ubuntu下面安装glpk

然而在我的电脑里。安装命令为sudo apt-get install glpk-utils

 

 

作者：jostree 转载请注明出处 http://www.cnblogs.com/jostree/p/4156204.html

glpk是一个开源的求解线性规划的包。

添加源：

deb http://us.archive.ubuntu.com/ubuntu saucy main universe

更新源并安装：

sudo apt-get update

sudo apt-get install glpk

 

 写入如下glpsolEx.mod 文件

 1 /* Variables */
 2 var x1 >= 0;
 3 var x2 >= 0;
 4 var x3 >= 0;
 5 
 6 /* Object function */
 7 maximize z: x1 + 14*x2 + 6*x3;
 8 
 9 /* Constrains */
10 s.t. con1: x1 + x2 + x3 <= 4;
11 s.t. con2: x1  <= 2;
12 s.t. con3: x3  <= 3;
13 s.t. con4: 3*x2 + x3  <= 6;
14 
15 end;

 

运行 glpsol -m glpsolEx.mod -o glpsolEx.sol，输出到glpsolEx.sol文件中

结果为：

 

 1 Problem:    glpsolEx
 2 Rows:       5
 3 Columns:    3
 4 Non-zeros:  10
 5 Status:     OPTIMAL
 6 Objective:  z = 32 (MAXimum)
 7 
 8    No.   Row name   St   Activity     Lower bound   Upper bound    Marginal
 9 ------ ------------ -- ------------- ------------- ------------- -------------
10      1 z            B             32                             
11      2 con1         NU             4                           4             2 
12      3 con2         B              0                           2 
13      4 con3         B              3                           3 
14      5 con4         NU             6                           6             4 
15 
16    No. Column name  St   Activity     Lower bound   Upper bound    Marginal
17 ------ ------------ -- ------------- ------------- ------------- -------------
18      1 x1           NL             0             0                          -1 
19      2 x2           B              1             0               
20      3 x3           B              3             0               
21 
22 Karush-Kuhn-Tucker optimality conditions:
23 
24 KKT.PE: max.abs.err = 0.00e+00 on row 0
25         max.rel.err = 0.00e+00 on row 0
26         High quality
27 
28 KKT.PB: max.abs.err = 4.44e-16 on row 4
29         max.rel.err = 1.11e-16 on row 4
30         High quality
31 
32 KKT.DE: max.abs.err = 0.00e+00 on column 0
33         max.rel.err = 0.00e+00 on column 0
34         High quality
35 
36 KKT.DB: max.abs.err = 0.00e+00 on row 0
37         max.rel.err = 0.00e+00 on row 0
38         High quality
39 
40 End of output

帮助文档中一个求解八皇后的例子：

 1 /* QUEENS, a classic combinatorial optimization problem */
 2 
 3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
 4 
 5 /* The Queens Problem is to place as many queens as possible on the 8x8
 6    (or more generally, nxn) chess board in a way that they do not fight
 7    each other. This problem is probably as old as the chess game itself,
 8    and thus its origin is not known, but it is known that Gauss studied
 9    this problem. */
10 
11 param n, integer, > 0, default 8;
12 /* size of the chess board */
13 
14 var x{1..n, 1..n}, binary;
15 /* x[i,j] = 1 means that a queen is placed in square [i,j] */
16 
17 s.t. a{i in 1..n}: sum{j in 1..n} x[i,j] <= 1;
18 /* at most one queen can be placed in each row */
19 
20 s.t. b{j in 1..n}: sum{i in 1..n} x[i,j] <= 1;
21 /* at most one queen can be placed in each column */
22 
23 s.t. c{k in 2-n..n-2}: sum{i in 1..n, j in 1..n: i-j == k} x[i,j] <= 1;
24 /* at most one queen can be placed in each "\"-diagonal */
25 
26 s.t. d{k in 3..n+n-1}: sum{i in 1..n, j in 1..n: i+j == k} x[i,j] <= 1;
27 /* at most one queen can be placed in each "/"-diagonal */
28 
29 maximize obj: sum{i in 1..n, j in 1..n} x[i,j];
30 /* objective is to place as many queens as possible */
31 
32 /* solve the problem */
33 solve;
34 
35 /* and print its optimal solution */
36 for {i in 1..n}
37 {  for {j in 1..n} printf " %s", if x[i,j] then "Q" else ".";
38    printf("\n");
39 }
40 
41 end;