LP緩和による近時問題の実装について

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ファイブマン

LP緩和による近時問題の実装について

#1

投稿記事 by ファイブマン » 14年前

こんにちは。今これとはまた別の問題でここにお世話になっている者なのですが、そっちに気を取られ、べつの課題(期限が水曜夜)があったのを忘れていました。
そこで厚かましいのですが、そちらの方の解答を教えていただけないでしょうか。これまでのグリーディー法のことなどをうまく使ったりしてやる課題なのですが、それに時間がかかってしまい期限中にこのLP緩和までたどり着くことはできませんでした。

もちろん、期限が終わった後にこの問題はじっくり考え、モノにしたいと考えています。
ですのでよろしければ解答よろしくお願いします。
以下、問題と参考のソースコードになっています。

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資料をもとにLP緩和による重みつき集合被服問題の近似アルゴリズムを実装しなさい。
また、前問(現在お世話になっているtxtファイルから入力するグリーディー法の問題)の問題例について、それぞれの実行結果を示しなさい。

資料: glpk.c

コード:

#include<glpk.h>

int main(int argc, char *argv[])
{
glp_prob *lp;
int ia[6], ja[6];
double ar[6], z, x1, x2;

lp = glp_create_prob();
glp_set_obj_dir(lp, GLP_MAX);
glp_add_cols(lp, 2);
glp_set_obj_coef(lp, 1, 1.0);
glp_set_obj_coef(lp, 2, 1.0);
glp_set_col_bnds(lp, 1, GLP_LO, 0.0, 0.0);
glp_set_col_bnds(lp, 2, GLP_LO, 0.0, 0.0);

glp_add_rows(lp, 3);
glp_set_row_bnds(lp, 1, GLP_UP, 0, 10.0);
glp_set_row_bnds(lp, 2, GLP_UP, 0, 12.0);
glp_set_row_bnds(lp, 3, GLP_UP, 0, 16.0);
ia[1] = 1, ja[1] = 1, ar[1] = 1.0;
ia[1] = 1, ja[1] = 2, ar[1] = 2.0;
ia[1] = 2, ja[1] = 1, ar[1] = 2.0;
ia[1] = 2, ja[1] = 2, ar[1] = 1.0;
ia[1] = 3, ja[1] = 2, ar[1] = 4.0;
glp_load_matrix(lp, 5, ia, ja, ar);

glp_simplex(lp, NULL);
z = glp_get_obj_val(lp);
x1 = glp_get_col_prim(lp, 1);
x2 = glp_get_col_prim(lp, 2);
printf("\n");
printf("z = %g; x1 = %g; x2 = %g\n", z, x1, x2);
glp_delete_prob(lp);
return 0; 
}
前問の問題例
U = {e1,e2,....,e14},
S = {S1,S2,S3,S4,S5}

S1 = {e1,e8},
S2 = {e2,e3,e9,e10},
S3 = {e4,e5e6,e7,e11,e12,e13,e14},
S4 = {e1,e2,...,e7},
S5 = {e8,e9,...,e14},

c(S1,)=1,c(S2,)=1,c(S3,)=1,c(S4,)=1,c(S5,)=1

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bitter_fox
記事: 607
登録日時: 15年前
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Re: LP緩和による近時問題の実装について

#2

投稿記事 by bitter_fox » 14年前

ファイブマン さんが書きました:
資料をもとにLP緩和による重みつき集合被服問題の近似アルゴリズムを実装しなさい。
また、前問(現在お世話になっているtxtファイルから入力するグリーディー法の問題)の問題例について、それぞれの実行結果を示しなさい。

資料: glpk.c

コード:

#include<glpk.h>

glp_prob *lp;

lp = glp_create_prob();
glp_set_obj_dir(lp, GLP_MAX);
glp_add_cols(lp, 2);
glp_set_obj_coef(lp, 1, 1.0);
glp_set_col_bnds(lp, 1, GLP_LO, 0.0, 0.0);

glp_set_row_bnds(lp, 1, GLP_UP, 0, 10.0);
glp_load_matrix(lp, 5, ia, ja, ar);

glp_simplex(lp, NULL);
z = glp_get_obj_val(lp);
x1 = glp_get_col_prim(lp, 1);
glp_delete_prob(lp);
関数がどういった動作をするのかやglp_probがどういったものなのか(構造体をtypedefしたもの?)、またglpk.hの内容が分からないので手の付けようがありません。

ファイブマン

Re: LP緩和による近時問題の実装について

#3

投稿記事 by ファイブマン » 14年前

すみません。ヘッダファイルと共有ライブラリ、ドキュメントが他にあるのを書き込むのを忘れてました。長くなるのでまずヘッダファイルを書き込み、次に共有ライブラリ、ドキュメントを書き込みます。
これで不足はないと思うのですが何かあったら宜しくお願い致します。

コード:

/* glpk.h */

/***********************************************************************
*  This code is part of GLPK (GNU Linear Programming Kit).
*
*  Copyright (C) 2000,01,02,03,04,05,06,07,08,2009 Andrew Makhorin,
*  Department for Applied Informatics, Moscow Aviation Institute,
*  Moscow, Russia. All rights reserved. E-mail: <mao@mai2.rcnet.ru>.
*
*  GLPK is free software: you can redistribute it and/or modify it
*  under the terms of the GNU General Public License as published by
*  the Free Software Foundation, either version 3 of the License, or
*  (at your option) any later version.
*
*  GLPK is distributed in the hope that it will be useful, but WITHOUT
*  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
*  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
*  License for more details.
*
*  You should have received a copy of the GNU General Public License
*  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/

