2004 10 10 100026788 (2004) 1020054207 1, 1, 2 2, (1., 430074; 2., 510430), M G IS (m ilitary geograph ic info rm ation system ), ; ; F282 A T he M u lti2ob jective L ocation M odel Based on O verlay A lgo rithm of H ierarch ical M ap s W EN G Dong2feng 1, FE I Q i 1, L IU X iao2jing 2, J IAN G Yun 2 ( 1. In stitu te of System Engineering, H uazhong U n iversity of Science and T echno logy, W uhan 430074, Ch ina; 2. Guangzhou N avy A cadem y, Guangzhou 510430, Ch ina) Abstract T h is paper gives an analysis of the objects and restriction conditions of the defense facility location, and a m ultiobjective model of the facility location is set up. By using the overlay algo rithm of the theo ry of m ilitary geograph ic info rm ation system, the p roblem of search ing feasible set o r lim ited schem es in decision space based on overlay algo rithm of h ierarch ical m ap s com es up. T he so lu tion m ethod by constructing the criterion decision m atrix of facility location is put fo rw ard, and an examp le is given. Key words facility location; m ulti2objective decision m ak ing; model 1, 20 60 70,, ; 80 90, [ 1 ] ; n q i (qi1, q i2) (i = 1, 2,, n), x (x 1, x 2), m ax i{gx 1 - q i1g + gx 2 - q i2g } (M in- M ax) F rancis [ 2 ] 20 60 H alpern [ 3 ] M cginn is W h ite [ 4 ] H an sen [ 5 ], O h saw a Im ai [ 6, 7 ] [ 8 (B icriteria M odel) ], 2003204226 (02GJ 207-026) (1959- ),,,
10 55 [9 ]- [12 ], (m ilitary geograph ic info rm ation system, M G IS), [ 13, 14 ] 2 8, x = (x 1, x 2), q i = (qi1, qi2) (i = 1, 2,, n), n, s j = (sj1, sj2) (j = 1,, m ), m, rk = (rk1, rk2) (k = 1,, p ), p 1), ( ) m in im ax, m in 1 (x) = m ax w i x - i {1,, n } q i, (1) w i i 2),,, m in im izef 2 (x) = 6 m w j x - j= 1 s j, (2) w j j 3),,,, m ax im in w k m ax F 3 (x) = k m in w k x - rk, (3) k { 1,, p } 4) P 1, P 2, P 3 m ax F 4 (x) = 1 - P 1 (1 - P 2) P 3. (4) 5) C l (l = 1, 2,, s), m in F 5 (x) = 6 s C l. (5) (1) - (3), (4) (5)
56 2004 10 1) t1 v 1 d 1 = v 1t1, q i g Φ d 1. (6) 2) t2 v 2 d 2 = v 2t2 s jg Φ d 2. (7) j {1,, m } 3), d 3 k {1,, p } rkg Ε d 3. (8) 4),, d 4 S (x) S (x) Ε d 4. (9) 5) 8, d 5 V (x) V (x) Ε d 5. (10) 6) d 6 d 6 Φ 1 - P 1 (1 - P 2) P 3 Φ 1. (11) 7),,,, d 7, 6 s C l Φ d 7. (12),, D R m inf 1 (x) = m ax x 8 F 3 (x) = m in F 5 (x) = 6 s C l s. t. q i g Φ d 1, s j g Φ d 2, j {1,, m } rk k {1,, p } S (x) V (x) Ε d 4, Ε d 5, g Ε d 3, m ax w i x - m in w k x - k { 1,, p } x 8 q i, m in im izef 2 (x) = 6 m w j x - j= 1 j (1,, m ) rk, m ax F 4 (x) = 1 - P 1 (1 - P 2) P 3, s j, (13)
