KHOA HQC - CONG NGHE
Tap chi GTVT 3/2011 1
N A N G CAO HIEU QUA THUAT TOAN GIAI CAC BAI TOAN TOI tfU HOA XEP HANG TRONG CAC HE THONG KHO V A N
NCS
TSKT. V.E., EOLNOKIN, E.E. KOVSHOV Vien Nghien cdu Khoa hgc & Thtfc nghiem
dien td tu dgng va thiet bi dien Moskva DO TRUNG THOAI, NCS. N G U Y I N DJNH CHUNG
Trudng Dai hgc Hang hai Viet Nam
Tdm t i t : Bai toan chit xep, ddng gdi cac ddi tugng hang hda da dugc phat sinh trong nhieu linh vtfc hoat ddng nhU: San xuit cdng nghiep, logistics, an toan hoat dgng dan sinh, bao ve sdc khoe con ngudi, va nhit la - khi xep hang vao container, lap ke hoach van chuyen hang hda. Trong bai bao xem xet cac luan de chinh cda phuong phap dugc de xuit de giai bai toan ddng gdi cac ddi tugng tren co sd cac thuat toan tien hda dudi dang software thu vien lap trmh. Ban chit cua phuong phap nay la tao ra phuang phap thdng nhit de sdp xep cac dang ddi tugng khac nhau vao mgt the tich cho trudc.
Abstract: Loading and packing are problems arising in many fields of social activities, such as:
industrial production, logistics, civil safety, human health protection, and especially in containerized cargoes, scheduling cargo transport. In the article, we also consider the major treatise of proposed method of solving the problem, basing on evolutionary algorithm, under software of a programme library. The nature of this method is to create a consistent method to arrange different types of objects into a fixed volume.
PHUONG PHAP GIAI BAI TOAN
Trong khong gian container bd trf cac diem dac biet, trudng hpp nay la nhOng "nut", de theo dd cd the tien hanh xep ndi nhOng ddi tOPng ddng gdi. C i c nOt deu cd chOa thdng tin ve kieu dang, phuong hodng va vi tri cua mdi ddi tupng dupe xep. Container chOa thong tin ve c i c ddi topng da xep dodi dang la khdi nut. To hpp e i c nut trong container tao thanh mach chu tuyen, ma e i e ddi tupng khac cd the xep ndi tiep vao dd. T i t e i e i c nut dope phan loai theo thO to giam d i n ve c i p dd Ou tien cua cac ddi topng de xep ndi. ddng thdi c i p dd dd Igi phy thude vao vi tri cua moi nut trong khdng gian cua container.
Nhu vay, each giai bai toan xep hang hoa dupe the hien nhu mot trinh to ma xep cac ddi tupng mpc tieu. PhUPng p h i p ma hda da de xua't la phuong phap bat bien ddi vdi c i c thuat toan khac nhau de tim g i i i nghiem tdi Uu. Nhung ddi tuong xep trong container dupc phan logi so bd theo kieu loai ddi tupng cd kich thode hinh hpc k h i e nhau. C i c h g i i i bai t o i n xep N ddi tupng dupc the hien nho day sd to nhien (chudi cac nhidm s i c the), vdi dd dai b i n g 2/V:
A,B,A2B,„,A;vB^, (1) Trong dd. tri sd A, l i sd thO to cua ddi tupng thO i:
va tn sd B,- l i thdng tin djnh hodng cua ddi tupng dd trong khong gian container.
PhOOng p h i p kiem tra c h i t lOOng c i c h giai b i i
toan tren bao gdm nhOng budc sau day:
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5 j K i c ^ T M nak ckc nfcifi M M kta( n K Mas
i
L r a ckoa t h « < » tM mk»t
' Xep ndi ddi tupng vao nut cd dd Uu tien xep Idn n h i t trong sd cac nut cdn trdng:
' Thay ddi khdi nut va tao ra cac nut trdng mdi:
' Phan loai cac nut theo chieu giam d i n dp uu tien dope xep ddi tupng vao dd:
* D i n h gia c h i t lOpng xep.
