KHOA HOC Cong nghe
NANG CAO DO TIN CAY CUA THUAT TOAN
khi giai bai toan chat xep hang hoa trong td hop ben bai - kho hang
Bai bao nay de xuat nhiing luan diem cabin va thdng nhat degiai cac bai toan chai xep hang hda, dong thdi cung da xem xet kha nang img dung nhung thuat toan tien hda khac nhau degiai bai toan niu trin. Da lua chon dugc cac thdng so' td'i uu ciia thuat toan gd'c khi giai cac bai toan chat xep hang hda.
Mddau
Bai toan chat xep hang hda xuat hien trong cac ITnh vyc hoat dpng khac nhau nhu cdng nghiep, djch vu logistics, bao dam an ninh trong ddi sdng xa hpi, bao ve sire khoe... Cu the nhu khi thyc hien chat xep hang hda vao thiing container (chat day the tich mpt each tdi uu), hoac khi lap ke hoach van chuyen hang (djch vu van tai logistics).
Md rpng bai toan sang cac ITnh vyc khac lam cho viec tim Idi giai ciia nd cang cd y nghTa thyc tien va cap bach.
Bai toan chat xe'p hang hda thupc loai bai toan toan phan - NP. De giai loai bai toan nay can thiet ap dung cac thuat toan theo phuong phap tu duy (Evristica). Trong bai viet nay, tif quan diem thyc tien phai xet tdi kha nang ap dung thuat toan gdc va thuat toan u de giai loai bai toan chat xep hang hda.
Va tren co sd thuat toan tien hda dudi dang thu vien lap trinh da xet de'n cac luan diem co ban cua quan diem tho'ng nhat da de xuat de giai bai toan chat xep hang hda.
Quan diem nay dupc de cap trong viec thiet lap phuang phap duy nhat de sap xe'p, bo tri cac ddi tupng khac nhau vao trong mpt the tich da cho, thi du sap xep hang hda vao container, cung nhu trong viec si) dung so do ma hda thdng nhat de giai bai toan bing thuat toan tien hda khac nhau.
Phuong phap luan
Trong khdng gian thung container bd tri nhting diem dac biet, dupc gpi la cac "nuf, de kit nd'i cac ddi tupng. Cac nut chira dung thdng tin ve loai, hudng va vj tri cua ddi tupng dupc chat xep. Thiing container chira dyng thdng tin ve cac dd'i tupng dudi dang khdi nut. Toan bp eac niit trong thiing con- tainer dupc tao thanh dudng bao de lien ke't vdi nhting ddi tupng khac. Tat ca cac nut dupc phan loai theo trinh ty giam dan sy uu tien lien kit ddi tupng vdi nut, edn sy uu tien d i n lupt minh lai phu thude vao vi tri ciia nut trong khdng gian thiing container.
Giai bai toan xIp chd la thyc hien trinh ty ma hda sy sap xep cae ddi tupng.
Phuong phap, ma hda dupe de xuat la phuang phap bat bien cho eae thuat toan khac nhau d l nhan dupc ldi giai td'i uu. Cac ddi tupng sap xep vao container dupe phan loai ban dau theo eac thdng sd hinh hpc khac nhau. Giai bai toan x I p chd N dd'i tupng dupc bieu diln dudi dang ddng ke (nhilm sac the) ciia cac sd ty nhien vdi dp dai 2N:
A^B^A^2-^N^N- (1)
So Aj chira dyng sd dang " i " cua dd'i tupng dupc sap xep; sd B, chira dyng thdng tin ve djnh hudng trong khdng gian thiing container ciia ddi tupng nay.
Trinh ty kiem tra chat lupng Idi giai bao gom cac budc sau:
+ Ket ndi dd'i tupng vdi niit cd mire dp uu tien cao nhat trong so tat ca cac nut ty do
GS. TSKH. KOVSOV E.E.
