20深圳杯全國大學(xué)生數(shù)學(xué)建模夏令營承諾書我們仔細(xì)閱讀了中國大學(xué)生數(shù)學(xué)建模競賽的競賽規(guī)則.我們完全明白，在競賽開始后參賽隊(duì)員不能以任何方式（包括、電子郵件、網(wǎng)上咨詢等）與隊(duì)外的任何人（包括指導(dǎo)教師）研究、討論與賽題有關(guān)的問題。我們知道，抄襲別人的成果是違反競賽規(guī)則的,如果引用別人的成果或其他公開的資料（包括網(wǎng)上查到的資料），必須按照規(guī)定的參考文獻(xiàn)的表述方式在正文引用處和參考文獻(xiàn)中明確列出。我們鄭重承諾，嚴(yán)格遵守競賽規(guī)則，以保證競賽的公正、公平性。如有違反競賽規(guī)則的行為，我們將受到嚴(yán)肅處理。我們參賽選擇的題號(hào)是（從A/B/C/D中選擇一項(xiàng)填寫）：D 我們的參賽報(bào)名號(hào)為（如果賽區(qū)設(shè)置報(bào)名號(hào)的話）：所屬學(xué)校（請?zhí)顚懲暾娜簠①愱?duì)員(打印并簽名)：1.2.3.指導(dǎo)教師或指導(dǎo)教師組負(fù)責(zé)人(打印并簽名)：日期：20年月日賽區(qū)評閱編號(hào)（由賽區(qū)組委會(huì)評閱前進(jìn)行編號(hào)）：20深圳杯全國大學(xué)生數(shù)學(xué)建模夏令營編號(hào)專用頁賽區(qū)評閱編號(hào)（由賽區(qū)組委會(huì)評閱前進(jìn)行編號(hào)）：賽區(qū)評閱記錄（可供賽區(qū)評閱時(shí)使用）：評閱人評分備注全國統(tǒng)一編號(hào)（由賽區(qū)組委會(huì)送交全國前編號(hào)）：全國評閱編號(hào)（由全國組委會(huì)評閱前進(jìn)行編號(hào)）：打孔機(jī)生產(chǎn)效能的提高【摘要】本文綜合考慮行徑路程與刀具轉(zhuǎn)換次數(shù)，對打孔機(jī)生產(chǎn)效能進(jìn)行優(yōu)化。把每一個(gè)孔都打完的最短路徑。這個(gè)問題可以轉(zhuǎn)化為經(jīng)典的旅行商問題（TSP）來解決，解決旅行商問題的算法很多，例如：可用改進(jìn)Hamilton圈的算法來實(shí)現(xiàn)，但求得的解不一定是最優(yōu)解；對于這個(gè)問題本文運(yùn)用模擬退火算法。第一問中，首先針對刀具轉(zhuǎn)換次數(shù)，把刀具的轉(zhuǎn)換次數(shù)和次序進(jìn)行合理安排：刀具轉(zhuǎn)換次序abc1def1gf2hc2對應(yīng)孔型A,CBC,ED,GD,IE,JF,GGH,II,J然后根據(jù)刀具對應(yīng)下來的孔，用模擬退火的算法求解，得到遍歷對應(yīng)下的所有孔的最短路徑。相當(dāng)于將所有孔分成十次來打，合理選取上一種刀具對應(yīng)下的打孔路徑的終點(diǎn)，與下一種對應(yīng)下的路徑起始點(diǎn)，銜接好，找到最短路程。綜合考慮刀具轉(zhuǎn)換次數(shù)少和作業(yè)行程短，建立第一個(gè)模型。路徑圖見模型一，所得的打孔順序表見附表二，換用了9次刀具，相鄰刀具之間轉(zhuǎn)換了15次，換刀成本為31.5元，行進(jìn)時(shí)間為108.19s，行進(jìn)成本為1199.98元。第二問中增加了一個(gè)鉆頭，可以將第一問得到的各種刀具對應(yīng)下的鉆孔最短路徑，進(jìn)行合理分配，從而讓兩個(gè)鉆頭按照不同路徑去鉆孔，兩個(gè)鉆頭鉆完各自分配到孔的總時(shí)間相差要不大，從而減少作業(yè)時(shí)間，提高生產(chǎn)效能。分配方案為：鉆頭一刀具轉(zhuǎn)換順序ac1bc2孔型A、CC、EBIJ鉆頭二刀具轉(zhuǎn)換順序degf1f2h孔型D、GD、IF、GE、JGH、F按照第一問中所得各個(gè)刀具打孔最短路徑，選取各個(gè)路徑的起點(diǎn)和終點(diǎn)，得到兩個(gè)鉆頭的行進(jìn)路徑（見模型二各圖）和打孔順序表（見附表一）。再考慮兩鉆頭在打孔的每個(gè)時(shí)刻間距不小于3cm的條件，比較兩鉆頭打孔順序表，找到不符合條件的孔(見表6）。之后鉆頭在這些孔的前后合理延時(shí)（見表7）。鉆頭一換用了4次刀具，相鄰刀具之間轉(zhuǎn)換了6次，轉(zhuǎn)刀成本為12.6元，行進(jìn)時(shí)間為68.72s,作業(yè)成本為730.19元；鉆頭二換運(yùn)用了5次刀具，相鄰刀具之間轉(zhuǎn)換了6次，換刀成本為12.6元。行進(jìn)時(shí)間45.09s，作業(yè)成本479.04元。雙鉆頭總的換刀成本為25.2元，作業(yè)成本為1209.23元，行進(jìn)時(shí)間為兩個(gè)鉆頭更大那個(gè)68.72s。