### 论文研究-大规模含整变量多目标决策基于目标期望水平的交互式分解协调方法.pdf

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19969 (MOP f(x)f(x)f,厂 fi(x f=(71,f2,,f (MOP) 4 (MOP) f1(x)f;, f1(x) (MOP) f1(x)<f;, f:(x) 6 (MOP) fi (x)-fi fi (x) (MOP) fi(x)fi(i (M OP 4 (MOP) (AP1) fi (x)-hi; fi (API fj H(=1,2,,n) 8 hi= G-C (AP1) (MOP) MOP f1(x)∫j(x)(j=1,2,n), h h ∑x h ∑ ∑ fi(e)-fi ∑1-∑>∑ (AP1) 9 33 (AP1) (MOP) (AP1) A, f(x)-ui hi fi fi (x)< u h;+fi H; hi+fi f1(x) (MOP (AP1) △=hj fk(x),△fkh (2c) f1(x)-fhj=1,2,,n △fk=fk(x)-f>h h fi(x)-fi ∑ fi (x)-fi h μk> ∑(x-=∑=+Ax= ∑(x)-+A>∑+ ∑ ∑(x)->∑可, G ∑ h ∑>∑ (AP1) (AP1) (MOP) 共<0 0(2) fi c 0 K仝{kf(x) k(1,2,,n)},/(j(1,2,,n)\K f k(x)) (5a) G (AP2) fi (x)-uih; fi,jJ (5c) fk(x) fk,h K (5d) (AP1) (AP2)J=[1,2,,n,K (AP2) 19969 (x, u; ),j J (AP2) (MOP) (M OP) f(x)fi c fi(x)-fi f(x)-fi h fr(a) fk(x) f K ∑ ∑/(x)∑ ∑1Ax-+∑/(x)>∑ ∑ ∑山+∑f( AP2) AP (MOP) (M OP) K J G fk(x) fkh k fi(x)-fi (AP1) (AP1)(AP2) (M OP) (AP (AP2) (AP1) (AP2) (AP2) (AP2) [5] (AP2) z-m ax ∑+∑∑fa(x) (6a) gi(xi) (6c) (6d) 9 35 ∑:(x)-4h17 (6e) ∑ (a i) fk, h K 1.2 (P),x ni n? (P) gi,g( m ax ∑山+∑∑f(x) ∑ B h(x)0 (7c) (7d) fi uih+ (7e) (7r gi(x g (7g) (7h) fik(xi) f (7i) (7k) ih (71) gi g (7n g (7n ik f ik f i (7 J, kK z(U U max μ+ 空∑/x)+空g- 1 K (LR) +∑∑v(-f+∑∑ s. t h2(x)0 ∑f。Hh+f 36 19969 ∑47 gi (x i fii(xi f fik(xi f fi=fi fi f 1,2 J, kK S∑+S+S∑n+S∑ h(x)0 g:(x) fik(xi)fk =1,2, kK t m ax ∑-∑-∑∑0)+∑∑,( ;h;+ ∫; f ik f k fik f ik fik i=1.2 kK m ax iht it ligi h(x)0 gi(x fii(x i fi 9 37 J,kK +ma∑-∑-∑∑v(f1)-∑∑”a(fa s. t ∑ ∑/7 8i gi gi i fi gi fik fik fsk kK (LP P+1 (u,)=ma∑fa(x)+ug1+∑”+∑fk ga hi(xi) 0 9 (SPi (ui, vi)) gi (x i) (9d fi (xi f 9e) f ik( i fik kK Z(u,n)=max∑-∑ uig ∑v(f)-∑∑”a(fa (10a) (SP0(u,) ∑/h+7 (10c) (10d (10e) f: fi g kK 19969 Z(l,v1)+z0(u,D) (11) U, D (LDD) 2(u, v)= m in >z: (u:;, v)+Zo(u, vy min ik(xi)+ uil gi-gi ∑∑-+∑∑ +∑ S1m∑ ∑(7-f7 (1 (LDD:) (ui, vi)=min ∑ fin(xi)+uicg U; i C i-fu) (LDD) (LDD) (P+1) ,(SP0(u,v))(SP(u2,U)) (14) (P)( LDD (u,n) (P) (LDD) (LDD) (P) SP Zi O x>fiki+uig:+ D Dibf 5a k K h(x)0 (15c) ( SPi(ui, vi) gi(xi) gi fi(xi) f (15e) f ik(x i) f (15f) J, kK fi=(i,f g (SP(u1,U)) (x,f,g)(t=2,,k)(S (x,f,.)=∑ lig (15a) 9 39 ,f},g1)4(x2,f2,g2) 1(x,广,g含 (16) B=∑wx,f,g (17 (P) 8 max ∑A+∑∑∑((x)At 18a) ∑∑ ∑∑(x)-u17 (18c) ∑∑(;(x)F.kK (18d) ∑N 18e) t=1,2,,h (18f SPi(ui, vi)) MP 0 (17 UB (MP) (A"),p LB=Z= ∑+∑∑((x(x) (19) UB-LB (20) 06=W(x1,f},g!)-4(x,f,g) (21) ψ(x},f},g2)-△ (MP) 6 6;△(i=1,2 P LB LB LB<z (SPi(ui, vi)) (x÷f,g),t>k,W( g >LB ∑(xf},g)+W(xf ∑(x,/},g1)+(x+,fH,g)+(x:/;g)+z0(a, =UB-6UB-△=LB LB 4 (SP(u,), 4(xis fissi<ri (P) SPi(ui, vi)) t s) (xsf, gi)<ri z LB ∑(x,f},g)+业 0(u,) ∑Wx

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