PGS. TS. NGUYfeN NGQC HUfe + Thay ddi khdi niit vdi sy hinh thanh cac niit ty do mdi
+ Phan loai cac nut theo mirc dp giam dan sy uu tien sap xep cac ddi tupng
+ Danh gia chat lupng ldi giai
Ham muc tieu (HMT) dupc diing de danh gia mirc dp chinh xac ciia Idi giai. Chat lupng cLia ldi giai dupc danh gia tren co sd phan tich khdi nut va dupc xac djnh bing ty sd giiia tdng t h i tich ciia cac ddi tupng dupc s i p xep va the tich khdi hop bao phii toan bp cac ddi tupng dd. Nhu vay, gia trj cua ham muc tieu la n i m trong khoang tif "0"
de'n " 1 " . Giai bai toan xep chd cac ddi tirpng dupc quy ve viec tim Idi giai cd gia trj ldn nhat theo danh gia da dupc thyc hien. Qua trinh tim Idi giai tdi uu thir cap cho bai toan xep chd ddi tupng dupc md ta dudi dang so dd khdi tren Hinh 1.
Thiet lap tap hop cac loi giai ban dau, danh gia loi giai
Tao loi giai moi nhd toan tir thuat loan tie'n hoa, danh gia loi giai
ao vung^~~~
uong 7 ^ , . . ^
Sai
Dung
Doi nn6i tap hop cac loi giai, danli gia
cac loi giai
Hinh 1-Thuat toan t i m loi giai toi uu thir cap bang thuat toan tien hoa
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Thuat toan gdc (TTG) - phuong phap tim kilm tren co sd lya chpn nhCing yeu td tdt nhat trong phd bien [1]. TTG cd ca sd la md hinh tien hda sinh hpc va cac phuang
phap tim kiem nglu nhien.
Cac lpi the co ban cua viec sir dung bp may TTG khi giai bai toan xe'p chd hang hda:
4 2 - Tapchf HdnghdiVietNam • 10/2009
KHOA HOC Cong nghe
- Nhan ddng thdi mdt sd ldi giai tdt nhat trong tap hop cac Idi giai cho trudc
- Cd nhieu bien sd ciia thuat toan.
Tuy nhien, TTG cung cd nhirng khiem khuyet:
- Giam sd phuang an Idi giai trong phd bien trong qua trinh tien hda [3]
- Khdng cd phuang phap van nang tdi uu hda (cho mdi bai toan cd lya chpn che dp dieu chinh thuat toan rieng).
Thuat toan ii (TTU) md hinh hda qua trinh ddt vat the dat den trang thai ndng chay ciing vdi qua trinh lam lanh timg budc tiep theo [2]. Khi nhiet dp cao, viec tim kiem Idi giai tdi uu (td'i uu thir cap) duoc thuc hien tren pham vi toan bp viing Idi giai; khi giam nhiet dp thi VLing tim kiem bi giam de'n vimg nhd xung quanh ldi giai hien tai.
TTU cho phep di ra tir mpt tdi uu dja phuang va di vao mdt td'i uu khac sau hon [3]. Mat khac, thuat toan nay trong mdi phep lap thi chi ddi mdi dupc mpt Idi mpt each giai nglu nhien va dieu nay rat quan trpng ddi vdi phan Idn cac ddi tuong dupc sap xep (cd nghTa la dd'i vdi cac nhiem sac the ldn).
Oe tim kiem cac Idi giai, chimg ta de xuat thuat toan gdc bien ddi (TTGBD). TTGBO cung tuong tyTTG, ngoai tni trudng hpp cac Idi giai vdi HMT nhd han HMT trung binh cua phd bien trudc dd, chiing dupc lya chpn vao phd bien mdi vdi xac suat dupc tinh theo cdng thirc:
C(Si2)-C(Sii)
P = e (2) t
Trong dd C(Si ^) - HMT Idi giai thir i cua phd bien hien tai; C(S| j) - HMT Idi giai thir i cua phd bien mdi; t - sd thdi dai ciia thuat toan tien hda.
Tren Hinh 2 la dd thi bleu dien sy phu thupc cua xac suat tiep nhan Idi giai vao sd thdi dai da trai qua. Tir dd thj nay cd the tha'y ring xac suat tiep nhan cac ldi giai xau bi giam theo ham sd mu cimg vdi sy gia tang sd thdi dai (dudng cong tren dd thj dupc bieu dien bing net dam). Xac suat tiep nhan cac Idi giai mdi nhu vay nhim loai tar cac Idi giai thifa khdng chat lupng d trinh dp tie'n hda cao va bao dam sy da dang ciia ddng thdng tin gdc.