比較可知，雖然雙鉆頭在作業(yè)成本上比單鉆頭多9.25元，但是行進(jìn)時(shí)間少了39.46s。單鉆頭的總作業(yè)時(shí)間為378.19s,雙鉆頭的作業(yè)時(shí)間為153.09s,即加工一塊板的效率提高了一倍多，所以雙鉆頭的效能明顯高于單鉆頭。第三問兩鉆頭的合作間距，由于建立模型為顧及作業(yè)路程最短，為對兩鉆頭各自的作業(yè)路徑進(jìn)行調(diào)整，所以對作業(yè)線路無影響，僅使各個(gè)鉆頭的作業(yè)時(shí)間都增加了1.9s。關(guān)鍵字：旅行商問題模擬退火算法密集區(qū)域換刀次數(shù)最少路程最少延時(shí)一問題重申過孔是印刷線路板（也稱為印刷電路板）的重要組成部分之一，過孔的加工費(fèi)用通常占制板費(fèi)用的30%到40%，打孔機(jī)主要用于在制造印刷線路板流程中的打孔作業(yè)。打孔機(jī)的生產(chǎn)效能主要取決于以下幾方面：（1）單個(gè)過孔的鉆孔作業(yè)時(shí)間；（2）打孔機(jī)在加工作業(yè)時(shí)，鉆頭的行進(jìn)時(shí)間；（3）針對不同孔型加工作業(yè)時(shí)，刀具的轉(zhuǎn)換時(shí)間。目前，實(shí)際采用的打孔機(jī)普遍是單鉆頭作業(yè)，即一個(gè)鉆頭進(jìn)行打孔。本問題旨在提高某類打孔機(jī)的生產(chǎn)效能。需要解決的問題有：1、由提供的某塊印刷線路板過孔中心坐標(biāo)的數(shù)據(jù)，單位是密爾（mil）（也稱為毫英寸，1inch=1000mil），給出單鉆頭作業(yè)的最優(yōu)作業(yè)線路（包括刀具轉(zhuǎn)換方案）、行進(jìn)時(shí)間和作業(yè)成本。2、為提高打孔機(jī)效能，現(xiàn)在設(shè)計(jì)一種雙鉆頭的打孔機(jī)（每個(gè)鉆頭的形狀與單鉆頭相同），兩鉆頭可以同時(shí)作業(yè)，且作業(yè)是獨(dú)立的，即可以兩個(gè)鉆頭同時(shí)進(jìn)行打孔，也可以一個(gè)鉆頭打孔，另一個(gè)鉆頭行進(jìn)或轉(zhuǎn)換刀具。為避免鉆頭間的觸碰和干擾，在過孔加工的任何時(shí)刻必須保持兩鉆頭間距不小于3cm（稱為兩鉆頭合作間距）。為使問題簡化，可以將鉆頭看作質(zhì)點(diǎn)。針對所給數(shù)據(jù)，給出雙鉆頭作業(yè)時(shí)的最優(yōu)作業(yè)線路、行進(jìn)時(shí)間和作業(yè)成本，并與傳統(tǒng)單鉆頭打孔機(jī)進(jìn)行比較，其生產(chǎn)效能提高多少。3、研究打孔機(jī)的兩鉆頭合作間距對作業(yè)路線和生產(chǎn)效能產(chǎn)生的影響。二符號(hào)說明遍訪每個(gè)孔恰好一次的所有回路的解空間回路中直接相連的兩點(diǎn)間路徑直接相連的兩點(diǎn)間的距離模擬退火算法的溫度值模擬退火算法中接受程度遍歷每個(gè)孔的代價(jià)函數(shù)鉆頭行進(jìn)速度在一塊線路板中的作業(yè)路徑的總路程打一塊線路板的作業(yè)時(shí)間鉆頭的行進(jìn)時(shí)間每次轉(zhuǎn)刀與同時(shí)行進(jìn)的重合時(shí)間鉆頭調(diào)整路徑來回行走的路程行進(jìn)成本刀具轉(zhuǎn)換的時(shí)間成本一塊線路板的鉆孔作業(yè)成本三模型假設(shè)3.1基本假設(shè)1、鉆頭的行進(jìn)速度:180mm/s2、行進(jìn)成本：0.06元/mm3、刀具轉(zhuǎn)換的時(shí)間成本：7元/min4、相鄰刀具轉(zhuǎn)換刀具時(shí)間：18s3.2其他假設(shè)5、所用鉆頭共有八種刀具，刀具依次排列呈圓環(huán)形，順序固定，不能調(diào)換，可以順時(shí)針，也可以逆時(shí)針旋轉(zhuǎn)換刀6、刀具可以在行進(jìn)過程同時(shí)進(jìn)行刀具轉(zhuǎn)換，費(fèi)用不減7、對于同一孔型鉆孔作業(yè)時(shí)間相同，即鉆孔數(shù)一定，時(shí)間固定8、兩個(gè)鉆頭可以簡化為質(zhì)點(diǎn)9、兩個(gè)鉆頭起始刀具可以自由設(shè)定10、兩個(gè)鉆頭鉆孔時(shí)，只考慮鉆孔時(shí)鉆頭間的距離，在行進(jìn)過程中鉆頭相遇會(huì)平行著擦肩而過。11、兩個(gè)鉆頭在打孔的過程中可以停止延時(shí)，且延時(shí)值可以自由設(shè)定。四問題分析由于同一孔型的作業(yè)時(shí)間都是相同的，所以打孔時(shí)間是一定的。優(yōu)化問題也就只針對作業(yè)路徑和刀具轉(zhuǎn)換方案的選擇。對于問題1，需要選擇最短打孔路徑，這類似于大數(shù)量級的旅行商問題。旅行商問題是指旅行商必須輪流到N城市去旅游，每個(gè)城市僅去一次，最后返回原出發(fā)城市，任務(wù)是為了旅行商找到滿足上述條件的最短路徑。