O verlay A lgo rithm of H ierarch ical M ap s

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1 (2004) , 1, 2 2, (1., ; 2., ), 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 , Ch ina; 2. Guangzhou N avy A cadem y, Guangzhou , 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, ,, ; 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 ] 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) ], (02GJ ) (1959- ),,,

2 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)

3 ) 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)

4 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 k- 1 8 k (14), X = ,, 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)

5 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 = , ( ) 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,

6 10 59, B A = x 1 x 2 x 3 x 4 x 5 F 1 F 2 F 3 F 4 F 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 = [ ] (24) (17) A Y = (18) Y Z = (19) x 3 = ( ) x - = ( ) (20) S 3 i = z i - x 3 = ( , , , , ) T S ī = z i - x - = ( , , , , ) T (28) (21) C i = ( ) T (29) x 2 x1 x 4 x5 x 3 (25) (26) (27) 5,, M G IS, TO PS IS [1 ],. [J ]., 2001, (3) 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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