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Hinh 2-Bieu do xac suat tiep nhan loi giai theo TTGBD Phan thuc nghiem
Oe giai loai bai toan chat xep hang hda bing ngdn ngir lap trinh ISO/ANSI C++ da xay dyng thu vien van nang cac Idp Packer, chay trong mdi trudng Microsoft Win32. Co sd nghien ciru xay dyng sir dung phuang phap djnh hudng ddi tupng. Khi lya chpn thuat toan de nhan Idi giai tdi uu cho bai toan chat xe'p hang hda, da thy& hien phan tich so sanh thuat toan tu duy tren co sd thu vien da dupc thie't lap.
Dp tin cay cua TTG, TTGBD, TTU khi giai bai toan chat xep hang hda ba chieu dupc the hien tren Hinh 3.
Ket qua thu dupc tren Hinh 3 cho thay TTU khong thich hop de giai loai bai toan sap xe'p ddi tupng tren quan diem chat lupng Idi giai. Van hanh TTGBD ta cd Idi giai tdt nhat so vdi cac thuat toan khac nhd vao viec tiep nhan cac Idi giai khdng ciing hp kem chat
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lupng vdi xac suat cho trudc ddi vdi mdi thdi dai, tai dd chimg cho phep di ra khdi cac tdi uu dja phuong. Tuy nhien tdc dp giai TTGBD la cham nhat trong sd cac thuat toan da xem xet.
Oe giai loai bai toan chat xep hang hda, chiing ta da de xuat td'i Lfu hda cac thdng sd TTG nhim nhan dupc Idi giai tdt nhat vdi tdc dp tim kiem Idi giai td'i uu. Tren Hinh 3 bieu diln dp tin cay ciia TTG va TTGBO vdi xac suat thyc hien cac toan tir gdc khuyen nghj de giai cac bai toan khac nhau trong [2], cu the la, ddi vdi toan tijf crossingover (pha trpn) - 0,8, ddi vdi toan ti; nghjeh dao - 0,1, ddi vdi toan tir hoan vi xuyen Idp - 0, va ddi vdi toan tir lam mdi Idi giai - 0,1. Trong cac cdng trinh nghien ciftj da xac djnh thyc nghiem gia tri td'i uu CLia cac xac sua't thyc hien cac toan tijf TTG khac nhau, cho mdi toan tiJf gdc da tien hanh mdt loat gdm 25 thyc nghiem.
Toan tu kroxingover (pha trgn)
Toan tir kroxingover la ket cau cho phep xay dyng cac nhiem sac the con chau [1] tren co sd pha trdn nhiem sac the ciia cha me (hoac cac bp phan cua hp).
Toan tir mpt diem pha trpn dupc thyc hien theo 3 budc:
- Hai nhiem sic the dupc lya chpn ngau nhien tir phd bien hien tai
- Lya chpn diem elt nhiim sic the mdt each nglu nhien. Sau diem elt - ma di truyen thyc hien cat nhiem sac the
- Hai nhiem sac the mdi dupc hinh thanh bing each sip xep eac manh da dupc lya chpn nam ben phai eua dilm cit.
Oo thj Hinh 4 the hien sy phu thudc gia tri trung binh HMT cua Idi giai vao xac suit thyc hien toan tiji pha trdn.
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Hinh 4- Do thj ve sy phu thupc L(0 vao xac suat thuc hien toan tu pha trpn
Hinh 4 cho thay, cimg vdi gia tang xac suat thyc hien toan tir pha trpn thi gia tri trung binh HMT ciia Idi giai tang len.
Toan tu nghich dao
Toan tu nghjeh dao la kit ca'u cho phep xay dung nhiem sic the con chau [1 ] tren co sd dao ngupe nhilm sic the cha me (hoac cac bp phan ciia hp).
Toan tir gdc nghich dao dupc thyc hien theo 3 budc:
- Nhilm sic the dupc lya chpn nglu nhien tif phd bien hien tai
Tapchf HdnghdiVietNam • 1 0 / 2 0 0 9 - 4 3
KHOA HOC Cong nghe
- Lya chpn nglu nhien diem elt nhilm sic the
- Nhilm sic the mdi dupc hinh tharih tir nhilm sic the da lya chpn bing each dao ngupe cac manh nim ben phai dilm cat.
Tren Hinh 5 cd the hien dd thj sy phu thudc gia trj trung binh ldi giai HMT vao xae suit thyc hien toan tir nghjeh dao.
