二次規(guī)劃解法

1、2、對于二次規(guī)劃模型求解問題 1：先求出 c ，結果如下表：ij330.7320.3300.2258.6198180.5163.1181.2224.2 252256266281.2288302370.7360.3345.2326.6266250.5241226.2269.2297301311326.2333347385.7375.3355.2336.6276260.5251241.2203.2237241251266.2273287420.7410.3395.2376.6316300.5291276.2244.2222211221236.2243257410.7400.3380.2361.63

2、01285.5276266.2234.2212188206226.2228242415.7405.3385.2366.6306290.5281271.2234.2212201195176.2161178435.7425.3405.2386.6326310.5301291.2259.2237226216198.2185162由于二次規(guī)劃模型中約束條件藝X G0u500,s ,i二1,2,7，的存 jij=1在，必須加以處理。引進0-1變量n ,i = 1,2,15，貝UiIlX G0u500,s ,i = 1,2,7,可以等價轉(zhuǎn)換為下面的三個約束條件：jij=1L X sij ij=1L15 X

3、 500*nijij=1其中 M 為一個很大數(shù)。這樣就可以得到下面的 lingo 程序：sets:s/1.7/:sx;a/1.15/:z,y,n,t;links(s,a):c,x;endsetsdata: sx=800 800 1000 2000 2000 2000 3000;t=104 301 750 606 194 205 201 680 480 300 220 210 420 500 0;c=330.7 320.3 300.2 258.6 198 180.5 163.1 181.2252 256 266 281.2 288 302360.3 345.2 326.6 266 250.5 2

4、41 226.2297 301 311 326.2 333 347375.3 355.2 336.6 276 260.5 251 241.2237 241 251 266.2 273 287410.3 395.2 376.6 316 300.5 291 276.2222 211 221 236.2 243 257400.3 380.2 361.6 301 285.5 276 266.2212 188 206 226.2 228 242405.3 385.2 366.6 306 290.5 281 271.2212 201 195 176.2 161 178425.3 405.2 386.6 3

5、26 310.5 301 291.2237 226 216 198.2 185 162renddata!目標函數(shù); min=sum(links:c*x)+0.05*sum(a(j):z(j)*(z(j)+1)+ y(j)*(y(j)+1);!每個工廠產(chǎn)量的限制;for(s(i):sum(a(j):x(i,j)=sx);for(s(i):sum(a(j):x(i,j)=500*n(i); !每個結點運量的限制;for(a(j):sum(s(i):x(i,j)=z(j)+y(j);!區(qū)間長度的限制;for(a(j)|j#le#14:z(j+1)+y(j)=t(j);!初始條件;z(1)=0;y(1

6、5)=0;!設置0-1變量;for(a(j):bin(n(j);Local optimal solution found at iteration:5800Objective value: 1278632.問題3sets:s/1.7/:sx; a/1.21/:z,y,n,t; links(s,a):c,x;endsets data:sx=800 800 1000 2000 2000 2000 3000;t=104 301 750 606 194 205 201 680 480 300 220 210 420 500 0 0 0 0 0 0 0;c=330.7 320.3 300.2 258.6

7、 198 180.5 163.1 181.2252 256 266 281.2 288 302220 255260265275 285360.3 345.2 326.6 266 250.5 241 226.2297 301 311 326.2 333 347265 300 305 310 320330375.3 355.2 336.6 276 260.5 251 241.2237 241 251 266.2 273 287199240 245 250 260 270410.3 395.2 376.6 316 300.5 291 276.2222 211 221 236.2 243 257240

8、210 215 220 230 240400.3 380.2 361.6 301 285.5 276 266.2212 188 206 226.2 228 242230187 205 205 220 230405.3 385.2 366.6 306 290.5 281 271.2212 201 195 176.2 161 178230200 183 186 160 150425.3 405.2 386.6 326 310.5 301 291.2237 226 216 198.2 185 162245225 210 215 192 189;enddata!目標函數(shù);min=sum(links:c

9、*x)+0.05*sum(a(j):z(j)*(z(j)+1)+y(j)*(y(j)+1)+0.05*yd1*(yd1+1)+0.05*yd2*(yd2+1)+0.05*yd3*(yd3+1);!每個工廠產(chǎn)量的限制;for(s(i):sum(a(j):x(i,j)=sx);for(s(i):sum(a(j):x(i,j)=500*n(i);!每個結點運量的限制;for(a(j)|j#ne#9 #and# j#ne#11 #and#j#ne#17:sum(s(i):x(i,j)=z(j)+y(j);sum(s(i):x(i,9)=z(9)+y(9)+yd1;sum(s(i):x(i,11)=z(11)+y(11)+yd2;sum(s(i):x(i,17)=z(17)+y(17)+yd3;!區(qū)間長度的限制;for(a(j)|j#le#14:z(j+1)+y(j)=t(j)y(16)+yd1=42;y(17)+yd2=10;z(17)+y(18)=130;yd3+y(19)=190;z(19)+y(20)=260;z(20)+y(21)=100;!初始條件;z(1)=