Ham muc tieu xep (U<t>) dupc dung de danh gia muc dp thich Ong cua nghiem giai. Danh g i i djnh tinh hay c h i t lOpng cua nghiem giai [1] dope tien hanh tren eP sd phan tich khdi nut va dupc the hien nhu ty sd cua tdng khdi lOpng cac ddi tupng xep tren the tich cua khdi hinh hdp tao ra bdi ddng xep thu dupc. Nhu vay, g i i tri eua ham muc tieu se n i m trong khoang tO 0 den 1. Va viec giai bai toan xep cac ddi tuong da dope quy ve viec tim nghiem cd gia tri ldn n h i t trong d i n h gia dope tinh toan.
Trinh to tim nghiem a tdi Uu cua bai toan c h i t xep cac ddi tupng muc tieu da dupc the hien dudi dang so dd khdi nhu tren hinh 1.
Thuat toan di truyen (TA) - la phuong phap tim kiem dpa tren eO sd phep chpn nhOng p h i n tu tdt nhat trong mot tap hpp [2]. Thuat toan di truyen (VA) la thuat toan dua tren md hinh tien hda smh vat va
KHOA H Q C - C O N G NGHE
nhOng phOOng p h i p tim kiem n g i u nhien.
Cac Ou diem eP b i n khi suf dyng edng cy t h u i t t o i n di truyen (FA) de g i i i b i i t o i n c h i t xep e i e ddi typng l i :
- Cd tap hpp rdng Idn nhOng tham sd bien ddi eua thuat t o i n ;
- Cd so chuyen giao nghiem tdt n h i t tO the he n i y sang the he k h i e .
Ddng thdi TA eung khdng tranh khdi nhOng khiem khuyet, ma cy the la:
- L i m g i i m e i e phOPng i n nghiem sd eua tap hpp nghiem trong qua trinh tien hda [3];
- Khdng ed phOOng p h i p tdi Ou hda tdng q u i t (vdi mdi bai toan deu phai cd sy dieu chinh thuat t o i n rieng).
Thuat t o i n ui nhiet (AO) md hinh hda q u i trinh nung nhiet vat the den trgng t h i i ndng c h i y v i l i m ngudi nd d i n d i n tiep theo [3]. O nhiet dd eao, vide tim kiem nghiem tdi Ou (hay i tdi Ou) dope tien hanh tren toan bd d i i nghiem, cdn khi nhiet dd hg xudng mien tim kiem se thu Igi ve mien nhd xung quanh nghiem hien tai. AO la thuat t o i n cho phep ta ed the ra khdi nghiem tdi Ou eye bd nay chuyen sang nghiem tdi Ou k h i c sau hon [4]. Mat k h i e , thuat t o i n n i y sau mdi phep lap Igi cd the t i i sinh n g i u nhien dope mdt nghiem, dd la dieu r i t thiet yeu ddi vdi mdt sd Idn c i c ddi topng e i n chi't xep (nghTa l i ddi vdi lOpng nhidm s i c Idn).
De tim nghiem tdi Ou ngOdi ta edn de x u i t nen sO dyng thuat t o i n di truyen bien the (MTA). Thuat t o i n lAA cung tyong tO nhO thuat t o i n FA, nhOng chi k h i c la e i e nghiem eua ham myc tidu (UO) nhd hon Ll<D trung binh trong tap ham tryde nd se dope chpn dOa vao tap mdi vdi x i c s u i t dope tfnh theo cdng thOc sau:
cfe.2)-c(-^/,i)
p=r ' , (2)
trong dd C (S| i) - l i UO eua nghiem thO i eua tap mdi; cdn t- la sd thdi ky cua thuat t o i n tien hda.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
So lirong cic thm ki
Hinh 2. Bieu dd xac suit quyet dinh giai phap trong thuat toan MFA
Tren hinh 2 the hien bieu dd phy thude vide quyet dinh g i i i p h i p v i o sd thdi ky di qua, TO bieu dd, ta tha'y x i c s u i t de gap p h i i nhOng giai p h i p xau se giam theo ham sd mu khi sd thdi ky tang len (la dodng bao udn net dam tren hinh ve), X i c s u i t dd khi quyet dinh giai p h i p se dam bao dope so b i o t o i n khdi nhOng giai phap phi c h i t lopng khi d mOc tien hda eao va giup lam tang ludng thdng tin di truyen dope
chuyen den.