10 57 d 6 Φ 1 - P 1 (1 - P 2) P 3 Φ 1, 6 s C l Φ d 7. 3 (13) (overlay), ; (T echn ique fo r O rder P reference by Sim ilarity to Ideal So lu tion, TO PS IS) 1) (M G IS) (6) - (12) 8 k 2) (TRU E, FAL SE) 8 1,, 3) 8 3 = 8 1 8 2,, 8 k- 1 8 k (14), X = 8 1 8 2,, 8 k- 1 8 = {x 1,, x n} (15),,, [ 15 V o rono i ], (2), 4) (13) A = x 1 x 2 g x n F 1 (x) F 2 (x) F m (x) x 11 x 12 x 1m x 21 x 22 x 2m x n1 x n2 x nm 5) TO PS IS, A Y = (y ij) n m, g (16) x ij y ij =, i = 1,, n; j = 1,, m. (17) 6 n x 2 ij i= 1, Y Z = (z ij) n m, w j j, x 3 j x - j x 3 j z ij = w j y ij, i = 1,, n; j = 1,, m. (18) = m ax i z ij, j T 1; x 3 j = m in i z ij, j T 2 x - j = m in z i ij, j T 1; x 3 j = m axz i ij, j T 2. T 1 T 2 (19)
58 2004 10 S 3 i = z i - x 3, i = 1,, n. S ī = z i - x -, i = 1,, n. (20) C i = S ī g(s 3 i + S ī ), 0 Φ C i Φ 1; i = 1,, n. (21), C i 4 B q i g Φ d 1 = 150km, s j g Φ d 2 = 300km, j {1,, m } rk k {1,, p } g Ε d 3 = 30km, S (x) Ε d 4 = 0. 2km 2, S (x) Ε d 4 = 0. 5km 2, (22) V (x) Ε d 5 = 4tgm 2, V (x) Ε d 5 = 7m, 6 s C l Φ d 7 = 260000, ( ) S (x), S (x), V (x), V (x) ; d 4, d 4, d 5, d 5 (13) 9 8 M G IS, 9 X 1 1, X,
10 59, B A = x 1 x 2 x 3 x 4 x 5 F 1 F 2 F 3 F 4 F 5 120 220 105 0. 65 230000 102 230 94. 5 0. 55 210000 130 181 73. 5 0. 73 245000 98 270 84 0. 60 225000 145 280 126 0. 75 250000 x 1,, x 5, F 1 m in im ax, F 2 m in isum, F 3 m ax im in, F 4, F 5, A H P (23) w j = [0. 3191 0. 2051 0. 2251 0. 1280 0. 1227 ] (24) (17) A Y = 0. 4462 0. 4118 0. 4778 0. 4402 0. 4425 0. 3793 0. 4306 0. 4300 0. 3725 0. 4040 0. 4834 0. 3388 0. 3345 0. 4944 0. 4714 0. 3644 0. 5054 0. 3823 0. 4063 0. 4329 0. 5391 0. 5242 0. 5734 0. 5079 0. 4810 (18) Y Z = 0. 1424 0. 0845 0. 1076 0. 0564 0. 0543 0. 1210 0. 0883 0. 0968 0. 0477 0. 0496 0. 1542 0. 0695 0. 0753 0. 0633 0. 0578 0. 1163 0. 1037 0. 0860 0. 0520 0. 0531 0. 1720 0. 1075 0. 1291 0. 0650 0. 0590 (19) x 3 = (0. 1163 0. 0695 0. 1291 0. 0650 0. 0496) x - = (0. 1720 0. 1075 0. 0753 0. 4769 0. 0590) (20) S 3 i = z i - x 3 = (0. 03828, 0. 04145, 0. 06637, 0. 05657, 0. 68140) T S ī = z i - x - = (0. 05049, 0. 05935, 0. 04479, 0. 05739, 0. 05650) T (28) (21) C i = (0. 56874 0. 58879 0. 40296 0. 50358 0. 45332) T (29) x 2 x1 x 4 x5 x 3 (25) (26) (27) 5,, M G IS, TO PS IS [1 ],. [J ]., 2001, (3) 45-48. W eng Dongfeng, Fei Q i. Scien tific decision2m ak ing on defence engineering con struction under heigh t tech condition s
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