Robust Network Interdiction with Invisible Interdiction Assets

HTML
DOWNLOAD

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "Robust Network Interdiction with Invisible Interdiction Assets"

Αδελφά Βασιλείου
6 χρόνια πριν
Προβολές:

University of Arkansas, Fayetteville ScholarWorks@UARK Theses and Dissertations 5-2014 Robust Network Interdiction with Invisible Interdiction Assets Nail Orkun Baycik University of Arkansas,

1 University of Arkansas, Fayetteville Theses and Dissertations Robust Network Interdiction with Invisible Interdiction Assets Nail Orkun Baycik University of Arkansas, Fayetteville Follow this and additional works at: Part of the Operational Research Commons Recommended Citation Baycik, Nail Orkun, "Robust Network Interdiction with Invisible Interdiction Assets" (2014). Theses and Dissertations This Thesis is brought to you for free and open access by It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of For more information, please contact

7 25 60 R =0 73 R =4 45 R =6 38 R =13 28 R R =1 417 R =5 212 R = R =66 171

8 n

9 c d c

10 x y

11 z y x G =(N,A) N = {1,...n} A (i, j) c ij c ij + d ij d ij 0 x ij 1 (i, j) A x =ˆx (i, j) c ij +d ij ˆx ij z ij 1 (i, j) A 0 y ij 0 y ij d ij ˆx ij (i, j) c ij + y ij

12 y =ŷ 1 n c ij +ŷ ij (ŷ) ŷ)] : z [c ij +ŷ ij ] z ij, (i,j) A j (i) j (i) 1 i =1 z ij z ji = 0 i =2,...,n 1 1 i = n z ij 0, (i, j) A. z u 1 u n, u i u j c ij +ŷ ij, (i, j) A, u i,i N i

13 d ij x ij x =ˆx (ˆx) (ˆx y,z [c ij + d ij ˆx ij ] z ij, (i,j) A y ij R, (i,j) A 0 y ij d ij ˆx ij (i, j) A, z y. R (i, j) d ij x ij =1 x ij =0 z y x =ˆx

14 (ˆx u,y,z (i,j) A (i,j) A [c ij + d ij ˆx ij ] z ij, y ij R, 0 y ij d ij ˆx ij, (i, j) A, j (i) z ij j (i) 1 i =1 z ji = 0 i =2,...,n 1 1 i = n u i u j c ij + y ij, (i, j) A, [c ij + y ij ] z ij = u 1 u n, (i,j) A z ij {0, 1}, (i, j) A. y ij z ij z w ij (i, j) A y ij z ij w ij y ij w ij d ij ˆx ij w ij 0 w ij y ij d ij ˆx ij (1 z ij ) (i, j) A x =ˆx

15 ˆx) u,w,y,z [c ij + d ij ˆx ij ] z ij, (i,j) A y ij R, (i,j) A 0 y ij d ij ˆx ij, (i, j) A, 1 i =1 z ij z ji = 0 i =2,...,n 1 j (i) j (i) 1 i = n u i u j c ij + y ij, (i, j) A, [c ij z ij + w ij ]=u 1 u n, (i,j) A w ij y ij, (i, j) A, w ij d ij ˆx ij, (i, j) A, w ij y ij d ij ˆx ij (1 z ij ), (i, j) A, w ij 0, (i, j) A, z ij {0, 1}, (i, j) A. (i,j) A (c ijz ij +y ij z ij ) u 1 u n w ij y ij z ij, (i, j) A z ij {0, 1} (i,j) A (c ijz ij + w ij ) (i,j) A (c ijz ij + y ij z ij ) u 1 u n w ij = y ij z ij

16 (i, j) w x ij f(x) x X { f(x) (x) X = x : } (i,j) A x ij B; x ij {0, 1} ; (i, j) A z 1 n 1 n I = {1,..., m} 1 n λ i 1 i I 0 i P i γ(p i ) (k,l) A (c kl + d klˆx kl ) i