但是有的孔型需要多種刀具處理。結(jié)合刀具轉(zhuǎn)換次數(shù)少、路程短，首先合理安排刀具轉(zhuǎn)換（詳見摘要或表2），每次轉(zhuǎn)換，使當(dāng)前刀具鉆完對應(yīng)的孔，分十次處理孔，每次所要處理的孔只需遍歷一次，正好解決有的孔型需要多種刀具處理的問題，使最短打孔路徑與旅行商問題（TSP）吻合，簡化了問題。分十次運(yùn)用模擬退火算法，得到十個(gè)最短遍歷路徑之后，這些路徑是閉合回路。之后再合理安排起始點(diǎn)與終點(diǎn)，將十條分開處理得到的路徑連接起來，得到最終最短路徑。根據(jù)最短路徑算得作業(yè)路程與時(shí)間，問題1獲得了解決。針對問題2,可以借鑒問題1中的各個(gè)刀具對應(yīng)下的最短路徑，給兩個(gè)鉆頭分配不同的打孔任務(wù)，即讓他們轉(zhuǎn)換到不同的刀具，按照不同的打孔路徑打孔。分配的原則是：1）兩個(gè)鉆頭對同一塊線路板的作業(yè)時(shí)間相差不大；2）對需要運(yùn)用不同刀具處理，且刀具運(yùn)用有先后順序的孔，兩個(gè)鉆頭要在時(shí)間上配合好，保證不同刀具的先后處理。針對需要運(yùn)用不同刀具先后處理的孔，且運(yùn)用的不同刀具分配在不同的鉆頭上時(shí)，要前一個(gè)鉆頭用前一個(gè)刀具處理完，才讓另一個(gè)鉆頭用下一個(gè)刀具處理。這就要合理地選擇各個(gè)鉆頭刀具使用先后順序，即合理的安排刀具轉(zhuǎn)換。各個(gè)鉆頭分配到打孔任務(wù)后，合理選擇各個(gè)打孔路徑的起始點(diǎn)和終點(diǎn)，讓分配給兩個(gè)鉆頭的打孔路徑各自相互之間首尾相接，連成打孔路徑。之后找到不符合鉆頭打孔間距小于3cm的孔，可以考慮采取調(diào)換打孔順序等策略，使得兩鉆頭在每個(gè)打孔時(shí)刻間距都不小于3cm。從而得到符合要求的兩個(gè)鉆頭各自的打孔路徑和打孔順序表，再計(jì)算題目要求答案。針對問題3，參照問題二的求解過程，總結(jié)合作間距這個(gè)條件，對作業(yè)路線、作業(yè)時(shí)間和作業(yè)成本的影響，分析得到結(jié)果。五建模前的準(zhǔn)備所給的數(shù)據(jù)時(shí)text格式的，轉(zhuǎn)存為excel格式以后，對孔的坐標(biāo)進(jìn)行了單位換算：1/100mile=0.000254mm六模型的建立和求解6.1模型一的建立6.1.1最短路線和模擬退火算法這個(gè)打孔問題，可看成旅行商問題(TravellingSalesmanProblem，簡記為TSP)。TSP問題是要找遍訪每個(gè)城市恰好一次的一條回路，且其路徑總長度為最短。孔與城市相對應(yīng)，打孔則是遍歷所有的孔，路徑要求最短。設(shè)有n個(gè)孔，用數(shù)字1,…,n代表。孔i和孔j之間的距離為：6.1.2TSP的模擬退火算法的實(shí)現(xiàn)TSP是典型的組合優(yōu)化問題，模擬退火算法是一種隨機(jī)性解決組合優(yōu)化方法。將TSP與模擬退火算法相結(jié)合，以實(shí)現(xiàn)對其求解。6.1.3打孔問題類比TSP問題的解空間和初始解解空間S是遍訪每個(gè)孔恰好一次的所有回路，是{1，……，n}的所有循環(huán)排列的集合，S中的成員記為并記。初始解可選為(1，……，n)1）最短路徑目標(biāo)函數(shù)此時(shí)的目標(biāo)函數(shù)即為訪問所有孔的路徑總長度，或稱為行程代價(jià)函數(shù)：求此代價(jià)函數(shù)的最小值。現(xiàn)在打孔問題的求解就是通過模擬退火算法求出目標(biāo)函數(shù)的最小值，相應(yīng)地即為問題的最優(yōu)解。2）新解的產(chǎn)生隨機(jī)產(chǎn)生1和n之間的兩相異數(shù)k和m，若k<m，則將變?yōu)椋喝绻莐>m，則將變?yōu)椋荷鲜鲎儞Q方法可簡單說成是“逆轉(zhuǎn)中間或者逆轉(zhuǎn)兩端”。3）代價(jià)函數(shù)差設(shè)將變換為,則代價(jià)函數(shù)差為：6.1.4Metropolis接受準(zhǔn)則根據(jù)目標(biāo)函數(shù)的差值和概率接受作為新的當(dāng)前接受準(zhǔn)則：6.1.5模擬退火算法的步驟1)選作為初始狀態(tài),令,同時(shí)設(shè)初始溫度T,令。2)令,以和調(diào)用Metropolis抽樣算法,返回狀態(tài)作為本算法的當(dāng)前解,。3)按照一定方式降溫,即,其中。4)檢查終止條件,如果滿足則轉(zhuǎn)步驟5),否則轉(zhuǎn)步驟2)。5)當(dāng)前解為最優(yōu)解,輸出結(jié)果,停止。