CPLEX模型运行报错：表达式提取失败及数组索引越界求助

问题概述 #

刚接触CPLEX，为大学项目从零学习使用，用论文给定数据验证模型时，第一个约束出现以下错误：

-CPLEX cannot extract expression: forall...
-Index out of bound for array "y#0#0":0
-OPL cannot extract expression: forall...
-OPL cannot extract expression: sum...

原MOD文件 #

int n=...; //set of terminals
range N=1..n;

int t=...; //set of time periods
range T=1..t;

int v=...; //set of vehicles
range V=1..v;

range Np=1..n; range Vp=1..v;
   float p[Vp][Np][Np] =...;
   
range Nc=1..n; range Vc=1..v;
   float c[Vc][Nc][Nc] =...;
   
range Nd=1..n; range Td=1..t;
   float d[Td][Nd][Nd] =...;

range Nm=1..n; range Tm=1..t; range Vm=1..v;
   int m[Vm][Nm][Tm] =...;
   
range NA=1..n; range VA=1..v;
   int A[VA][NA][NA] =...;
   
range Ntau=1..n;;
   int tau[Ntau][Ntau] =...;
   
dvar boolean x[N][N][T][V]; 
dvar boolean y[N][N][T][V]; 

dexpr float f=sum(i in N,j in N:i!=j,t in T, v in V)(p[v][i][j]*x[i][j][t][v] - c[v][i][j]*y[i][j][t][v]);
   
maximize f;
subject to {
  forall(i in N, t in T, v in V)sum(j in N)(x[i][j][t][v] + y[i][j][t][v])- sum(k in N: k != i, t_ in T: t_ > tau[k][i])(x[k][i][t_-tau[k][i]][v] + y[k][i][t_-tau[k][i]][v])- y[i][i][t-1][v] == m[v][i][t];

  forall(i in N, j in N, t in T)
    sum(v in V) x[i][j][t][v] <= d[t][i][j];

  forall(i in N, j in N, t in T, v in V)
    A[v][i][j] == 0 => x[i][j][t][v] == 0 && y[i][j][t][v] == 0;

  forall(i in N, j in N, t in T, v in V)
    x[i][j][t][v] >= 0 && x[i][j][t][v] <= 1 && y[i][j][t][v] >= 0 && y[i][j][t][v] <= 1;
}

原DAT文件 #

n = 6;
t = 6;
v = 2;

c = [[  [0 1 2 2 2 2]
 [1 0 2 2 2 2]
 [2 2 0 2 1 1]
 [2 2 2 0 1 1]
 [2 2 1 1 0 1]
 [2 2 1 1 1 0]]
 
 [  [0 3 3 2 2 2]
 [3 0 3 3 2 2]
  [3 3 0 1 2 2]
  [2 3 1 0 3 3]
  [2 2 2 3 0 3]
  [2 2 2 3 3 0]]
  ]; 
  
p = [[  [0 1.8 3.6 3.6 3.6 3.6]
 [1.8 0 3.6 3.6 3.6 3.6]
 [3.6 3.6 0 3.6 1.8 1.8]
 [3.6 3.6 3.6 0 3.6 3.6]
 [3.6 3.6 1.8 3.6 0 1.8]
 [3.6 3.6 1.8 3.6 1.8 0]]
 
 [  [0 4.2 4.2 3.6 3.6 3.6]
 [4.2 0 4.2 4.2 3.6 3.6]
  [4.2 4.2 0 4.5 3.6 3.6]
  [3.6 4.2 4.5 0 4.2 4.2]
  [3.6 3.6 3.6 4.2 0 4.2]
  [3.6 3.6 3.6 4.2 4.2 0]]
  ]; 
  
//d_ijt
d = [[[0 0 0 0 0 0] 
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]]
 
  [[0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 3 0 0 0 0]
  [0 0 0 0 0 1]
  [0 0 0 0 0 0]]
  
  [[0 0 0 0 0 0]
  [0 0 3 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]]
  
  [[0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]]
  
  [[0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [2 0 0 0 0 0]
  [0 0 0 0 0 0]]
  
  [[0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]]
  ]; 
  
  
m = [[  [0 0 0 0 0 0] //m_itv
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [1 0 0 0 0 0]]
 
