有没有办法在 CPLEX 中计算 multi objective？

Question

我的问题有 2 个 objective 函数，我尝试了“staticLex”，但它向我显示错误：“CPLEX（默认）无法提取表达式：最小化 nulti crit [2] {-> e1-> e2->}->."

dexpr float e1 = sum(k in Day)(W [k])^2;
dexpr float e2 = sum(i in Task) (q [i]*n[i]*m[i]);
minimize staticLex(e1, e2);
//Error:"CPLEX(default) cannot extract expression: minimize nulti crit [2] {-> e1-> e2->}->."

是否有任何方法可以修复此错误或任何其他方法来计算 CPLEX 中的多 objective 问题？提前致谢！

我的完整代码：

int NumbDay =...;
int NumbTask =...;

range Day = 1 .. NumbDay;
range Task = 1 .. NumbTask;

float h [Day]=...;
float c [Day]=...;
float d [Day]=...;
float R [Task]=...;
float E [Task]=...;
float O [Task]=...;
float t [Task]=...;

dvar float+ q [Task];
dvar float+ n [Task];
dvar float+ m [Task];
dvar float+ W [Day];
dvar boolean X [Day][Task];

execute PRE_PROCESSING {
  cplex.epgap = 0.1;
  cplex.tilim = 100;
}

dexpr float e1 = sum(k in Day)(W [k])^2;

dexpr float e2 = sum(i in Task) (q [i]*n[i]*m[i]);

minimize staticLex(e1, e2);

subject to 
{
    constraint_1:
        forall (k in Day){
            sum(i in Task) t [i]*X [k][i] == W [k];
    }  
    constraint_2:
        forall (i in Task){
            sum(k in Day) X [k][i] == 1;
    }
    constraint_3:
        forall (k in Day, i in Task){
            X [k][i] == 0 || X [k][i] == 1;
    }
    constraint_4:
        forall (i in Task){
            sum(k in Day) X [k][i] * h [k] <= R [i];
    }
    constraint_5:
        forall (k in Day, i in Task){
            q [i] == R [i] - sum(k in Day) X [k][i] * h [k];
    }
    constraint_6:
        forall (i in Task){
            sum(k in Day) X [k][i] * c [k] <= E [i];
    }
    constraint_7:
        forall (k in Day, i in Task){
            n [i] == E [i] - sum(k in Day) X [k][i] * c [k];
    }
    constraint_8:
        forall (i in Task){
            sum(k in Day) X [k][i] * d [k] <= O [i];
    }
    constraint_9:
        forall (k in Day, i in Task){
            m [i] == O [i] - sum(k in Day) X [k][i] * d [k];
    }
}

Answer 1

  q [i] * n [i]* m [i]

不是线性的。

您可以尝试使用线性表达式或使用 cpoptimizer 吗？

有没有办法在 CPLEX 中计算 multi objective？

Is there a way to calculate multi objective in CPLEX?

mathematical-optimization

cplex

opl