6.1.7合理表110種孔型所需加工刀具及加工次序孔型ABCDEFGHIJ所需刀具aba,cd,e*c,fg,h*d,g,fhe,cf,c依據(jù)表1，充分考慮到有的孔型需要多種刀具處理，合理安排好刀具轉(zhuǎn)換順序。轉(zhuǎn)換到一個(gè)刀具，同時(shí)安排好它需要鉆的全部孔，使得每次轉(zhuǎn)到的刀具需要處理的孔只需遍歷一次。這正好與旅行商問題吻合，從而可以使用模擬退火算法求取最短路徑。如表2。表2順序轉(zhuǎn)換到的刀具對應(yīng)的孔的類型刀具轉(zhuǎn)換次序abdegh對應(yīng)孔型A,CBC,ED,GD,IE,JF,GGH,II,J其中、、、分別表示第一次和第二次選用,刀具。6.1.8根據(jù)算法，運(yùn)用matlab編程運(yùn)用模擬退火算法，處理得到各次轉(zhuǎn)換所得刀具的鉆孔最短路徑。但是在處理的過程中發(fā)現(xiàn)：根據(jù)模擬退火算法編得程序，計(jì)算機(jī)可以很好的處理較少的孔的集合，但是當(dāng)孔較多時(shí)，計(jì)算機(jī)處理得到的方案就不是非常優(yōu)化。為此，在要處理的孔很多時(shí)，進(jìn)行分區(qū)域處理，按照坐標(biāo)合理劃分區(qū)域，使得各個(gè)區(qū)域中的孔數(shù)不會(huì)太多，從而使得各個(gè)孔的集合獲得較優(yōu)化的處理。Ⅰ、轉(zhuǎn)換刀具對應(yīng)所要處理的孔圖a→ACb→Bc1→C，Ed→D，Ge→D，Ig→F,Gh→H，If1→E,Jf2→Gc2→I，J需要鉆的所有孔Ⅱ、對應(yīng)的路徑1）a需處理孔分區(qū)域路徑a→AC(1)a→AC(2)a→AC(3)a→AC(4)a刀具處理孔a刀具分區(qū)處理孔路徑組合圖2)b刀具分區(qū)域處理孔的路徑b→B（1）b→B(2)b→B(3)b→B(4)b→B(5)b→B(6)b刀具處理孔圖b刀具處理孔徑圖3)第一次使用c刀具分區(qū)域處理孔的路徑c→C,E（1）c→C,E（3）c→C,E（2）c→C,E（4）c→C,E打孔點(diǎn)圖c→C,E打孔路徑圖4)d刀具分區(qū)域處理孔的路徑d→DG(1)d→D,G(2)d→DG(3)d刀具打孔點(diǎn)圖d刀具打孔路徑圖5)e刀具分區(qū)域處理孔的路徑e→D,I(1)e→D,I(3)e→D,I(2)e→D,I全部點(diǎn)e刀具打孔路徑圖6) f刀具處理孔的路徑（E，J）7）g刀具鉆孔路徑（孔型為F,G）8)第二次使用f刀具處理孔的路徑（孔型為G）圖f2→G9）h刀具處理孔路徑圖圖h→HF10）第二次使用c刀具處理孔路徑圖圖c2→IJ6.1.9選取各個(gè)圖的起點(diǎn)和終點(diǎn)，確定最短路徑在利用模擬退火算法進(jìn)行優(yōu)化之前，必須首先選取一個(gè)優(yōu)先的起始點(diǎn)，優(yōu)先起始點(diǎn)可以隨機(jī)選取也可根據(jù)經(jīng)驗(yàn)選取。在運(yùn)用程序得到以上各環(huán)時(shí)，各環(huán)起始點(diǎn)是隨機(jī)生成的。為尋找最短路徑，需要將各個(gè)環(huán)拆成非閉合環(huán)，確定各個(gè)非閉合環(huán)的起始點(diǎn)和終點(diǎn)，按照次序，將上一個(gè)環(huán)的終點(diǎn)與下一個(gè)環(huán)的起點(diǎn)連接起來，最前面環(huán)的起點(diǎn)與最后面環(huán)的終點(diǎn)相連，得到最終的最短路徑環(huán)。為使作業(yè)行程最短，選取各個(gè)圖的起點(diǎn)和終點(diǎn)的選取對象，可以從兩方面考慮：1）各個(gè)閉環(huán)中，很長的兩點(diǎn)間連線的端點(diǎn)，為該圖的起點(diǎn)和終點(diǎn)的選取對象；2）與上一個(gè)圖終點(diǎn)較近的點(diǎn)，為該圖起點(diǎn)的考慮對象，與該點(diǎn)相連的兩個(gè)點(diǎn)為該圖的終點(diǎn)選取對象。綜合考慮這兩方面，找到使作業(yè)路徑最短的方案。各個(gè)刀具分區(qū)域處理的各個(gè)圖的起點(diǎn)和終點(diǎn)如下表：表3各個(gè)刀具分區(qū)域處理的各個(gè)圖的起點(diǎn)和終點(diǎn)路徑圖X坐標(biāo)Y坐標(biāo)路徑圖X坐標(biāo)Y坐標(biāo)a→AC(2)起點(diǎn)-56.2864132.6358c1→CE(3)起點(diǎn)46.0248167.5892終點(diǎn)-59.0804129.8418終點(diǎn)71.5264180.2892a→AC(1)起點(diǎn)-56.2864218.948d→DG(3)起點(diǎn)55.3974172.0342終點(diǎn)0.8636185.42終點(diǎn)29.1592180.7464a→AC(3)起點(diǎn)-16.7132120.2944