#ifndef GLPK_H
#define GLPK_H

#ifdef __cplusplus
extern "C" {
#endif

#include <stdarg.h>
#include <stddef.h>

/* library version numbers: */
#define GLP_MAJOR_VERSION  4
#define GLP_MINOR_VERSION  39

#ifndef GLP_PROB
#define GLP_PROB
typedef struct { double _opaque_prob; } glp_prob;
/* LP/MIP problem object */
#endif

/* optimization direction flag: */
#define GLP_MIN            1  /* minimization */
#define GLP_MAX            2  /* maximization */

/* kind of structural variable: */
#define GLP_CV             1  /* continuous variable */
#define GLP_IV             2  /* integer variable */
#define GLP_BV             3  /* binary variable */

/* type of auxiliary/structural variable: */
#define GLP_FR             1  /* free variable */
#define GLP_LO             2  /* variable with lower bound */
#define GLP_UP             3  /* variable with upper bound */
#define GLP_DB             4  /* double-bounded variable */
#define GLP_FX             5  /* fixed variable */

/* status of auxiliary/structural variable: */
#define GLP_BS             1  /* basic variable */
#define GLP_NL             2  /* non-basic variable on lower bound */
#define GLP_NU             3  /* non-basic variable on upper bound */
#define GLP_NF             4  /* non-basic free variable */
#define GLP_NS             5  /* non-basic fixed variable */

/* scaling options: */
#define GLP_SF_GM       0x01  /* perform geometric mean scaling */
#define GLP_SF_EQ       0x10  /* perform equilibration scaling */
#define GLP_SF_2N       0x20  /* round scale factors to power of two */
#define GLP_SF_SKIP     0x40  /* skip if problem is well scaled */
#define GLP_SF_AUTO     0x80  /* choose scaling options automatically */

/* solution indicator: */
#define GLP_SOL            1  /* basic solution */
#define GLP_IPT            2  /* interior-point solution */
#define GLP_MIP            3  /* mixed integer solution */

/* solution status: */
#define GLP_UNDEF          1  /* solution is undefined */
#define GLP_FEAS           2  /* solution is feasible */
#define GLP_INFEAS         3  /* solution is infeasible */
#define GLP_NOFEAS         4  /* no feasible solution exists */
#define GLP_OPT            5  /* solution is optimal */
#define GLP_UNBND          6  /* solution is unbounded */

#ifndef GLP_BFCP
#define GLP_BFCP
typedef struct glp_bfcp glp_bfcp;
#endif

struct glp_bfcp
{     /* basis factorization control parameters */
      int msg_lev;            /* (reserved) */
      int type;               /* factorization type: */
#define GLP_BF_FT          1  /* LUF + Forrest-Tomlin */
#define GLP_BF_BG          2  /* LUF + Schur compl. + Bartels-Golub */
#define GLP_BF_GR          3  /* LUF + Schur compl. + Givens rotation */
      int lu_size;            /* luf.sv_size */
      double piv_tol;         /* luf.piv_tol */
      int piv_lim;            /* luf.piv_lim */
      int suhl;               /* luf.suhl */
      double eps_tol;         /* luf.eps_tol */
      double max_gro;         /* luf.max_gro */
      int nfs_max;            /* fhv.hh_max */
      double upd_tol;         /* fhv.upd_tol */
      int nrs_max;            /* lpf.n_max */
      int rs_size;            /* lpf.v_size */
      double foo_bar[38];     /* (reserved) */
};

typedef struct
{     /* simplex method control parameters */
      int msg_lev;            /* message level: */
#define GLP_MSG_OFF        0  /* no output */
#define GLP_MSG_ERR        1  /* warning and error messages only */
#define GLP_MSG_ON         2  /* normal output */
#define GLP_MSG_ALL        3  /* full output */
#define GLP_MSG_DBG        4  /* debug output */
      int meth;               /* simplex method option: */
#define GLP_PRIMAL         1  /* use primal simplex */
#define GLP_DUALP          2  /* use dual; if it fails, use primal */
#define GLP_DUAL           3  /* use dual simplex */
      int pricing;            /* pricing technique: */
#define GLP_PT_STD      0x11  /* standard (Dantzig rule) */
#define GLP_PT_PSE      0x22  /* projected steepest edge */
      int r_test;             /* ratio test technique: */
#define GLP_RT_STD      0x11  /* standard (textbook) */
#define GLP_RT_HAR      0x22  /* two-pass Harris' ratio test */
      double tol_bnd;         /* spx.tol_bnd */
      double tol_dj;          /* spx.tol_dj */
      double tol_piv;         /* spx.tol_piv */
      double obj_ll;          /* spx.obj_ll */
      double obj_ul;          /* spx.obj_ul */
      int it_lim;             /* spx.it_lim */
      int tm_lim;             /* spx.tm_lim (milliseconds) */
      int out_frq;            /* spx.out_frq */
      int out_dly;            /* spx.out_dly (milliseconds) */
      int presolve;           /* enable/disable using LP presolver */
      double foo_bar[36];     /* (reserved) */
} glp_smcp;

typedef struct
{     /* interior-point solver control parameters */
      int msg_lev;            /* message level (see glp_smcp) */
      int ord_alg;            /* ordering algorithm: */
#define GLP_ORD_NONE       0  /* natural (original) ordering */
#define GLP_ORD_QMD        1  /* quotient minimum degree (QMD) */
#define GLP_ORD_AMD        2  /* approx. minimum degree (AMD) */
#define GLP_ORD_SYMAMD     3  /* approx. minimum degree (SYMAMD) */
      double foo_bar[48];     /* (reserved) */
} glp_iptcp;

