IBM ILOG CPLEX运行配置无效及OPL模型不可行问题求助

安全阿岳

2026-6-15

枢纽选址路径问题（HLRP）求解中的约束不可行性与配置错误分析及解决方法

问题背景

使用IBM ILOG CPLEX Optimization Studio 22.1.1求解枢纽选址路径问题（Hub Location Routing Problem）时，遇到两类核心问题：

运行配置错误：在Project->(run configuration)->configuration(default)中指定CSAHLRPSTW3.mod和CSAHLRPSTW3.dat后，系统提示run configuration 'configuration' is invalid。
约束不可行性错误：通过命令行执行oplrun CSAHLRPSTW3.mod CSAHLRPSTW3.dat时，首先触发Infeasibility row 'ct5(1)': 0 = 1错误；注释ct5约束后，又出现Infeasibility row 'ct8(1)(1)': 0 >= 8错误，调整数据规模（n从4改为8）后问题依然存在。

模型文件

/*********************************************
 * OPL 22.1.1.0 Model
 * Author: 
 * Creation Date: 2025/01/05 at 1:54:46
CSAHLRPSTW3.mod
 *********************************************/
// Data section
int n = ...;  // number of nodes from node.dat
range N = 1..n;
range C = N;   // set of customers (non-hub nodes)
range H = N;   // set of potential hubs

// Data reading from external files
tuple Coordinate {
   float x;
   float y;
}
Coordinate coordinates[N] = ...;

float d[N][N] = ...; // demand matrix
float F[N] = ...;    // fixed costs for hubs
float Qh[N] = ...;   // hub capacities
int K = ...;         // number of vehicles
float t[N][N] = ...; // travel times
tuple TimeWindow {
   float start;
   float end;
}
TimeWindow timewindows[N] = ...;

// Constants
float Qv = 1100;     // vehicle capacity
float M = 1000000;   // big M
float alpha = 0.004; // unit inter-hub transportation cost
float beta = 1.0;    // unit local delivery cost
float zeta = 1.0;    // early arrival penalty coefficient
float gamma = 2.0;      // late arrival penalty coefficient

// Calculate distances between nodes
float c[i in N][j in N] = sqrt(pow(coordinates[i].x - coordinates[j].x, 2) + 
                              pow(coordinates[i].y - coordinates[j].y, 2));

// Decision Variables
dvar boolean x[N][N][H]; // routing variable
dvar boolean y[H];       // hub location variable
dvar float+ z[C][C][H][H]; // flow variable
dvar float+ u[N][H];    // pickup amount
dvar float+ v[N][H];    // delivery amount
dvar float+ s[N];       // service start time
dvar float+ P[N];       // time window penalty
dvar float+ visitOrder[i in N];  // exclude sub-tour 

// Optimization Model
minimize
    beta * sum(i in N, j in N, m in H) c[i][j] * x[i][j][m] +
    sum(m in H) F[m] * y[m] +
    alpha * sum(m in H, n in H, i in C, j in C) d[i][j] * z[i][j][m][n] * c[m][n] +
    sum(i in N) P[i];

subject to {
    //self roop protection
    forall(i in N, m in H)
    ct0:x[i][i][m] == 0;
    //return to the hubs
    forall(m in H)
    ct1:sum(i in N: i != m) x[i][m][m] == sum(j in N: j != m) x[m][j][m];
    // Constraint (2): All demand must be routed through hubs
    forall(i in C, j in C)
        ct2:sum(m in H, n in H) z[i][j][m][n] == 1;
    
    // Constraint (3): Hub capacity constraints
    forall(m in H)
        ct3:sum(i in C, j in C, n in H) d[i][j] * z[i][j][m][n] +
        sum(i in C, j in C, n in H: n != m) d[i][j] * z[i][j][n][m] <= Qh[m] * y[m];
    
    // Constraint (4): Vehicles can only depart from established hubs
    forall(m in H)
        ct4:sum(j in N) x[m][j][m] <= M * y[m];
    
    // Constraint (5): Each customer must be visited exactly once
    forall(i in C)
        ct5:sum(j in N: j != i, m in H) x[i][j][m] == 1;
    
    // Constraint (6): Flow conservation
    forall(i in N, m in H)
        ct6:sum(j in N) x[i][j][m] == sum(j in N) x[j][i][m];
    
    // Constraint (7): No inter-hub routes in local delivery
    forall(m in H)
        ct7:sum(j in N, n in H: n != m) x[n][j][m] == 0;
    
    // Constraint (8): Link between flow and routing variables
    forall(i in C, m in H)
        ct8:M * sum(j in N) x[i][j][m] >= 
        sum(j in C, n in H) z[i][j][m][n] + sum(j in C, n in H) z[j][i][n][m];
    
    // Constraint (9): Pickup load continuity
    forall(i in N, j in C, m in H: i != j)
        ct9:u[i][m] + sum(t in C, n in H) d[j][t] * z[j][t][m][n] - 
        M * (1 - x[i][j][m]) <= u[j][m];
    
    // Constraint (10): Delivery load continuity
    forall(i in C, j in N, m in H: i != j)
        ct10:v[i][m] - sum(t in C, n in H) d[t][i] * z[t][i][n][m] + 
        M * (1 - x[i][j][m]) >= v[j][m];
    
    // Constraint (11): Vehicle capacity constraint for delivery
    forall(i in C, m in H)
        ct11:v[i][m] <= Qv;
    
    // Constraint (12): Vehicle capacity constraint considering loading/unloading
    forall(i in C, m in H)
        ct12:u[i][m] + v[i][m] - sum(t in C, n in H) d[t][i] * z[t][i][n][m] <= Qv;
    
    // Constraint (13): Number of vehicles limit
    ct13:sum(m in H) sum(j in N) x[m][j][m] <= K;
    
    // Constraint (14): Time consistency
    forall(i in N, j in N, m in H)
        ct14:s[i] + t[i][j] - s[j] <= M * (1 - x[i][j][m]);
    
    // Constraint (15): Time window penalties
    forall(i in C) {
        ct15:P[i] >= zeta * (timewindows[i].start - s[i]);
        P[i] >= gamma * (s[i] - timewindows[i].end);
        P[i] >= 0;};
    //Constraint (16): prohibit subtour
    forall(i in N, j in N, m in H: i != j && i != m && j != m)
       ct16: visitOrder[i] - visitOrder[j] + n * x[i][j][m] <= n - 1;

};

// Solver configuration
execute {
    cp.tilim = 10800; // Time limit: 10800 seconds
}

数据文件

/*********************************************
 * OPL 22.1.1.0 Data
 * Author: 
 * Creation Date: 2025/01/05 at 1:55:06
 CSAHLRPSTW3.dat
 *********************************************/

n = 4;

coordinates = [
<12944.330389, 19522.690462>,
<23487.769950, 14749.226168>,
<31004.306839, 21458.349354>,
<49728.492698, 17946.318136>
];

d = [
[5.705460, 9.801600, 5.028110, 3.105340], 
[21.242070, 38.706030, 18.462480, 10.396320],
[5.763190, 9.909430, 9.328980, 8.665890],
[3.820190, 6.300870, 9.807810, 10.572880]
];

F = [
28766.736921,
28376.761527,
29774.238965,
24301.334212
];

Qh = [
2198.532635,
6106.711881,
2226.593104,
4515.466789
];

K = 4;

timewindows = [
<0,10000>,
<0,10000>,
<0,10000>,
<0,10000>

];

t = [
[0.00 233.68 19.41 529.92],
[233.68 0.00 436.25 352.77],
[19.41 436.25 0.00 339.71], 
[529.92 352.77 339.71 0.00]

];

原因分析

1. 运行配置错误

文件路径不匹配：配置中指定的mod/dat文件不在项目根目录，或文件名拼写错误。
配置类型冲突：误将MIP模型配置为CP求解器运行，或求解器版本与模型不兼容。
软件配置损坏：CPLEX Studio的默认配置文件损坏，导致配置无法加载。

2. 约束不可行性

ct5约束问题

当前模型定义C=N且H=N，即所有节点既是客户又是潜在枢纽，但存在逻辑矛盾：

ct5要求所有节点（包括枢纽）必须被访问一次，但ct7禁止跨枢纽的路径，若枢纽未被选中（y[m]=0），ct4会限制该枢纽的所有出发路径为0，导致无法满足ct5的“必须离开一次”要求。
若枢纽无需作为客户访问，C的定义错误，应将纯客户节点与枢纽节点分离。

ct8约束问题

ct8试图关联流变量z与路径变量x，但逻辑存在缺陷：

ct2强制所有客户需求必须通过枢纽流转（sum(m,n)z[i][j][m][n]=1），但当ct5被注释后，sum(j)x[i][j][m]可能为0（即节点i无路径关联枢纽m），此时右边的流量和大于0，导致0 >= 正数的矛盾。

解决方法

1. 修复运行配置错误

校验文件路径：确保mod/dat文件在项目目录下，或在配置中指定完整绝对路径。
重建运行配置：删除现有默认配置，重新创建配置并选择正确的模型、数据文件及MIP求解器。
重启软件：若配置文件损坏，重启CPLEX Studio或重新导入项目。

2. 修复约束不可行性

调整ct5约束

分离客户与枢纽节点：重新定义集合，例如将前k个节点设为潜在枢纽，剩余为纯客户：
```
range N = 1..n;
range H = 1..2; // 潜在枢纽集合
range C = 3..n; // 纯客户集合
```

修改ct5仅约束纯客户：

forall(i in C)
    ct5:sum(j in N: j != i, m in H) x[i][j][m] == 1;

修复ct8约束

补充双向关联逻辑，确保流量与路径的一致性：

forall(i in C, m in H) {
    ct8:sum(j in C, n in H) z[i][j][m][n] + sum(j in C, n in H) z[j][i][n][m] <= M * sum(j in N) x[i][j][m];
    ct8_2:sum(j in N) x[i][j][m] >= (sum(j in C, n in H) z[i][j][m][n] + sum(j in C, n in H) z[j][i][n][m]) / M;
}

当x[i][j][m]的和为0时，右边流量和必须为0；当有流量时，必须存在对应的路径。

优化其他约束一致性

调整ct7约束：若允许枢纽间的中转路径，需删除或修改该约束，否则需确保流变量z的枢纽间流转不依赖x变量。
校准大M值：将M调整为合理范围（例如最大需求总量的2倍），避免因过大导致数值计算误差。

内容的提问来源于stack exchange，提问作者八木澤友輔

IBM ILOG CPLEX运行配置无效及OPL模型不可行问题求助

问题背景 #

模型文件 #

数据文件 #

原因分析 #

1. 运行配置错误 #

2. 约束不可行性 #