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Hinh 5-D6 thi ve sy phu thupc U;* vao xac suat thyc hien toan tu dao ngupe
Hinh 5 cho thay, cimg vdi gia tang xac suat thyc hien toan tir nghich dao thi gia tri trung binh ciia Idi giai HMT gia tang mpt each han che.
Toan tir hoan vi
Toan tir hoan vj la ket cau cho phep xay dung nhiem sic the con chau [1] tren co sd bien ddi nhiim sac the cha me (hoac bp phan CLia nhiim sic the). Toan tir hoan vi gdc dupc thyc hien theo 3 budc:
- Nhiim sic the dupc lya chpn nglu nhien tif phd bien hien tai - Nglu nhien lya chpn diem cit nhilm sic the
- Nhiim sic the mdi dupc hinh thanh tif nhiim sic the da lya chpn bing each hoan ddi vj tri ciia cac gen nim ben phai va ben trai diem elt.
Tren Hinh 6 trinh bay dd thj ve sy phu thupc ciia gia tri trung binh cua HMT vao xac suat thyc hien toan tir hoan vi.
Hinh 6^6 thj su phu thupc cua HMT vao xac suat thuc hien toan tu hoan vj
Hinh 6 cho thay, cimg vdi gia tang xac suit thyc hien toan tir hoan vj xuyen Idp thi gia tri trung binh ciia Idi giai ciia HMT bj giam.
Toin tu ddi mai
Toan tir ddi mdi la kit eau eho phep thay ddi nhiem sic thi khdi dilm bing mpt nhiem sic thi khae dupe xay dyng mdi mdt each tiiy y-
Tren Hinh 7 the hien dd thj sy phu thupc gia tri trung binh ciia Idi giai HMT vao xac suit thyc hien toan tir ddi mdi.
Hinh 7 cho thay ciing vdi gia tang xac suit thyc hien toan tijf ddi mdi thi gia trj trung binh ciia Idi giai HMT giam mdt each dn djnh.
Kit qua phan tich cac quan he phu thudc thyc nghiem da xac djnh cac thdng sd tdi uu cua TTG: xac suit thyc hien toan tir pha
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Hinh 7-D6 thi bieu diln sy phu thuoc ciia HMT vao thuc hien toan tu ddi mdi
trpn la 0,8, ciia toan tir nghjeh dao la 0,5, cua toan tir hoan vj xuyen ldp la 0,1. Toan tir ddi mdi tir TTG da dupc loai trir. TTG vdi nhOng thdng sd nhu vay cho nhiing Idi giai tdt hon. Tren Hinh 8 la dp tin cay ciia cac thuat toan tu duy cd xet den sy dieu chinh TTG va TTGBO.
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Nhd bien ddi TTG da dupc thyc hien, ta cd the nhan dupc ldi giai tdi uu thir cap tdt hon ddi vdi bai toan sap xep ddi tupng ma khong lam mat tdc dp tim kiem. Chiing ta da lya chpn dupc cac thong so tdi uu ciia TTG tai dd thuat toan eho cac Idi giai tdt nhat.
Lya chpn thuat toan de giai bai toan sap xep ddi tupng va cac thdng sd tdi uu ciia nd da dupc tien hanh tren co sd thu vien dirpc xay dung tren bang phuang phap thd'ng nhat vdi nhtrng uu the sau:
- Kha nang giai bai toan bing cac thuat toan khac nhau - Tinh thich nghi cua co eau eac ldp ddi vdi cac ddi tupng ba chilu mdi
- Tinh van nang eiia cac phuong phap danh gia chat lupng ldi giai
- Kha nang giai bai toan sip xIp dd'i tupng hai chieu va mpt chilu
- Tinh don gian ciia viec bien ddi Idi giai da dupc ma hda.
Kit qua giai bai toan xep chd hang hda ba chieu cd the dUpc bao quan trong djnh dang trao ddi van nang XLM, thdng qua dd cd the kit ndi vdi he thdng PDM.
Tai lieu tham khao
1 GLADKOV L.A., KURETRIK V.V., KURETRIK V.M., Cac thuat toan gdc. M.: - OHSMAHT 2006
2 DJONS M.T. Lap trinh tri tue nhan tao trong cac chuang trinh dinh kem; djch tirtieng Anh. OXIPOV A.!. -JI,MK Press, 2006,312 trang, cd minh hpa
3. Ll K. Ca sd CAHP (GAD/CAM/CAE). Cn6.: - Piter, 2004