#ifndef GLP_TREE
#define GLP_TREE
typedef struct { double _opaque_tree; } glp_tree;
/* branch-and-bound tree */
#endif

typedef struct
{     /* integer optimizer control parameters */
      int msg_lev;            /* message level (see glp_smcp) */
      int br_tech;            /* branching technique: */
#define GLP_BR_FFV         1  /* first fractional variable */
#define GLP_BR_LFV         2  /* last fractional variable */
#define GLP_BR_MFV         3  /* most fractional variable */
#define GLP_BR_DTH         4  /* heuristic by Driebeck and Tomlin */
#define GLP_BR_HPC         5  /* hybrid pseudocost */
      int bt_tech;            /* backtracking technique: */
#define GLP_BT_DFS         1  /* depth first search */
#define GLP_BT_BFS         2  /* breadth first search */
#define GLP_BT_BLB         3  /* best local bound */
#define GLP_BT_BPH         4  /* best projection heuristic */
      double tol_int;         /* mip.tol_int */
      double tol_obj;         /* mip.tol_obj */
      int tm_lim;             /* mip.tm_lim (milliseconds) */
      int out_frq;            /* mip.out_frq (milliseconds) */
      int out_dly;            /* mip.out_dly (milliseconds) */
      void (*cb_func)(glp_tree *T, void *info);
                              /* mip.cb_func */
      void *cb_info;          /* mip.cb_info */
      int cb_size;            /* mip.cb_size */
      int pp_tech;            /* preprocessing technique: */
#define GLP_PP_NONE        0  /* disable preprocessing */
#define GLP_PP_ROOT        1  /* preprocessing only on root level */
#define GLP_PP_ALL         2  /* preprocessing on all levels */
      double mip_gap;         /* relative MIP gap tolerance */
      int mir_cuts;           /* MIR cuts       (GLP_ON/GLP_OFF) */
      int gmi_cuts;           /* Gomory's cuts  (GLP_ON/GLP_OFF) */
      int cov_cuts;           /* cover cuts     (GLP_ON/GLP_OFF) */
      int clq_cuts;           /* clique cuts    (GLP_ON/GLP_OFF) */
      int presolve;           /* enable/disable using MIP presolver */
      int binarize;           /* try to binarize integer variables */
      int fp_heur;            /* feasibility pump heuristic */
      double foo_bar[30];     /* (reserved) */
} glp_iocp;

typedef struct
{     /* additional row attributes */
      int level;
      /* subproblem level at which the row was added */
      int origin;
      /* the row origin flag: */
#define GLP_RF_REG         0  /* regular constraint */
#define GLP_RF_LAZY        1  /* "lazy" constraint */
#define GLP_RF_CUT         2  /* cutting plane constraint */
      int klass;
      /* the row class descriptor: */
#define GLP_RF_GMI         1  /* Gomory's mixed integer cut */
#define GLP_RF_MIR         2  /* mixed integer rounding cut */
#define GLP_RF_COV         3  /* mixed cover cut */
#define GLP_RF_CLQ         4  /* clique cut */
      double foo_bar[7];
      /* (reserved) */
} glp_attr;

/* enable/disable flag: */
#define GLP_ON             1  /* enable something */
#define GLP_OFF            0  /* disable something */

/* reason codes: */
#define GLP_IROWGEN     0x01  /* request for row generation */
#define GLP_IBINGO      0x02  /* better integer solution found */
#define GLP_IHEUR       0x03  /* request for heuristic solution */
#define GLP_ICUTGEN     0x04  /* request for cut generation */
#define GLP_IBRANCH     0x05  /* request for branching */
#define GLP_ISELECT     0x06  /* request for subproblem selection */
#define GLP_IPREPRO     0x07  /* request for preprocessing */

/* branch selection indicator: */
#define GLP_NO_BRNCH       0  /* select no branch */
#define GLP_DN_BRNCH       1  /* select down-branch */
#define GLP_UP_BRNCH       2  /* select up-branch */

/* return codes: */
#define GLP_EBADB       0x01  /* invalid basis */
#define GLP_ESING       0x02  /* singular matrix */
#define GLP_ECOND       0x03  /* ill-conditioned matrix */
#define GLP_EBOUND      0x04  /* invalid bounds */
#define GLP_EFAIL       0x05  /* solver failed */
#define GLP_EOBJLL      0x06  /* objective lower limit reached */
#define GLP_EOBJUL      0x07  /* objective upper limit reached */
#define GLP_EITLIM      0x08  /* iteration limit exceeded */
#define GLP_ETMLIM      0x09  /* time limit exceeded */
#define GLP_ENOPFS      0x0A  /* no primal feasible solution */
#define GLP_ENODFS      0x0B  /* no dual feasible solution */
#define GLP_EROOT       0x0C  /* root LP optimum not provided */
#define GLP_ESTOP       0x0D  /* search terminated by application */
#define GLP_EMIPGAP     0x0E  /* relative mip gap tolerance reached */
#define GLP_ENOFEAS     0x0F  /* no primal/dual feasible solution */
#define GLP_ENOCVG      0x10  /* no convergence */
#define GLP_EINSTAB     0x11  /* numerical instability */
#define GLP_EDATA       0x12  /* invalid data */
#define GLP_ERANGE      0x13  /* result out of range */

/* condition indicator: */
#define GLP_KKT_PE         1  /* primal equalities */
#define GLP_KKT_PB         2  /* primal bounds */
#define GLP_KKT_DE         3  /* dual equalities */
#define GLP_KKT_DB         4  /* dual bounds */
#define GLP_KKT_CS         5  /* complementary slackness */

