fgoalattain
标规划优问题多目化
fgoalattain
工程应用中fgoalattain 函数调用格式如下：
[x,fval]=fgoalattain (fun,x0,goal,weight,A,b,Aeq,beq,lb,ub,nonlcon)
help fgoalattain
FGOALATTAIN Solves the multi-objective goal attainment optimization problem.
Solve minimize value problem.
X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B) solves the goal attainment problem subject to the linear inequalities A*X <= B .
X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq) solves the goal attainment problem
subject to the linear equalities Aeq*X = Beq as well.
X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq,LB,UB) defines a set of lower and upper bounds on the design variables, X, so that the solution is in
the range LB <= X <= UB. Use empty matrices for LB and U if no bounds
exist. Set LB(i) = -Inf if X(i) is unbounded below; set UB(i) = Inf if X(i) is
unbounded above.
X=FGOALATTAIN(FUN,X0,GOAL,WEIGHT,A,B,Aeq,Beq,LB,UB,NONLCON) subjects the
goal attainment problem to the constraints defined in NONLCON (usually an
M-file: NONLCON.m). The function NONLCON should return the vectors
C and Ceq, representing the nonlinear inequalities and equalities respectively,
when called with feval: [C, Ceq] = feval(NONLCON,X). FGOALATTAIN
optimizes such that C(X)<=0 and Ceq(X)=0.
For more details, type the M-file FGOALATTAIN.M.
See also OPTIMSET, OPTIMGET.
例1. 程序（利用fgoalattain 函数求解）
23222
12
3222132min )3()2()1(min x x x x x x ++?+?+?
0,,6
..321321≥=++x x x x x x t s
①建立M 文件.
function y = fun(sol, options)
%([sol, eval]提示未定义)
x1 = sol(1);
x2 = sol(2);
x3 = sol(3);
%y1=y(1);
%y2=y(2);
y(1) = (x1-1)^2+(x2-2)^2+(x3-3)^2;
y(2) = x1^2+2*x2^2+3*x3^2;
②在命令窗口中输入.
[x, feval] = fgoalattain('fun', [1 1 1], [1 1], [1 1], [], [], [1 1 1], [6], [0 0 0], [])
③得到结果.
lower upper ineqlin ineqnonlin
2
x =
3.2727 1.6364 1.0909
feval =
8.9422 19.6364
例2.某钢铁公司因生产需要欲采购一批钢材，市面上的钢材有两种规格，第1种规格的单价为3500元/t ，第2种规格的单价为4000元/t.要求购买钢材的总费用不超过1000万元，够得钢材总量不少于2000t.问如何确定最好的采购方案，使购买钢材的总费用最小且购买的总量最多.
解：设采购第1、2种规格的钢材数量分别为和.根据题意建立如下多目标优化问题的数学模型.
1x 2x 0,2000
100000
40003500max 40003500)(min
212121211≥≥+≤++=x x x x x x x x x f ①建立M 文件. 在Matlab 编辑窗口中输入：
function y = fun(sol)
x1 = sol(1);
x2 = sol(2);
y = 3500*x1 + 4000*x2;
②在命令窗口中输入.
[x, feval] = fgoalattain('fun', [1 1],[1], [10000000], [3500 4000; -1 -1], [10000000; -2000], [], [], [0 0], []) %初始值的要求可以不严，但目标值关键，设置要贴近
Optimization terminated successfully:
Magnitude of directional derivative in search direction
less than 2*options.TolFun and maximum constraint violation
is less than options.TolCon
Active inequalities (to within options.TolCon = 1e-006):
lower upper ineqlin ineqnonlin
2 1
x =
1.0e+003 *
1.0000 1.0000
feval =
7.5000e+006