多目标规划问题Matlab示例_fgoalattain

多目标规划问题：

x = fgoalattain(fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon,... options) minimizes with the optimization options specified in the structure options.

Use optimset to set these options.

例子：三个目标函数：求最大值的：

f(1)=0.082*x(1)+0.072*x(2)+0.065*x(3)+0.054*x(4)+0.038*x(5)+0.057*x(6)+0.045*x(7)求最小值的：

f(2)=0.072*x(1)+0.063*x(2)+0.057*x(3)+0.05*x(4)+0.032*x(5)+0.0442*x(6)+0.0675*x(7)f(3)=128*x(1)+78.1*x(2)+64.1*x(3)+43*x(4)+58.1*x(5)+36.9*x(6)+50.5*x(7)

约束条件：

0.082*x(1)+0.072*x(2)+0.065*x(3)+0.054*x(4)+0.038*x(5)+0.057*x(6)+0.045*x(7)>=7.2

0.072*x(1)+0.063*x(2)+0.057*x(3)+0.05*x(4)+0.032*x(5)+0.0442*x(6)+0.0675*x(7)<=264.4

128*x(1)+78.1*x(2)+64.1*x(3)+43*x(4)+58.1*x(5)+36.9*x(6)+50.5*x(7)<=69719

lb=[0,0,0,0,0,0,0]

ub=[426,390,430,374,445,534,476]

f(1),f(2),f(3)的权值分别是：0.193，0.083，0.724 %======================

function z=fgoalattain

% 多目标最优化

clear all; clc

% 给定目标，权重按目标比例确定，给出初值

options = optimset('TolCon',1e-008)

goal = [-7 264 69000];

weight = [0.193 0.083 0.724];

x0 = [1 1 1 1 1 1 1];

% 给出约束条件的系数

A=[-0.082 -0.072 -0.065 -0.054 -0.038 -0.057 -0.045;0.072 0.063 0.057 0.05 0.032 0.0442 0.0675;128 78.1 64.1 43 58.1 36.9 50.5]

B=[-7.2; 264.4;69719]

Aeq = [];

Beq = [];

lb=[0,0,0,0,0,0,0]

ub=[426,390,430,374,445,534,476]

% 求解

[x,fval,attainfactor,exitflag] = fgoalattain(@ObjFun,x0,goal,weight,A,B,Aeq,Beq,lb,ub)

% ------------------------------------------------------------------

function f = ObjFun(x)

f1=0.082*x(1)+0.072*x(2)+0.065*x(3)+0.054*x(4)+0.038*x(5)+0.057*x(6)+0.045*x(7);

f2=0.072*x(1)+0.063*x(2)+0.057*x(3)+0.05*x(4)+0.032*x(5)+0.0442*x(6)+0.0675*x(7);

f3=128*x(1)+78.1*x(2)+64.1*x(3)+43*x(4)+58.1*x(5)+36.9*x(6)+50.5*x(7);

f=[-f1;f2;f3];

结果：

A =

-0.0820 -0.0720 -0.0650 -0.0540 -0.0380 -0.0570 -0.0450

0.0720 0.0630 0.0570 0.0500 0.0320 0.0442 0.0675

128.0000 78.1000 64.1000 43.0000 58.1000 36.9000 50.5000

B =

1.0e+004 *

-0.0007

0.0264

6.9719

lb =

0 0 0 0 0 0