/* MPS file format: */
#define GLP_MPS_DECK       1  /* fixed (ancient) */
#define GLP_MPS_FILE       2  /* free (modern) */

typedef struct
{     /* MPS format control parameters */
      int blank;
      /* character code to replace blanks in symbolic names */
      char *obj_name;
      /* objective row name */
      double tol_mps;
      /* zero tolerance for MPS data */
      double foo_bar[17];
      /* (reserved for use in the future) */
} glp_mpscp;

typedef struct
{     /* CPLEX LP format control parameters */
      double foo_bar[20];
      /* (reserved for use in the future) */
} glp_cpxcp;

#ifndef GLP_TRAN
#define GLP_TRAN
typedef struct { double _opaque_tran; } glp_tran;
/* MathProg translator workspace */
#endif

glp_prob *glp_create_prob(void);
/* create problem object */

void glp_set_prob_name(glp_prob *P, const char *name);
/* assign (change) problem name */

void glp_set_obj_name(glp_prob *P, const char *name);
/* assign (change) objective function name */

void glp_set_obj_dir(glp_prob *P, int dir);
/* set (change) optimization direction flag */

int glp_add_rows(glp_prob *P, int nrs);
/* add new rows to problem object */

int glp_add_cols(glp_prob *P, int ncs);
/* add new columns to problem object */

void glp_set_row_name(glp_prob *P, int i, const char *name);
/* assign (change) row name */

void glp_set_col_name(glp_prob *P, int j, const char *name);
/* assign (change) column name */

void glp_set_row_bnds(glp_prob *P, int i, int type, double lb,
      double ub);
/* set (change) row bounds */

void glp_set_col_bnds(glp_prob *P, int j, int type, double lb,
      double ub);
/* set (change) column bounds */

void glp_set_obj_coef(glp_prob *P, int j, double coef);
/* set (change) obj. coefficient or constant term */

void glp_set_mat_row(glp_prob *P, int i, int len, const int ind[],
      const double val[]);
/* set (replace) row of the constraint matrix */

void glp_set_mat_col(glp_prob *P, int j, int len, const int ind[],
      const double val[]);
/* set (replace) column of the constraint matrix */

void glp_load_matrix(glp_prob *P, int ne, const int ia[],
      const int ja[], const double ar[]);
/* load (replace) the whole constraint matrix */

void glp_del_rows(glp_prob *P, int nrs, const int num[]);
/* delete specified rows from problem object */

void glp_del_cols(glp_prob *P, int ncs, const int num[]);
/* delete specified columns from problem object */

void glp_copy_prob(glp_prob *dest, glp_prob *prob, int names);
/* copy problem object content */

void glp_erase_prob(glp_prob *P);
/* erase problem object content */

void glp_delete_prob(glp_prob *P);
/* delete problem object */

const char *glp_get_prob_name(glp_prob *P);
/* retrieve problem name */

const char *glp_get_obj_name(glp_prob *P);
/* retrieve objective function name */

int glp_get_obj_dir(glp_prob *P);
/* retrieve optimization direction flag */

int glp_get_num_rows(glp_prob *P);
/* retrieve number of rows */

int glp_get_num_cols(glp_prob *P);
/* retrieve number of columns */

const char *glp_get_row_name(glp_prob *P, int i);
/* retrieve row name */

const char *glp_get_col_name(glp_prob *P, int j);
/* retrieve column name */

int glp_get_row_type(glp_prob *P, int i);
/* retrieve row type */

double glp_get_row_lb(glp_prob *P, int i);
/* retrieve row lower bound */

double glp_get_row_ub(glp_prob *P, int i);
/* retrieve row upper bound */

int glp_get_col_type(glp_prob *P, int j);
/* retrieve column type */

double glp_get_col_lb(glp_prob *P, int j);
/* retrieve column lower bound */

double glp_get_col_ub(glp_prob *P, int j);
/* retrieve column upper bound */

double glp_get_obj_coef(glp_prob *P, int j);
/* retrieve obj. coefficient or constant term */

int glp_get_num_nz(glp_prob *P);
/* retrieve number of constraint coefficients */

int glp_get_mat_row(glp_prob *P, int i, int ind[], double val[]);
/* retrieve row of the constraint matrix */

int glp_get_mat_col(glp_prob *P, int j, int ind[], double val[]);
/* retrieve column of the constraint matrix */

void glp_create_index(glp_prob *P);
/* create the name index */

int glp_find_row(glp_prob *P, const char *name);
/* find row by its name */

int glp_find_col(glp_prob *P, const char *name);
/* find column by its name */

void glp_delete_index(glp_prob *P);
/* delete the name index */

void glp_set_rii(glp_prob *P, int i, double rii);
/* set (change) row scale factor */

void glp_set_sjj(glp_prob *P, int j, double sjj);
/* set (change) column scale factor */

double glp_get_rii(glp_prob *P, int i);
/* retrieve row scale factor */

double glp_get_sjj(glp_prob *P, int j);
/* retrieve column scale factor */

void glp_scale_prob(glp_prob *P, int flags);
/* scale problem data */

void glp_unscale_prob(glp_prob *P);
/* unscale problem data */

void glp_set_row_stat(glp_prob *P, int i, int stat);
/* set (change) row status */

void glp_set_col_stat(glp_prob *P, int j, int stat);
/* set (change) column status */

void glp_std_basis(glp_prob *P);
/* construct standard initial LP basis */

void glp_adv_basis(glp_prob *P, int flags);
/* construct advanced initial LP basis */

void glp_cpx_basis(glp_prob *P);
/* construct Bixby's initial LP basis */

int glp_simplex(glp_prob *P, const glp_smcp *parm);
/* solve LP problem with the simplex method */

int glp_exact(glp_prob *P, const glp_smcp *parm);
/* solve LP problem in exact arithmetic */

void glp_init_smcp(glp_smcp *parm);
/* initialize simplex method control parameters */