 [  [0 0 0 0 0 0]
 [0 0 0 0 0 0]
  [0 0 0 0 0 0]
  [0 1 0 0 0 0]
  [0 0 0 0 0 0]
  [0 0 0 0 0 0]]
  ]; 
  
A = [[  [1 0 1 1 1 1] //A_ijv
 [0 1 1 1 1 1]
 [1 1 1 1 1 1]
 [1 1 1 1 1 1]
 [1 1 1 1 1 1]
 [1 1 1 1 1 1]]
 
 [[1 0 1 1 1 1]
 [0 1 1 1 1 1]
  [1 1 1 1 1 1]
  [1 1 1 1 1 1]
  [1 1 1 1 1 1]
  [1 1 1 1 1 1]]
  ]; 
  
  
tau = [[1 2 1 1 1 2] //tau_ij
 [2 1 2 1 2 3]
 [1 2 1 1 3 2]
 [1 1 1 1 1 3]
 [1 2 3 1 1 1]
 [2 3 2 3 1 1]];

错误原因分析 #

1. 索引越界：第一个约束中的y[i][i][t-1][v]，当t=1时，t-1=0，超出了时间范围T=1..t，导致数组索引越界，这是报错的核心原因。
2. 无效的时间范围：第二个求和项sum(k in N: k != i, t_ in T: t_ > tau[k][i])中，t_-tau[k][i]可能小于1，导致x[k][i][t_-tau[k][i]][v]和y[k][i][t_-tau[k][i]][v]的时间索引超出有效范围，OPL无法提取该表达式。

修正方案 #

• 针对t=1的情况，添加条件判断：当t>1时取y[i][i][t-1][v]，否则该项为0。
• 修正第二个求和的时间范围，确保t_-tau[k][i]落在有效时间区间内，将t_ in T: t_ > tau[k][i]改为t_ in tau[k][i]+1..t，这样t_-tau[k][i]的最小值为1，最大值为t-tau[k][i]，均在T范围内。

修正后的MOD文件 #

int n=...; //set of terminals
range N=1..n;

int t=...; //set of time periods
range T=1..t;

int v=...; //set of vehicles
range V=1..v;

range Np=1..n; range Vp=1..v;
   float p[Vp][Np][Np] =...;
   
range Nc=1..n; range Vc=1..v;
   float c[Vc][Nc][Nc] =...;
   
range Nd=1..n; range Td=1..t;
   float d[Td][Nd][Nd] =...;

range Nm=1..n; range Tm=1..t; range Vm=1..v;
   int m[Vm][Nm][Tm] =...;
   
range NA=1..n; range VA=1..v;
   int A[VA][NA][NA] =...;
   
range Ntau=1..n;
   int tau[Ntau][Ntau] =...;
   
dvar boolean x[N][N][T][V]; 
dvar boolean y[N][N][T][V]; 

dexpr float f=sum(i in N,j in N:i!=j,t in T, v in V)(p[v][i][j]*x[i][j][t][v] - c[v][i][j]*y[i][j][t][v]);
   
maximize f;
subject to {
  // 修正后的第一个约束
  forall(i in N, t in T, v in V)
    sum(j in N)(x[i][j][t][v] + y[i][j][t][v]) 
    - sum(k in N: k != i, t_ in tau[k][i]+1..t)(x[k][i][t_-tau[k][i]][v] + y[k][i][t_-tau[k][i]][v]) 
    - (if t>1 then y[i][i][t-1][v] else 0) 
    == m[v][i][t];

  forall(i in N, j in N, t in T)
    sum(v in V) x[i][j][t][v] <= d[t][i][j];

  forall(i in N, j in N, t in T, v in V)
    A[v][i][j] == 0 => x[i][j][t][v] == 0 && y[i][j][t][v] == 0;

  // boolean变量默认0/1，此约束可省略，保留也不影响
  forall(i in N, j in N, t in T, v in V)
    x[i][j][t][v] >= 0 && x[i][j][t][v] <= 1 && y[i][j][t][v] >= 0 && y[i][j][t][v] <= 1;
}

内容的提问来源于stack exchange，提问作者tomasb21