d→DG(1)起點(diǎn)-56.0134141.2748終點(diǎn)-8.4328120.2944終點(diǎn)-46.22881.54645a→AC(4)起點(diǎn)28.194117.3d→DG(2)起點(diǎn)-16.25658.00039終點(diǎn)26.314488.9508終點(diǎn)42.926105.918b→B(6)起點(diǎn)39.217681.7372e→DI(2)起點(diǎn)42.926105.918終點(diǎn)-6.8834177.546終點(diǎn)-16.25658.00039b→B(5)起點(diǎn)3.327499.7712e→DI(1)起點(diǎn)-46.22881.54645終點(diǎn)-3.556103.3018終點(diǎn)-56.0134141.2748b→B(4)起點(diǎn)-7.87476.708e→DI(3)起點(diǎn)29.1592180.7464終點(diǎn)-18.846845.593終點(diǎn)57.3024180.9242b→B(3)起點(diǎn)-29.260827.2288f1→EJ起點(diǎn)37.7952200.2028終點(diǎn)-32.461226.416終點(diǎn)-1.3716119.1768b→B(1)起點(diǎn)-42.824445.4152g→FG起點(diǎn)1.26492179.5526終點(diǎn)-44.043646.4312終點(diǎn)-76.530221.4122b→B(2)起點(diǎn)-48.869673.3552f2→G起點(diǎn)-76.530221.4122終點(diǎn)-55.219698.9076終點(diǎn)54.102226.7204c1→CE(1)起點(diǎn)-53.4924221.742h→HF起點(diǎn)23.495179.5526終點(diǎn)-62.99293.7768終點(diǎn)80.6175743.32529c1→CE(2)起點(diǎn)-19.456469.6468c2→IJ起點(diǎn)83.667629.86532終點(diǎn)-9.855244.27576終點(diǎn)113.7412145.3896c1→CE(4)起點(diǎn)47.8536107.5436終點(diǎn)38.862141.6304遍歷各個(gè)孔時(shí)，各個(gè)圖的遍歷順序?yàn)椋篴→AC(2)、a→AC(1)、a→AC(3)、a→AC(4)、b→B(6)、b→B(5)、b→B(4)、b→B(3)、b→B(1)、b→B(2)、c1→CE(1)、c1→CE(2)、c1→CE(4)、c1→CE(3)、d→DG(3)、d→DG(2)、e→DI(2)e→DI(1)、e→DI(3)、f1→EJ、g→FG、f2→G、h→HF、c2→IJ其中a→AC(2)的起始點(diǎn)是總路徑的起點(diǎn)，c2→IJ的終點(diǎn)是最后一個(gè)鉆孔。所得的最短路徑圖如圖所示：所得最短路徑孔順序表詳見附表一。6.1.10作業(yè)時(shí)間、行進(jìn)時(shí)間和作業(yè)成本作業(yè)時(shí)間、行進(jìn)時(shí)間求取,有轉(zhuǎn)換了9次刀具，則有9個(gè)刀具轉(zhuǎn)換時(shí)間與鉆頭行進(jìn)時(shí)間的重合值，在刀具轉(zhuǎn)換過程中有15個(gè)18s，則行進(jìn)時(shí)間作業(yè)時(shí)間作業(yè)成本由：6.2模型二的建立6.2.1對兩個(gè)鉆頭進(jìn)行合理分配任務(wù)鉆頭一刀具轉(zhuǎn)換順序ac1bc2孔型A、CC、EBIJ鉆頭二刀具轉(zhuǎn)換順序degf1f2h孔型D、GD、IF、GE、JGH、F6.2.2選擇各個(gè)刀具打孔路徑的起點(diǎn)和終點(diǎn)合理選擇各個(gè)刀具打孔路徑的起點(diǎn)和終點(diǎn)，使各個(gè)鉆頭的打孔路徑最短。各個(gè)路徑圖的起始點(diǎn)和終點(diǎn)為：表4鉆頭一對應(yīng)各個(gè)路徑起始點(diǎn)與終點(diǎn)路徑圖X坐標(biāo)Y坐標(biāo)路徑圖X坐標(biāo)Y坐標(biāo)a→AC起點(diǎn)28.30754221.742b→B起點(diǎn)23.4442207.3402終點(diǎn)110.9218230.6066終點(diǎn)-0.1524206.2988c1→CE起點(diǎn)110.9218230.6066c2→IJ起點(diǎn)25.51354129.8418終點(diǎn)34.798228.4476終點(diǎn)113.7158230.6066表5鉆頭二對應(yīng)各個(gè)路徑圖起始點(diǎn)與終點(diǎn)路徑圖X坐標(biāo)Y坐標(biāo)路徑圖X坐標(