17 λ,y γ(p i )λ i, i I λ i =1, i I [c kl + y kl ] M(1 λ i ) (k,l) P i (k,l) P i [c kl + y kl ] 0, i, i I,i i (k,l) A y kl R, 0 y kl d klˆx kl, (k, l) A λ i {0, 1}, i I. R y y kl 0 i I λ i =1

18 x x X f(x) f(x) x X x x x d

19 (c ij v ij +(c ij + d ij )w ij ), (i,j) A 1 i =0 (v ij + w ij ) (v ij + w ij )= 0 i =1,...,n 1 (i,j) (i) (i,j) (i) 1 i = n u i u j d ij x ij c ij, (i, j) A, u n u 0 + ( cij v ij +( c ij + d ) ij )w ij =0, (i,j) A v ij + x ij 1, (i, j) A, w ij x ij 0, (i, j) A, v ij,w ij 0, (i, j) A, x X. c ij d ij c ij d ij x ij (i, j) A u i i N v ij w ij c = c d = d c d R

20 x x x T T α x x n f x x f x >f x x x e Δf(x)/T Δf(x) =f(x ) f(x R B =3 R =0 73

21 x x x x x t =1,.., m i =1,.., n x f(x ) f(x ) f(x ) f(x ) x x U(0, 1) e (f(x ) f(x ))/T x x x x f(x ) f(x ) x x T := α T (c ij,d ij : y ij ) (0, 9), (9, 10) (10, 19) R =0 R =4 45 (0, 9), (2, 3) (10, 19)

22 (0, 9) (10, 19) R =0 R =6 38 (2, 3), (9, 10) (10, 19) (2, 3) (10, 19) R =13 28 (0, 1), (0, 9) (0, 11) (0, 1) (0, 11) R R R

23 5 (1, 15) (2, 9) (3, 27) (4, 5) 20 (3, 26) (2, 16) (3, 19) (2, 30) (2, 31) (3, 8) (3, 27) (2, 14) (3, 25) (3, 17) 1 (4, 17) (1, 32) (1, 9) (3, 24) 21 (2, 28) (2, 29) (4, 24) (2, 13) (2, 33) (3, 7) (3, 25) (1, 6) (2, 5) (2, 27) 0 (1, 19) (2, 26) (3, 19) (3, 9) 24 (2, 31) (2, 21) (1, 24) (3, 32) (1, 27) (2, 20) (2, 10) (4, 33) (4, 30) (2, 12) 11 (1, 9) (3, 16) (3, 8) (4, 21) 22 (3, 14) (1, 7) (3, 9) (3, 8) (2, 22) (4, 25) (1, 13) (1, 21) (3, 25) (1, 25) 15 (2, 25) (4, 10) (3, 19) (3, 23) (i, j) (c ij,d ij )

24 5 (1, 15) (2, 9) (3, 27) (4, 5) 20 (3, 26) (2, 16) (3, 19) (2, 30) (2, 31) (3, 8) (3, 27) (2, 14) (3, 25) (3, 17) 1 (4, 17) (1, 32) (1, 9) (3, 24) 21 (2, 28) (2, 29) (4, 24) (2, 13) (2, 33) (3, 7) (3, 25) (1, 6) (2, 5) (2, 27) 0 (1, 19) (2, 26) (3, 19) (3, 9) 24 (2, 31) (2, 21) (1, 24) (3, 32) (1, 27) (2, 20) (2, 10) (4, 33) (4, 30) (2, 12) 11 (1, 9) (3, 16) (3, 8) (4, 21) 22 (3, 14) (1, 7) (3, 9) (3, 8) (2, 22) (4, 25) (1, 13) (1, 21) (3, 25) (1, 25) 15 (2, 25) (4, 10) (3, 19) (3, 23) 23 R =0 73 (i, j) (c ij,d ij )