PHAN THUC NGHIEM
De giai Idp b i i t o i n eha't xep bang ngdn ngO thuat t o i n tieu ehuan ISO/ANSI C++ ngOdi ta p h i i lap ra tho vien tdng hpp cac Idp Packer Ong dyng tren nen tang eua Microsoft Win32. Cd sd eua phddng p h i p nay la phddng thOe tiep can hodng tdi ddi toPng (object-oriented approach). Cdn khi Ida chpn t h u i t t o i n de tim nghiem tdi Ou trong b i i t o i n c h i t xep thi ngodi ta c i n p h i i phan tich so s i n h e i e thuat t o i n kinh nghiem heuristic tren cd sd eua tho vien da lap.
C i e ehl sd hogt ddng cija cac t h u i t t o i n Hinh 2.
Bieu dd xae suit quyet dinh giai phap trong thuat toan FA, Hinh 2. Bieu dd xae suat quyet djnh giai phap trong thuat toan MY A va Hinh 2. Bieu dd xae suit quyet dinh giai phap trong thuat toan VA trong q u i trinh g i i i nhOng bai t o i n c h i t xep ba chieu da dope the hien tren hinh 3. Va c i c thOe nghiem d day deu da dOPe thyc hien tren m i y dien t o i n PC (UD- AMD 1.79 r r U , 03Y - 896 MB). Trong dd, vdi mdi t h u i t t o i n , ngOdi ta deu da tien hanh c i logt 100 thO nghiem c h i t xep vdi 90 ddi topng ed kich thodc hinh hpc nhO neu trong chuyen k h i o [1], va c i e ehi sd hogt ddng trung binh eua mdi thuat t o i n eung da dope bleu dgt nho tren e i e hinh. TO hinh 3 ta thi'y, thuat t o i n AO da khdng thich hpp de g i i i Idp b i i t o i n eha't xep e i e ddi topng theo gde dd eha't loong cua nghiem thu dooc. Cdn MFA da tim ra nhOng nghiem sd tdt n h i t so vdi cac thuat t o i n k h i e dang xdt, dd l i do nd da chap nhgn nhOng nghiem sd khdng eung hp vdi x i c s u i t eho trOde tgi mdi thdi ky, m i nhd dd da eho phdp t h o i t khdi nhOng nghiem tdi Ou eye bd. Tuy nhien, tdc dd tim nghiem eua t h u i t t o i n MFA Igi thap n h i t trong sd e i e thuat t o i n da ndu.
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Thoat toao a nhiet . \ 0 ^
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Hinh 3. Chi sd hoat ddng cua cac thuat toan kinh nghiem heuristic.
De giai Idp bai t o i n c h i t xep ddi tdpng ddi hdi ta p h i i tdi Pu hda e i c tham sd eua thuat t o i n TA vdi mue tieu n h i m thu dope nhOng nghiem tdt nha't trong cung mpt tdc dd tim nghiem tdi Ou nhO nhau. Tren hinh 3 da bieu thj nhOng ehi sd hogt ddng cua e i c thuat t o i n TA va MFA vdi x i e s u i t thOe hien cae t o i n tO di truyen, ma da dOPe khuyen c i o de g i i i e i e bai t o i n khae nhau trong ehuyen k h i o [2], cy the nhO, vdi t o i n tO trao ddi cheo erossingover - thi xae s u i t dd b i n g 0.8, edn vdi t o i n tO nghjch d i o inversion - thi nd b i n g 0.1, t o i n to hoan vj mutation - b i n g 0.1, va vdi t o i n tO ddi mdi nghiem - cung b i n g 0.1. O nghien cOu n i y , b i n g c i c h thyc nghiem, da x i e djnh dypc g i i trj x i c s u i t tdi yu ed the thyc hien vdi nhOng t o i n tO k h i e nhau eua thuat t o i n TA, trong dd, mdi t o i n tO nho v i y d i tien hanh mdt xeri 25 thoc nghiem k h i e nhau.
KHOA HQC - CONG NGHE
Tap Chi GTVT 3/2011 I
1. Toan td erossingover (trao ddi eheo):
T o i n tO erossingover - la c i u trOe eho phdp b i n g each trao ddi eheo c i c nhidm s i c the cha me (hay c i e bd p h i n cua chung) de tgo ra nhOng nhidm sac the cua the he sau [2].