biāo)Y坐標(biāo)d→DG起點(diǎn)29.1592180.7464f1→EJ起點(diǎn)-56.399925.4終點(diǎn)-56.0134141.2748終點(diǎn)-68.1736-16.5608e→DI起點(diǎn)-56.0134141.2748f2→G起點(diǎn)-76.530221.4122終點(diǎn)29.1592180.7464終點(diǎn)54.102226.7204g→FG起點(diǎn)1.26492179.5526h→HF起點(diǎn)-79.0702-13.3096終點(diǎn)-76.530221.4122終點(diǎn)17.526-0.4572鉆頭一打孔路徑圖：a→ACc1→CEb→Bc2→IJ鉆頭一總路徑鉆頭一打孔順序表（附表二）鉆頭二打孔路徑圖：d→DGe→DIg→FGf1→EJf2→Gb→HF鉆頭二總路徑：鉆頭二打孔順序表（見附表三）6.2.3分析兩鉆頭在同一時(shí)間所打孔相互間距小于3cm時(shí)的那些孔將兩個(gè)鉆頭打孔路徑順序按照模型一得到的打孔路徑列出，根據(jù)鉆頭到達(dá)各個(gè)孔時(shí)走過的路程，得到從鉆頭啟動(dòng)之后不間斷打孔的情況下，到達(dá)各個(gè)孔的時(shí)間。假設(shè)兩個(gè)鉆頭同時(shí)啟動(dòng)的情況下，運(yùn)用excel將兩個(gè)鉆頭的鉆孔按照時(shí)間先后，合并在一起排序，觀察處于相鄰時(shí)間次序的兩個(gè)鉆頭要鉆的孔的距離，小于3cm的選出來。考慮前后時(shí)間間隔下，打前一個(gè)孔的鉆頭可以走到距離打下一個(gè)孔的鉆頭超過3cm的孔，符合打孔時(shí)兩鉆頭距離不小于3cm。表6不符合條件的孔孔的序號(hào)X坐標(biāo)Y坐標(biāo)鉆頭在開始到到達(dá)孔的時(shí)間與另一個(gè)鉆頭所鉆孔的距離212429.1592193.44640.07055625.76087032513.97205.5370.1641619.413643882249-16.25654.00044.40182517.352109182250-16.25656.00044.41293613.51543638156-28.136367.35424.4397315.120722212252-46.22881.546454.63579624.77332881264383.667629.8653294.7463123.64140582141665.989239.24394.7758920.01166432264477.317633.680494.7874712.62042651141765.989236.779294.7895811.74458207264574.777634.950494.803248.9766633141865.989234.112294.804398.828281475264674.777637.490494.817369.415317828141965.989231.572294.818510.59533226264774.777640.030494.8314712.19742275142065.887626.009694.8494116.60165452265831.85167.11295.8528326.006920961531-73.4568110.23698.559045.8930737012676-77.9526101.34698.628259.9621442291532-68.5292139.522298.7240328.656164732752-9.855241.48176105.641628.949140621885-35.712431.0388105.658127.886380296.2.4處理同一時(shí)間下不符合兩鉆頭打孔相距不小于3cm的孔改變打孔順序，雖然能保證使得已知不符合條件的孔在修改后符合條件，但是也很有可能會(huì)出現(xiàn)新的不符合條件的孔?；谶@種考慮，采取以下方案：在不符合條件的孔前面不遠(yuǎn)的某個(gè)孔，鉆頭向另一個(gè)鉆頭另外一個(gè)鉆頭在適當(dāng)?shù)奈蛔飨嗤拈L度的行走，作為補(bǔ)償，保證后面兩鉆頭在打其他孔時(shí)，相同時(shí)間的相對位置不因前面調(diào)整而改變，從而避免出現(xiàn)新的不符合條件的孔。打孔順序不變，避開不符合條件的孔。一個(gè)鉆頭避開的方向?yàn)檫h(yuǎn)離另一個(gè)鉆頭所要打的下一個(gè)孔。以下圖所示為例：當(dāng)鉆頭一鉆孔10時(shí)，鉆頭二在鉆孔20，鉆完后，鉆頭一繼續(xù)往它所需鉆的不符合要求孔11，鉆頭二則向遠(yuǎn)離孔11的位置2，按照設(shè)置，到達(dá)位置2后返回；當(dāng)鉆頭一到達(dá)孔12時(shí)，做遠(yuǎn)離鉆頭二在相同時(shí)間段中要打的孔22，所走路程與鉆頭一為避開鉆頭二打孔11時(shí)的路程相同。