Ubuntu 下 glpk 的安装及使用

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 <[email protected]> */

 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;