所有的操作都完成。位于螞蟻

82、9;K'狀態(tài)'R'移動狀態(tài)'s'使用下面的狀態(tài)轉(zhuǎn)移規(guī)則：</p><p>　　其中，τ（r，s的）被稱為信息素的水平。τ（r，s的）的在運(yùn)行時改變，當(dāng)“r”狀態(tài)，并用來表示如何有用它是移動的。</p><p>　　表3 分配切削工具，最佳的操作順序</p><p>　　η（r，s的）是一個啟發(fā)式的函數(shù)，該函數(shù)評估該實(shí)用程序移動

83、的'在“r”。在目前的工作中，它是逆從“r”到移動所需的數(shù)量的單位轉(zhuǎn)“S”。</p><p>　　參數(shù)'β'重量的相對重要性啟發(fā)式功能。 “q”是一個隨機(jī)選擇的值均勻的概率在[0,1]，和 ‘q0’(0<=q0<=1) 是一個參數(shù)。較小的‘q0’的概率就越高做一個隨機(jī)的選擇?？傊?，‘q0’決定相對重要性的開發(fā)與探索式Eq.1。</p><p>　　Jk(

84、r)表示仍然應(yīng)當(dāng)訪問的狀態(tài)的數(shù)目使用‘k’螞蟻‘r’。</p><p>　　S是一個隨機(jī)變量，根據(jù)分布的選擇式給出的。如圖2所示，其中給出的概率螞蟻在操作“r”選擇'S'移動到。</p><p>　　圖2 ATC刀具位置上的最佳順序</p><p>　　這種狀態(tài)轉(zhuǎn)移規(guī)則將有利于過渡向短邊連接的節(jié)點(diǎn)與大量的線索。</p><p&g

85、t;　　4.1 局部更新規(guī)則</p><p>　　雖然螞蟻構(gòu)建一個解決方案，改變他們的應(yīng)用創(chuàng)新下面的局部更新規(guī)則：</p><p>　　τ(r,s)=(1-ρ)τ(r,s)+ρτ0</p><p>　　其中τ0代表初始信息素值。</p><p>　　4.2 全局更新規(guī)則</p><p>　　全球跟蹤更新提供了更高的線索

86、較短的解決方案。從某種意義上說，這是加固學(xué)習(xí)更好的解決方案，其中獲得更高的加固。</p><p>　　一旦所有的螞蟻都完成了他們的解決方案，（R，S）邊緣屬于由一只螞蟻?zhàn)疃探鉀Q方案有其跟蹤更改應(yīng)用以下全局更新規(guī)則。</p><p>　　在ITER里面是最好的解決方案，在一個迭代中獲得的具有最小的總的索引時間?！痢切畔⑺厮p參數(shù)，該參數(shù)是一個值，該值在0和1之間。該參數(shù)的值被設(shè)置為β=2

87、，q0=0.9和β=α=0.1。</p><p>　　4.3 本地搜索機(jī)制</p><p>　　許多信息系統(tǒng)的混合算法，采用一些種本地優(yōu)化技術(shù)，如2-opt選擇技術(shù)，一旦每只螞蟻的禁忌搜索算法，模擬退火等構(gòu)建了一個解決方案，本地搜索機(jī)制使用，以進(jìn)一步改善其局部最優(yōu)的解決方案和最后的信息素的水平，是根據(jù)它的更新的解決方案。這種集成顯著增加的效力蟻群算法的效率。在目前的工作，2-opt選擇的技

88、術(shù)被用作本地搜索。</p><p><b>　　圖3 收斂ACA</b></p><p>　　5 目前的工作中采取的例子所示圖。它包含18個功能和它們的縮寫列于表1中。所需要的操作執(zhí)行的功能的展示于表2中。預(yù)先假定固定的操作順序和分配每個操作的切削工具被示于表3。最大數(shù)量的切削刀具和索引ATC的時間分別為為28和0.69秒。研究的目的在于找到的位置切割完成序列工具，

89、刀庫操作：M1-M2-M3，M4，M5，M6，M7，M8，M9，M10-M11-M12-</p><p>　　M13-M14-M15-M16-M17-M18-M19- M20-M21-M22-M23-M24-M25-M26-M27。相應(yīng)的工具在順序執(zhí)行上述操作所需T1-T1-T2-T3-T4-T2-T2-T2-T2-T5-T6-T5-</p><p>　　T7-T5-T5-T8-T9-T5

90、-T10-T5-T11- T5-T12-T5-T13-T5-T14。不同的工具，這里需要的總?cè)藬?shù)是14，因此有14套的測序切割方式工具。</p><p>　　此處描述的問題落入第2種情況（a）在該索引位置的總數(shù)的數(shù)量大于切削刀具的不重復(fù)的工具。 ACA應(yīng)用得到的切削工具的集合的位置的結(jié)果在完成上述最低總的索引時間表示固定的操作順序。</p><p><b>　　6結(jié)果與比較<

91、;/b></p><p>　　ATC刀具位置的最佳順序應(yīng)用所提出的算法是T1-T2-T3-T4-T14-T6-T7-T10-T5-T11-T12-T13-T8-T9。這是描繪在圖2。</p><p>　　最優(yōu)序列50個單位轉(zhuǎn)ATC或者換句話說，一個總的索引時間為34.5S。越慢，ATC更高的增益。 ACA和遺傳算法（GA）與參照所取的參數(shù)[1]被編碼在Turbo C++和執(zhí)行，在奔騰

92、IV2.8 GHz處理器中。 GA的所花費(fèi)的時間解決方案是26秒。在另一方面，當(dāng)ACA是使用執(zhí)行時間已減少到14秒。據(jù)觀察所得ACA在更快的時間比GA的最佳解決方案。圖3顯示ACA的融合。最好在每次迭代中獲得的溶液繪制在迭代次數(shù)。最優(yōu)解中得到的10日迭代。為了確保最佳的解決方案，該圖是延長的和最多18次迭代。</p><p><b>　　6 結(jié)束語</b></p><p&