表7兩鉆頭路徑調(diào)整方案作出調(diào)整時(shí)鉆頭所處孔的序號(hào)X坐標(biāo)(mm)Y坐標(biāo)（mm）鉆頭自開始到行走到孔的時(shí)間（s）打孔鉆頭鉆頭互相遠(yuǎn)離的距離（mm）來回總路程（mm）322.71954221.7420.04391鉆頭21.508243.0164212522.5552231.08920.2828762鉆頭21.508243.01642248-19.202413.74144.1775652鉆頭47.188894.3776167-22.2504113.7924.701881鉆頭47.188894.3776141467.208452.755894.699931鉆頭37.588575.177264825.425.495.117582鉆頭37.588575.177265725.6032-16.560895.716812鉆頭13.663827.3276145555.9816-7.74795.868631鉆頭13.663827.32762674-73.406151.739698.346772鉆頭34.588869.17761533-68.5546140.792298.731091鉆頭34.588869.17761883-37.896835.814105.627891鉆頭16.290932.58182753-17.932412.4714105.80892鉆頭16.290932.5818每個(gè)鉆頭要走的調(diào)整路程為341.66mm，花費(fèi)時(shí)間為1.9s，調(diào)整總成本為41.0元6.2.5作業(yè)時(shí)間、行進(jìn)時(shí)間和作業(yè)成本鉆頭一有轉(zhuǎn)換了3次刀具，則有3個(gè)刀具轉(zhuǎn)換時(shí)間與鉆頭行進(jìn)時(shí)間的重合值，在刀具轉(zhuǎn)換過程中有4個(gè)18s，則得行進(jìn)時(shí)間作業(yè)時(shí)間鉆頭一作業(yè)成本由：得鉆頭二有轉(zhuǎn)換了4次刀具，則有4個(gè)刀具轉(zhuǎn)換時(shí)間與鉆頭行進(jìn)時(shí)間的重合值，在刀具轉(zhuǎn)換過程中有6個(gè)18s，則得行進(jìn)時(shí)間作業(yè)時(shí)間作業(yè)成本由：得雙鉆頭總作業(yè)成本：6.3分析兩鉆頭合作間距對作業(yè)路線和生產(chǎn)效能的影響為說明合作間距對作業(yè)路線和生產(chǎn)效能的影響，分別在假定生產(chǎn)合作間距要求為2cm和1cm時(shí),處理得到對應(yīng)的不符合要求的孔、路程增加量和作業(yè)時(shí)間。由于模型一作業(yè)路徑最短，在特定位置對兩鉆頭各自的作業(yè)路線進(jìn)行了調(diào)整。當(dāng)合作間距為3cm時(shí)，與最短路徑相比，各個(gè)鉆頭的作業(yè)路程增加了341.66mm,各個(gè)鉆頭的作業(yè)時(shí)間增加了1.9s，使生產(chǎn)效能降低了一些。當(dāng)假定合作間距為2cm時(shí)，不符合要合作間距要求的孔、路程增加量和作業(yè)時(shí)間增加量如下表。表8假定合作間距2cm時(shí)不符合要求的孔孔序號(hào)X坐標(biāo)Y坐標(biāo)鉆頭自開始到到達(dá)孔時(shí)間（s)與另一個(gè)鉆頭所鉆孔的距離153-27.336267.35424.38450.80012249-16.25654.00044.40182517.35210918154-27.635262.9924.408814.50293292155-28.114862.4844.412680.6985930162250-16.25656.00044.41293613.515436382251-16.25658.000394.4240471.99999156-28.136367.35424.4397315.12072221264477.317633.680494.7874712.62042651141765.989236.779294.789611.74458207264574.777634.950494.803248.9766633141865.989234.112294.80448.828281475264674.777637.490494.817369.415317828141965.989231.572294.818510.59533226264774.777640.030494.8314712.19742275142065.887626.009694.849416.601654522674-73.406151.739698.34677168.56259091531-73.4568110.23698.5595.8930737012676-77.9526101