T o i n tO mdt diem trong phep trao ddi cheo dope thOc hien theo ba giai dogn nhO sau:
1, Chpn n g i u nhien hai nhidm s i c tO tap hpp n h i i m s i c hien tgi,
2, Chpn n g i u nhien mdt diem dOn tren tiet didn nhidm sac, Mdi diem dd trdn mat tiet dien - se la mdt ma glen de sau dd thOc hien vide c i t nhidm s i c .
3, Hai n h i i m s i c mdi se dope hinh t h i n h khi h o i n vj nhOng p h i n dogn n h i i m s i c nam d ben phai diem c i t .
Tren hinh 4 da the hien bieu dd so phy thude g i i tri trung binh ham myc tieu UO eae nghiem vao xac s u i t thoc hien t o i n tO cua phep trao ddi cheo erossingover. C i e diem bien ddi len xudng nhieu tren dd thj l i do vide ngOng hoat ddng cua thuat t o i n TA khi nghiem bi roi sau vao g i i tri tdi Ou eye bd. 5 day, hodng ed gia trj thoc tidn la sO gia tang gia trj ham mue tieu tuy thude vao x i e s u i t thyc hien t o i n tO, da dope bieu thj b i n g dodng cong net dam tren hinh ve.
Hinh 4. Bieu dd ve stf phg thugc cua ham mgc tieu Lf0 vao xac suit thtfc hign toan td erossingover.
TO hinh 4 ta thay, khi xac s u i t thyc thi toan tO erossingover tang len thi gia tri cua ham nghiem muc tieu cung tang.
2. Toan td nghich dao inversion.
T o i n tO nghjch d i o inversion - la eau true eho phep ta d i o nghjch eae nhidm s i c the cua cha me (hay e i e bd phan cua nd) de tgo ra nhiem s i c eua the he tiep theo [2],
02 04 06 08
Xac sua) tb<fc Ihl loan lii ngbjcb dao
Hmh 5. Dd thi stf phg thugc gia tri trung binh cua ham nghigm mgc tieu vao xac suit thuc thi toan td dao nghich.
Toin'tO di truyen nghjch dao dupe thyc thi theo ba
giai doan sau,
1. Chpn n g i u nhien mdt nhidm s i c the tO tap nhOng n h i i m s i c hien tgi,
2. Chpn n g i u nhien mdt diem c i t nhiem sac, 3. Mdt nhiem s i c mdi se dupe tao ra khi d i o nghich phan doan nam ben phai diem c i t ,
Tren hinh 5 la dd thj sy phy thude g i i tri trung binh cua ham nghiem myc tieu vao xae s u i t thue thi toan tO d i o nghjch.
TO hinh 5 ta tha'y, khi xac s u i t thOc thi t o i n tO dao nghjch tang len thi gia trj trung binh cua ham nghiem myc tieu cung tang len cd gidi hgn.
3. Toan td hoan vi mutation.
T o i n tO h o i n vj mutation - la c i u true cho phep ta tren cO sd bien ddi nhidm s i c the eua cha me (hay e i e bd phan eua nd) de tao ra nhidm s i c cua the he tiep theo [2],
Toan tO di truyen h o i n vj dope thoc hien theo ba giai dogn nho sau:
1. Chpn n g i u nhien mdt n h i i m s i c the tO tap c i e nhidm s i c hien cd.
2. Chpn n g i u nhien mdt diem e i t nhidm s i c . 3. Nhidm s i c the mdi se dope tao ra khi h o i n vj vj tri cua cac glen n i m d ben phai va ben t r i i eua diem e i t .
Tren hinh 6 da bieu dien dd thj sp phy thude cua gia trj trung binh ham nghiem mue tieu vao x i c s u i t thoc thi toan tO h o i n vi.
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Hinh 6. Do thi stf phu thugc cua gia trj trung binh ham nghiem muc tieu vao xac suit thtfc thi toan td hoan vi.
TO hinh 6 ta t h i y , khi xae s u i t thoc thi t o i n tO hoan vj tang len, thi gia trj trung binh cua ham nghiem mue tieu bi giam di.
4. Toan td ddi mdi nghiem
Hinh 7. Dd thi stf phu thugc cua ham muc tieu vao xac suit thtfc thi toan tu ddi mgi.
(Xem tiep trang 54)
