Gams math 可以直接在GAMS中求解双目标模型吗？

有没有可以直接求解多目标模型的命令？ 我的意思是，如果不使用加权和或ε约束方法，我们能在gams中解决多目标模型吗

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非常感谢

这是GAMS中的ε约束模型，适用于解决双目标优化问题和寻找帕累托最优前沿

$title Pareto optimal front determination

$onText
For more details please refer to Chapter 2 (Gcode2.16), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
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Model type: NLP
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Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
$offText

Variable of1, of2, x1, x2;
Equation eq1, eq2, eq3, eq4;

eq1.. 4*x1 - 0.5*sqr(x2) =e= of1;
eq2.. -sqr(x1) + 5*x2    =e= of2;
eq3.. 2*x1 + 3*x2        =l= 10;
eq4.. 2*x1 -   x2        =g=  0;

x1.lo = 1; x1.up = 2;
x2.lo = 1; x2.up = 3;

Model pareto1 / all /;

Set counter / c1*c21 /;
Scalar E;
Parameter report(counter,*), ranges(*);

solve pareto1 using nlp maximizing of1;
ranges('OF1max') = of1.l;
ranges('OF2min') = of2.l;

solve pareto1 using nlp maximizing of2;
ranges('OF2max') = of2.l;
ranges('OF1min') = of1.l;

loop(counter,
   E = (ranges('OF2max') - ranges('OF2min'))*(ord(counter) - 1)/(card(counter) - 1) + ranges('OF2min');
   of2.lo = E;
   solve pareto1 using nlp maximizing of1;
   report(counter,'OF1') = of1.l;
   report(counter,'OF2') = of2.l;
   report(counter,'E')   = E;
);
display report;