.34698.628259.962144229表9假定合作間距2cm調(diào)整方案作出調(diào)整時(shí)鉆頭所處孔的序號(hào)X坐標(biāo)Y坐標(biāo)打孔鉆頭來回總多走的距離（mm）152-27.3362468.15431鉆頭40.79522251-16.25658.000392鉆頭40.7952264383.667629.865322鉆頭35.8596142165.50668.71221鉆頭35.85962674-73.406151.73962鉆頭67.90681532-68.5292139.52221鉆頭67.9068表10假定合作間距2cm調(diào)整方案總代價(jià)1鉆頭多走的總路程（mm）144.56162鉆頭多走的總路程（mm）144.56161鉆頭需多花費(fèi)的成本（元）8.6736962鉆頭需多花費(fèi)的成本（元）8.673696總共需多花費(fèi)的成本（元）17.347392鉆頭1所花時(shí)間（s)0.80312鉆頭2所花時(shí)間(s)0.80312當(dāng)假定合作間距為1cm時(shí)，不符合要合作間距要求的孔、路程增加量和作業(yè)時(shí)間增加量如下表。表11假定合作間距1cm時(shí)不符合要求的孔打孔序號(hào)X坐標(biāo)Y坐標(biāo)鉆頭自開始到到達(dá)孔時(shí)間（s)與另一個(gè)鉆頭所鉆孔的距離264574.777634.950494.803248.9766633141865.989234.112294.804398.8282815264674.777637.490494.817369.41531781531-73.4568110.23698.559045.89307372676-77.9526101.34698.628259.96214422677-71.6026107.06198.675728.54305132678-71.6026109.60198.689832.54表12假定合作間距1cm調(diào)整方案作出調(diào)整時(shí)鉆頭所處孔的序號(hào)X坐標(biāo)Y坐標(biāo)打孔的鉆頭來回的總路程(mm)264477.31833.68041鉆頭2.7927264674.77837.49042鉆頭2.79272674-73.406151.742鉆頭30.87542679-71.603112.1411鉆頭30.8754表13假定合作間距1cm調(diào)整方案總代價(jià)1鉆頭總多走的路徑（mm）67.33622鉆頭總多走的路徑（mm）67.33621鉆頭總需多花費(fèi)的成本（元）4.0401722鉆頭總需多花費(fèi)的成本（元）4.040172總需多花費(fèi)的成本（元）8.080344鉆頭1花費(fèi)的時(shí)間（s)0.37409鉆頭2花費(fèi)的時(shí)間（s)0.37409比較三個(gè)合作間距對應(yīng)的調(diào)整代價(jià)可知：合作間距越小，在最短路徑的條件下不符合要求的孔越少，鉆頭所受的限制越小，作業(yè)路線越少受影響，因?yàn)檎{(diào)整作業(yè)路線花費(fèi)的成本越低，花費(fèi)的時(shí)間越少。七、模型評價(jià)優(yōu)點(diǎn)：1、對于給出的大量的數(shù)據(jù)，我們首先對數(shù)據(jù)進(jìn)行處理，使之后更好觀察、計(jì)算；2、模型建立，思路簡單清晰，并且可以得到很好的效果；3、模型的假設(shè)符合實(shí)際生產(chǎn)，可以很好的運(yùn)用于相對應(yīng)的實(shí)際生產(chǎn)中；不足：1、在兩個(gè)鉆頭作業(yè)時(shí)，忽略較小的打孔時(shí)間，兩個(gè)打孔數(shù)不同時(shí)，時(shí)間上的配合就有所偏差；2、部分程序運(yùn)用matlab程序，程序復(fù)雜，較難調(diào)試成功。八、參考文獻(xiàn)[1]宋葉志，賈東永，MATLAB數(shù)值分析與應(yīng)用，北京：機(jī)械工業(yè)出版社，2021年[2]薛聲家、左小德，管理運(yùn)籌學(xué)，廣州：暨南大學(xué)出版社，2021年[3]馮杰、黃力偉等，數(shù)學(xué)建模原理與案例，北京：科學(xué)版社，2021年[4]王樹禾，圖論，北京：科學(xué)出版社，2021年[5]郭茂祖，姜俊峰，李靜海。模擬退火算法中冷卻調(diào)度選取方法的研究【J】。計(jì)算機(jī)工程，2021,26（9）：63,64.[6]陳萬里，程家興.基于模擬退火算法（SSA）求解列車控制問題[J].計(jì)算機(jī)工程，2021,26（9）：63,64.[7]劉向群，仇越.模擬退火算法和遺傳算法 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