int glp_get_status(glp_prob *P);
/* retrieve generic status of basic solution */

int glp_get_prim_stat(glp_prob *P);
/* retrieve status of primal basic solution */

int glp_get_dual_stat(glp_prob *P);
/* retrieve status of dual basic solution */

double glp_get_obj_val(glp_prob *P);
/* retrieve objective value (basic solution) */

int glp_get_row_stat(glp_prob *P, int i);
/* retrieve row status */

double glp_get_row_prim(glp_prob *P, int i);
/* retrieve row primal value (basic solution) */

double glp_get_row_dual(glp_prob *P, int i);
/* retrieve row dual value (basic solution) */

int glp_get_col_stat(glp_prob *P, int j);
/* retrieve column status */

double glp_get_col_prim(glp_prob *P, int j);
/* retrieve column primal value (basic solution) */

double glp_get_col_dual(glp_prob *P, int j);
/* retrieve column dual value (basic solution) */

int glp_get_unbnd_ray(glp_prob *P);
/* determine variable causing unboundedness */

int glp_interior(glp_prob *P, const glp_iptcp *parm);
/* solve LP problem with the interior-point method */

void glp_init_iptcp(glp_iptcp *parm);
/* initialize interior-point solver control parameters */

int glp_ipt_status(glp_prob *P);
/* retrieve status of interior-point solution */

double glp_ipt_obj_val(glp_prob *P);
/* retrieve objective value (interior point) */

double glp_ipt_row_prim(glp_prob *P, int i);
/* retrieve row primal value (interior point) */

double glp_ipt_row_dual(glp_prob *P, int i);
/* retrieve row dual value (interior point) */

double glp_ipt_col_prim(glp_prob *P, int j);
/* retrieve column primal value (interior point) */

double glp_ipt_col_dual(glp_prob *P, int j);
/* retrieve column dual value (interior point) */

void glp_set_col_kind(glp_prob *P, int j, int kind);
/* set (change) column kind */

int glp_get_col_kind(glp_prob *P, int j);
/* retrieve column kind */

int glp_get_num_int(glp_prob *P);
/* retrieve number of integer columns */

int glp_get_num_bin(glp_prob *P);
/* retrieve number of binary columns */

int glp_intopt(glp_prob *P, const glp_iocp *parm);
/* solve MIP problem with the branch-and-bound method */

void glp_init_iocp(glp_iocp *parm);
/* initialize integer optimizer control parameters */

int glp_mip_status(glp_prob *P);
/* retrieve status of MIP solution */

double glp_mip_obj_val(glp_prob *P);
/* retrieve objective value (MIP solution) */

double glp_mip_row_val(glp_prob *P, int i);
/* retrieve row value (MIP solution) */

double glp_mip_col_val(glp_prob *P, int j);
/* retrieve column value (MIP solution) */

int glp_print_sol(glp_prob *P, const char *fname);
/* write basic solution in printable format */

int glp_read_sol(glp_prob *P, const char *fname);
/* read basic solution from text file */

int glp_write_sol(glp_prob *P, const char *fname);
/* write basic solution to text file */

int glp_print_ipt(glp_prob *P, const char *fname);
/* write interior-point solution in printable format */

int glp_read_ipt(glp_prob *P, const char *fname);
/* read interior-point solution from text file */

int glp_write_ipt(glp_prob *P, const char *fname);
/* write interior-point solution to text file */

int glp_print_mip(glp_prob *P, const char *fname);
/* write MIP solution in printable format */

int glp_read_mip(glp_prob *P, const char *fname);
/* read MIP solution from text file */

int glp_write_mip(glp_prob *P, const char *fname);
/* write MIP solution to text file */

int glp_bf_exists(glp_prob *P);
/* check if the basis factorization exists */

int glp_factorize(glp_prob *P);
/* compute the basis factorization */

int glp_bf_updated(glp_prob *P);
/* check if the basis factorization has been updated */

void glp_get_bfcp(glp_prob *P, glp_bfcp *parm);
/* retrieve basis factorization control parameters */

void glp_set_bfcp(glp_prob *P, const glp_bfcp *parm);
/* change basis factorization control parameters */

int glp_get_bhead(glp_prob *P, int k);
/* retrieve the basis header information */

int glp_get_row_bind(glp_prob *P, int i);
/* retrieve row index in the basis header */

int glp_get_col_bind(glp_prob *P, int j);
/* retrieve column index in the basis header */

void glp_ftran(glp_prob *P, double x[]);
/* perform forward transformation (solve system B*x = b) */

void glp_btran(glp_prob *P, double x[]);
/* perform backward transformation (solve system B'*x = b) */

int glp_warm_up(glp_prob *P);
/* "warm up" LP basis */

int glp_eval_tab_row(glp_prob *P, int k, int ind[], double val[]);
/* compute row of the simplex tableau */

int glp_eval_tab_col(glp_prob *P, int k, int ind[], double val[]);
/* compute column of the simplex tableau */

int glp_ios_reason(glp_tree *T);
/* determine reason for calling the callback routine */

glp_prob *glp_ios_get_prob(glp_tree *T);
/* access the problem object */

void glp_ios_tree_size(glp_tree *T, int *a_cnt, int *n_cnt,
      int *t_cnt);
/* determine size of the branch-and-bound tree */

int glp_ios_curr_node(glp_tree *T);
/* determine current active subproblem */

int glp_ios_next_node(glp_tree *T, int p);
/* determine next active subproblem */

int glp_ios_prev_node(glp_tree *T, int p);
/* determine previous active subproblem */

int glp_ios_up_node(glp_tree *T, int p);
/* determine parent subproblem */

int glp_ios_node_level(glp_tree *T, int p);
/* determine subproblem level */

double glp_ios_node_bound(glp_tree *T, int p);
/* determine subproblem local bound */

int glp_ios_best_node(glp_tree *T);
/* find active subproblem with best local bound */

double glp_ios_mip_gap(glp_tree *T);
/* compute relative MIP gap */

void *glp_ios_node_data(glp_tree *T, int p);
/* access subproblem application-specific data */

void glp_ios_row_attr(glp_tree *T, int i, glp_attr *attr);
/* retrieve additional row attributes */

int glp_ios_pool_size(glp_tree *T);
/* determine current size of the cut pool */

int glp_ios_add_row(glp_tree *T,
      const char *name, int klass, int flags, int len, const int ind[],
      const double val[], int type, double rhs);
/* add row (constraint) to the cut pool */

void glp_ios_del_row(glp_tree *T, int i);
/* remove row (constraint) from the cut pool */

void glp_ios_clear_pool(glp_tree *T);
/* remove all rows (constraints) from the cut pool */

int glp_ios_can_branch(glp_tree *T, int j);
/* check if can branch upon specified variable */

void glp_ios_branch_upon(glp_tree *T, int j, int sel);
/* choose variable to branch upon */

void glp_ios_select_node(glp_tree *T, int p);
/* select subproblem to continue the search */

int glp_ios_heur_sol(glp_tree *T, const double x[]);
/* provide solution found by heuristic */

void glp_ios_terminate(glp_tree *T);
/* terminate the solution process */

void glp_init_mpscp(glp_mpscp *parm);
/* initialize MPS format control parameters */

int glp_read_mps(glp_prob *P, int fmt, const glp_mpscp *parm,
      const char *fname);
/* read problem data in MPS format */

int glp_write_mps(glp_prob *P, int fmt, const glp_mpscp *parm,
      const char *fname);
/* write problem data in MPS format */

void glp_init_cpxcp(glp_cpxcp *parm);
/* initialize CPLEX LP format control parameters */

int glp_read_lp(glp_prob *P, const glp_cpxcp *parm, const char *fname);
/* read problem data in CPLEX LP format */

int glp_write_lp(glp_prob *P, const glp_cpxcp *parm, const char *fname);
/* write problem data in CPLEX LP format */

glp_tran *glp_mpl_alloc_wksp(void);
/* allocate the MathProg translator workspace */

int glp_mpl_read_model(glp_tran *tran, const char *fname, int skip);
/* read and translate model section */

int glp_mpl_read_data(glp_tran *tran, const char *fname);
/* read and translate data section */

int glp_mpl_generate(glp_tran *tran, const char *fname);
/* generate the model */

void glp_mpl_build_prob(glp_tran *tran, glp_prob *prob);
/* build LP/MIP problem instance from the model */

int glp_mpl_postsolve(glp_tran *tran, glp_prob *prob, int sol);
/* postsolve the model */

void glp_mpl_free_wksp(glp_tran *tran);
/* free the MathProg translator workspace */

int glp_main(int argc, const char *argv[]);
/* stand-alone LP/MIP solver */

/**********************************************************************/

typedef struct _glp_graph glp_graph;
typedef struct _glp_vertex glp_vertex;
typedef struct _glp_arc glp_arc;

struct _glp_graph
{     /* graph descriptor */
      void *pool; /* DMP *pool; */
      /* memory pool to store graph components */
      char *name;
      /* graph name (1 to 255 chars); NULL means no name is assigned
         to the graph */
      int nv_max;
      /* length of the vertex list (enlarged automatically) */
      int nv;
      /* number of vertices in the graph, 0 <= nv <= nv_max */
      int na;
      /* number of arcs in the graph, na >= 0 */
      glp_vertex **v; /* glp_vertex *v[1+nv_max]; */
      /* v[i], 1 <= i <= nv, is a pointer to i-th vertex */
      void *index; /* AVL *index; */
      /* vertex index to find vertices by their names; NULL means the
         index does not exist */
      int v_size;
      /* size of data associated with each vertex (0 to 256 bytes) */
      int a_size;
      /* size of data associated with each arc (0 to 256 bytes) */
};

struct _glp_vertex
{     /* vertex descriptor */
      int i;
      /* vertex ordinal number, 1 <= i <= nv */
      char *name;
      /* vertex name (1 to 255 chars); NULL means no name is assigned
         to the vertex */
      void *entry; /* AVLNODE *entry; */
      /* pointer to corresponding entry in the vertex index; NULL means
         that either the index does not exist or the vertex has no name
         assigned */
      void *data;
      /* pointer to data associated with the vertex */
      void *temp;
      /* working pointer */
      glp_arc *in;
      /* pointer to the (unordered) list of incoming arcs */
      glp_arc *out;
      /* pointer to the (unordered) list of outgoing arcs */
};

struct _glp_arc
{     /* arc descriptor */
      glp_vertex *tail;
      /* pointer to the tail endpoint */
      glp_vertex *head;
      /* pointer to the head endpoint */
      void *data;
      /* pointer to data associated with the arc */
      void *temp;
      /* working pointer */
      glp_arc *t_prev;
      /* pointer to previous arc having the same tail endpoint */
      glp_arc *t_next;
      /* pointer to next arc having the same tail endpoint */
      glp_arc *h_prev;
      /* pointer to previous arc having the same head endpoint */
      glp_arc *h_next;
      /* pointer to next arc having the same head endpoint */
};

glp_graph *glp_create_graph(int v_size, int a_size);
/* create graph */

void glp_set_graph_name(glp_graph *G, const char *name);
/* assign (change) graph name */

int glp_add_vertices(glp_graph *G, int nadd);
/* add new vertices to graph */

void glp_set_vertex_name(glp_graph *G, int i, const char *name);
/* assign (change) vertex name */

glp_arc *glp_add_arc(glp_graph *G, int i, int j);
/* add new arc to graph */

void glp_erase_graph(glp_graph *G, int v_size, int a_size);
/* erase graph content */

void glp_delete_graph(glp_graph *G);
/* delete graph */

void glp_create_v_index(glp_graph *G);
/* create vertex name index */

int glp_find_vertex(glp_graph *G, const char *name);
/* find vertex by its name */

void glp_delete_v_index(glp_graph *G);
/* delete vertex name index */

int glp_read_graph(glp_graph *G, const char *fname);
/* read graph from plain text file */

int glp_write_graph(glp_graph *G, const char *fname);
/* write graph to plain text file */

void glp_mincost_lp(glp_prob *P, glp_graph *G, int names, int v_rhs,
      int a_low, int a_cap, int a_cost);
/* convert minimum cost flow problem to LP */

int glp_mincost_okalg(glp_graph *G, int v_rhs, int a_low, int a_cap,
      int a_cost, double *sol, int a_x, int v_pi);
/* find minimum-cost flow with out-of-kilter algorithm */

void glp_maxflow_lp(glp_prob *P, glp_graph *G, int names, int s,
      int t, int a_cap);
/* convert maximum flow problem to LP */

int glp_maxflow_ffalg(glp_graph *G, int s, int t, int a_cap,
      double *sol, int a_x, int v_cut);
/* find maximal flow with Ford-Fulkerson algorithm */

int glp_check_asnprob(glp_graph *G, int v_set);
/* check correctness of assignment problem data */

/* assignment problem formulation: */
#define GLP_ASN_MIN        1  /* perfect matching (minimization) */
#define GLP_ASN_MAX        2  /* perfect matching (maximization) */
#define GLP_ASN_MMP        3  /* maximum matching */

int glp_asnprob_lp(glp_prob *P, int form, glp_graph *G, int names,
      int v_set, int a_cost);
/* convert assignment problem to LP */

int glp_asnprob_okalg(int form, glp_graph *G, int v_set, int a_cost,
      double *sol, int a_x);
/* solve assignment problem with out-of-kilter algorithm */

int glp_asnprob_hall(glp_graph *G, int v_set, int a_x);
/* find bipartite matching of maximum cardinality */

int glp_read_mincost(glp_graph *G, int v_rhs, int a_low, int a_cap,
      int a_cost, const char *fname);
/* read min-cost flow problem data in DIMACS format */

int glp_write_mincost(glp_graph *G, int v_rhs, int a_low, int a_cap,
      int a_cost, const char *fname);
/* write min-cost flow problem data in DIMACS format */

int glp_read_maxflow(glp_graph *G, int *s, int *t, int a_cap,
      const char *fname);
/* read maximum flow problem data in DIMACS format */

int glp_write_maxflow(glp_graph *G, int s, int t, int a_cap,
      const char *fname);
/* write maximum flow problem data in DIMACS format */

int glp_read_asnprob(glp_graph *G, int v_set, int a_cost, const char
      *fname);
/* read assignment problem data in DIMACS format */

int glp_write_asnprob(glp_graph *G, int v_set, int a_cost, const char
      *fname);
/* write assignment problem data in DIMACS format */

int glp_read_ccformat(glp_graph *G, int v_wgt, const char *fname);
/* read graph in DIMACS clique/coloring format */

int glp_write_ccformat(glp_graph *G, int v_wgt, const char *fname);
/* write graph in DIMACS clique/coloring format */

int glp_netgen(glp_graph *G, int v_rhs, int a_cap, int a_cost,
      const int parm[1+15]);
/* Klingman's network problem generator */

int glp_gridgen(glp_graph *G, int v_rhs, int a_cap, int a_cost,
      const int parm[1+14]);
/* grid-like network problem generator */

int glp_rmfgen(glp_graph *G, int *s, int *t, int a_cap,
      const int parm[1+5]);
/* Goldfarb's maximum flow problem generator */

int glp_weak_comp(glp_graph *G, int v_num);
/* find all weakly connected components of graph */

int glp_strong_comp(glp_graph *G, int v_num);
/* find all strongly connected components of graph */

/**********************************************************************/

typedef struct { int lo, hi; } glp_long;
/* long integer data type */

const char *glp_version(void);
/* determine library version */

void glp_printf(const char *fmt, ...);
/* write formatted output to terminal */

void glp_vprintf(const char *fmt, va_list arg);
/* write formatted output to terminal */

#define glp_assert(expr) \
      ((void)((expr) || (glp_assert_(#expr, __FILE__, __LINE__), 1)))

void glp_assert_(const char *expr, const char *file, int line);
/* check for logical condition */

int glp_term_out(int flag);
/* enable/disable terminal output */

void glp_term_hook(int (*func)(void *info, const char *s), void *info);
/* install hook to intercept terminal output */

void *glp_malloc(int size);
/* allocate memory block */

void *glp_calloc(int n, int size);
/* allocate memory block */

void glp_free(void *ptr);
/* free memory block */

void glp_mem_usage(int *count, int *cpeak, glp_long *total,
      glp_long *tpeak);
/* get memory usage information */

void glp_mem_limit(int limit);
/* set memory usage limit */

void glp_free_env(void);
/* free GLPK library environment */

/**********************************************************************/

#ifndef GLP_DATA
#define GLP_DATA
typedef struct { double _opaque_data; } glp_data;
/* plain data file */
#endif

glp_data *glp_sdf_open_file(const char *fname);
/* open plain data file */

void glp_sdf_set_jump(glp_data *data, void *jump);
/* set up error handling */

void glp_sdf_error(glp_data *data, const char *fmt, ...);
/* print error message */

void glp_sdf_warning(glp_data *data, const char *fmt, ...);
/* print warning message */

int glp_sdf_read_int(glp_data *data);
/* read integer number */

double glp_sdf_read_num(glp_data *data);
/* read floating-point number */

const char *glp_sdf_read_item(glp_data *data);
/* read data item */

const char *glp_sdf_read_text(glp_data *data);
/* read text until end of line */

int glp_sdf_line(glp_data *data);
/* determine current line number */

void glp_sdf_close_file(glp_data *data);
/* close plain data file */

/**********************************************************************/

#define LPX glp_prob

/* problem class: */
#define LPX_LP          100   /* linear programming (LP) */
#define LPX_MIP         101   /* mixed integer programming (MIP) */

