[理学]02 LINGO.ppt

model: sets: constraint/1..7/:b; variable/1..7/:c,x; matrix(constraint,variable):A; endsets min=@sum(variable:c*x); @for(constraint(i): @sum(variable(j):A(i,j)*x(j))=b(i)); @for(variable:@gin(x)); data: c=1 1 1 1 1 1 1; b=50 50 50 50 50 90 90; A=1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1; enddata end 0－1规划 （0－1 programming） 旅行商问题 模型： min=8*x12+5*x13+6*x14+6*x21+8*x23+5*x24+7*x31+9*x32+5*x34+9*x41+7*x42+8*x43; x12+x13+x14=1; x21+x23+x24=1; x31+x32+x34=1; x41+x42+x43=1; x21+x31+x41=1; x12+x32+x42=1; x13+x23+x43=1; x14+x24+x34=1; u2-u3+4*x23=3; u2-u4+4*x24=3; u3-u2+4*x32=3; u3-u4+4*x34=3; u4-u2+4*x42=3; u4-u3+4*x43=3; @bin(x11);@bin(x12);@bin(x13);@bin(x14); @bin(x21);@bin(x22);@bin(x23);@bin(x24); @bin(x31);@bin(x32);@bin(x33);@bin(x34); @bin(x41);@bin(x42);@bin(x43);@bin(x44); @free(u1);@free(u2);@free(u3);@free(u4); model: sets: city/1..4/:u; link(city,city):dist,x; endsets data: dist=0 8 5 6 6 0 8 5 7 9 0 5 9 7 8 0; enddata n=@size(city); min=@sum(link:dist*x); @for(city(k):@sum(city(i)|i #ne# k:x(i,k))=1; @sum(city(j)|j #ne# k:x(k,j))=1;); @for(city(i):@for(city(j)|j #gt# 1 #and# i #ne# j: u(i)-u(j)+n*x(i,j)=n-1);); @for(city(i):u(i)=n-1); @for(link:@bin(x)); end 背包问题 模型： model: sets: WP/WP1..WP8/:A,c,x; endsets data: A=1 3 4 3 3 1 5 10; c=2 9 3 8 10 6 4 10; enddata max=@sum(WP:c*x); @sum(WP:A*x)=15; @for(WP:@bin(x)); end min=2*x1+9*x2+3*x3+8*x4+10*x5+6*x6+4*x7+10*x8; x1+3*x2+4*x3+3*x4+3*x5+x6+5*x7+10*x8=15; @bin(x1);@bin(x2);@bin(x3);@bin(x4); @bin(x5);@bin(x6);@bin(x7);@bin(x8); 指派问题 模型： …… model: sets: Worker/W1..W5/; Job/J1..J5/; links(Worker,Job):c,x; endsets data: c=4,8,7,15,12, 7,9,17,14,10, 6,9,12,8,7, 6,7,14,6,10, 6,9,12,10,6; enddata max=@sum(links:c*x); @for(Worker(i):@sum(Job(j):x(i,j))=1); @for(Job(j):@sum(Worker(i):x(i,j))=1); @for(links:@bin(x)); end …… 非线性规划 （nonlinear programming） 模型: