AMPL报错：hw3.dat中b[1]已定义，求问题排查方案

问题描述 #

使用AMPL求解最小费用网络流模型时，hw3.dat文件第14行出现b[1] already defined错误，尝试重命名参数b后问题依旧，附上model和dat文件请求排查。

报错信息 #

hw3.dat, line 14 (offset 262):
b[1] already defined
context: 1 1 >>> ; <<<

MODEL FILE #

# AMPL model for the Minimum Cost Network Flow Problem
#
# By default, this model assumes that b[i] = 0, c[i,j] = 0,
# l[i,j] = 0 and u[i,j] = Infinity.
#
# Parameters not specified in the data file will get their default values.
reset;
options solver cplex;
set NODES;                        # nodes in the network
set ARCS within {NODES, NODES};   # arcs in the network
set english;
set french;
param b {NODES} default 0;        # supply/demand for node i
param c {ARCS}  default 0;        # cost of one unit of flow on arc(i,j)
param l {ARCS}  default 0;        # lower bound on flow on arc(i,j)
param u {ARCS}  default Infinity; # upper bound on flow on arc(i,j)
var x {ARCS};                     # flow on arc (i,j)
maximize cost: sum{(i,j) in ARCS} c[i,j] * x[i,j];  #objective: minimize 
#arc flow cost


subject to flow_balance {i in NODES}:
sum{j in NODES: (i,j) in ARCS} x[i,j] - sum{j in NODES: (j,i) in ARCS} 
x[j,i] = b[i];A
subject to capacity {(i,j) in ARCS}: l[i,j] <= x[i,j] <= u[i,j];
subject to flow_conservation {i in english}:
    sum{j in french} x[i,j] = 1;
subject to flow_bounds {(i,j) in ARCS}:
    x[i,j] = 0 || x[i,j] <= 1;
#subject to Number: {(i,j) in ARCS} x[i,j]=0 || x[i,j] = 1;


data hw3.dat
solve;
printf "The optimal pair assignments with compatibility scores are: \n";
for {i in english, j in french} {
    printf "English Child %d and French Child %d with compatibility score %d \n", i, j, c[i,j];
}

DATA FILE #

data;
set NODES :=e1 e2 e3 f1 f2 f3;
set ARCS:= (e1,f1) (e1,f2) (e1,f3) (e2,f1) (e2,f2) (e2,f3) (e3,f1) (e3,f2) (e3,f3);

set english:=e1 e2 e3;
set french:=f1 f2 f3;
param: b:=
          1 1
          1 1
          1 1
          1 1
          1 1
          1 1;
param: c l u:=
        [e1,f1] 6  0 10
        [e1,f2] 3  0 10
        [e1,f3] 2  0 10
        [e2,f1] 9  0 10
        [e2,f2] 5  0 10
        [e2,f3] 1  0 10
        [e3,f1] 4  0 10
        [e3,f2] 10 0 10
        [e3,f3] 8  0 10
 ;

问题根源与解决方法 #

1. 参数b的索引不匹配（核心报错原因） #

模型中param b {NODES}定义b的索引是NODES集合中的字符串元素（e1、e2、e3、f1、f2、f3），但dat文件中用数字1作为索引重复赋值，导致b[1]被多次定义。

修正方案：将dat文件中b的赋值改为对应NODES的元素，同时根据配对场景调整供需值（英文节点供给为1，法文节点需求为-1）：

param: b:=
          e1 1
          e2 1
          e3 1
          f1 -1
          f2 -1
          f3 -1;

2. 模型语法错误 #

flow_balance约束行末尾多了一个无效字符A，会导致解析失败，需删除：

subject to flow_balance {i in NODES}:
sum{j in NODES: (i,j) in ARCS} x[i,j] - sum{j in NODES: (j,i) in ARCS} 
x[j,i] = b[i];

3. 目标函数矛盾 #

代码中写maximize cost但注释标注“最小化费用”，若为最小费用流需求，需改为：

minimize cost: sum{(i,j) in ARCS} c[i,j] * x[i,j];  #objective: minimize arc flow cost

4. 输出格式错误 #

节点名称是字符串类型，但printf用了整数格式符%d，会导致输出异常，需改为字符串格式符%s：

printf "English Child %s and French Child %s with compatibility score %d \n", i, j, c[i,j];

内容的提问来源于stack exchange，提问作者Sagar Singh