25 5 (1, 15) (2, 9) (3, 27) (4, 5) 20 (3, 26) (2, 16) (3, 19) (2, 30) (2, 31) (3, 8) (3, 27) (2, 14) (3, 25) (3, 17) 1 (4, 17) (1, 32) (1, 9) (3, 24) 21 (2, 28) (2, 29) (4, 24) (2, 13) (2, 33) (3, 7) (3, 25) (1, 6) (2, 5) (2, 27) 0 (1, 19 : 3) (2, 26) (3, 19 : 1) (3, 9) 24 (2, 31) (2, 21) (1, 24) (3, 32) (1, 27) (2, 20) (2, 10) (4, 33) (4, 30) (2, 12) 11 (1, 9) (3, 16) (3, 8) (4, 21) 22 (3, 14) (1, 7) (3, 9) (3, 8) (2, 22) (4, 25) (1, 13) (1, 21) (3, 25) (1, 25) 15 (2, 25) (4, 10) (3, 19) (3, 23) 23 R =4 45 (i, j) (c ij,d ij )

26 5 (1, 15) (2, 9) (3, 27) (4, 5) 20 (3, 26) (2, 16) (3, 19) (2, 30) (2, 31) (3, 8) (3, 27) (2, 14) (3, 25) (3, 17) 1 (4, 17) (1, 32 : 3) (1, 9) (3, 24) 21 (2, 28) (2, 29) (4, 24) (2, 13) (2, 33) (3, 7) (3, 25) (1, 6) (2, 5) (2, 27) 0 (1, 19) (2, 26) (3, 19 : 3) (3, 9) 24 (2, 31) (2, 21) (1, 24) (3, 32) (1, 27) (2, 20) (2, 10) (4, 33) (4, 30) (2, 12) 11 (1, 9) (3, 16) (3, 8) (4, 21) 22 (3, 14) (1, 7) (3, 9) (3, 8) (2, 22) (4, 25) (1, 13) (1, 21) (3, 25) (1, 25) 15 (2, 25) (4, 10) (3, 19) (3, 23) 23 R =6 38 (i, j) (c ij,d ij )

27 5 (1, 15) (2, 9) (3, 27) (4, 5) 20 (3, 26) (2, 16) (3, 19) (2, 30) (2, 31) (3, 8) (3, 27) (2, 14) (3, 25) (3, 17) 1 (4, 17) (1, 32) (1, 9) (3, 24) 21 (2, 29 : 6) (2, 28) (4, 24) (2, 13) (2, 33) (3, 7) (3, 25) (1, 6) (2, 5) (2, 27) (1, 19) (2, 26) (3, 19) (3, 9) (2, 21) (1, 24) (3, 32) (2, 31 : 7) (1, 27) (2, 20) (2, 10) (4, 33) (4, 30) (2, 12) 11 (1, 9) (3, 16) (3, 8) (4, 21) 22 (3, 14) (1, 7) (3, 9) (3, 8) (2, 22) (4, 25) (1, 13) (1, 21) (3, 25) (1, 25) 15 (2, 25) (4, 10) (3, 19) (3, 23) 23 R =13 28 (i, j) (c ij,d ij )

28 Δ

29 B R c d B R c d U (1, 25) U (1, 25) U (1, 20) U (0, 50) U (1, 15) U (1, 50) U (1, 10) U (1, 50) Δ Δ Δ m T α Δ m m n

30 1000 Δ m = 0 m =50 50 > 0 α Δ 0.10 R

31 R 2 m R 2 α T R 2 m R 2 α T R 2 m R 2 α T R 2 m R 2 α T Δ

32 m α T m (0.01/0.01) 100 = m (0.05/37) 100= , 2, 3 4 m n α T

33 α

34 α

35 α

36 9 2, 3 4 α T m m T m n 1000/m n m n 1000 α α

37 α ( )

38 c 1 10 d R 5 R R

39 R R 171 R =66 R R R R

40 R =1 417 R =5 212

41 R = R =66 171

42 R

43 n k n

Σχετικά έγγραφα

Approach: Romancing the Inanimate

Georgia State University ScholarWorks @ Georgia State University Art and Design Theses Ernest G. Welch School of Art and Design Summer 8-1-2013 Approach: Romancing the Inanimate Julia Gray Hines Georgia