/* type of auxiliary/structural variable: */
#define LPX_FR          110   /* free variable */
#define LPX_LO          111   /* variable with lower bound */
#define LPX_UP          112   /* variable with upper bound */
#define LPX_DB          113   /* double-bounded variable */
#define LPX_FX          114   /* fixed variable */

/* optimization direction flag: */
#define LPX_MIN         120   /* minimization */
#define LPX_MAX         121   /* maximization */

/* status of primal basic solution: */
#define LPX_P_UNDEF     132   /* primal solution is undefined */
#define LPX_P_FEAS      133   /* solution is primal feasible */
#define LPX_P_INFEAS    134   /* solution is primal infeasible */
#define LPX_P_NOFEAS    135   /* no primal feasible solution exists */

/* status of dual basic solution: */
#define LPX_D_UNDEF     136   /* dual solution is undefined */
#define LPX_D_FEAS      137   /* solution is dual feasible */
#define LPX_D_INFEAS    138   /* solution is dual infeasible */
#define LPX_D_NOFEAS    139   /* no dual feasible solution exists */

/* status of auxiliary/structural variable: */
#define LPX_BS          140   /* basic variable */
#define LPX_NL          141   /* non-basic variable on lower bound */
#define LPX_NU          142   /* non-basic variable on upper bound */
#define LPX_NF          143   /* non-basic free variable */
#define LPX_NS          144   /* non-basic fixed variable */

/* status of interior-point solution: */
#define LPX_T_UNDEF     150   /* interior solution is undefined */
#define LPX_T_OPT       151   /* interior solution is optimal */

/* kind of structural variable: */
#define LPX_CV          160   /* continuous variable */
#define LPX_IV          161   /* integer variable */

/* status of integer solution: */
#define LPX_I_UNDEF     170   /* integer solution is undefined */
#define LPX_I_OPT       171   /* integer solution is optimal */
#define LPX_I_FEAS      172   /* integer solution is feasible */
#define LPX_I_NOFEAS    173   /* no integer solution exists */

/* status codes reported by the routine lpx_get_status: */
#define LPX_OPT         180   /* optimal */
#define LPX_FEAS        181   /* feasible */
#define LPX_INFEAS      182   /* infeasible */
#define LPX_NOFEAS      183   /* no feasible */
#define LPX_UNBND       184   /* unbounded */
#define LPX_UNDEF       185   /* undefined */

/* exit codes returned by solver routines: */
#define LPX_E_OK        200   /* success */
#define LPX_E_EMPTY     201   /* empty problem */
#define LPX_E_BADB      202   /* invalid initial basis */
#define LPX_E_INFEAS    203   /* infeasible initial solution */
#define LPX_E_FAULT     204   /* unable to start the search */
#define LPX_E_OBJLL     205   /* objective lower limit reached */
#define LPX_E_OBJUL     206   /* objective upper limit reached */
#define LPX_E_ITLIM     207   /* iterations limit exhausted */
#define LPX_E_TMLIM     208   /* time limit exhausted */
#define LPX_E_NOFEAS    209   /* no feasible solution */
#define LPX_E_INSTAB    210   /* numerical instability */
#define LPX_E_SING      211   /* problems with basis matrix */
#define LPX_E_NOCONV    212   /* no convergence (interior) */
#define LPX_E_NOPFS     213   /* no primal feas. sol. (LP presolver) */
#define LPX_E_NODFS     214   /* no dual feas. sol. (LP presolver) */
#define LPX_E_MIPGAP    215   /* relative mip gap tolerance reached */

/* control parameter identifiers: */
#define LPX_K_MSGLEV    300   /* lp->msg_lev */
#define LPX_K_SCALE     301   /* lp->scale */
#define LPX_K_DUAL      302   /* lp->dual */
#define LPX_K_PRICE     303   /* lp->price */
#define LPX_K_RELAX     304   /* lp->relax */
#define LPX_K_TOLBND    305   /* lp->tol_bnd */
#define LPX_K_TOLDJ     306   /* lp->tol_dj */
#define LPX_K_TOLPIV    307   /* lp->tol_piv */
#define LPX_K_ROUND     308   /* lp->round */
#define LPX_K_OBJLL     309   /* lp->obj_ll */
#define LPX_K_OBJUL     310   /* lp->obj_ul */
#define LPX_K_ITLIM     311   /* lp->it_lim */
#define LPX_K_ITCNT     312   /* lp->it_cnt */
#define LPX_K_TMLIM     313   /* lp->tm_lim */
#define LPX_K_OUTFRQ    314   /* lp->out_frq */
#define LPX_K_OUTDLY    315   /* lp->out_dly */
#define LPX_K_BRANCH    316   /* lp->branch */
#define LPX_K_BTRACK    317   /* lp->btrack */
#define LPX_K_TOLINT    318   /* lp->tol_int */
#define LPX_K_TOLOBJ    319   /* lp->tol_obj */
#define LPX_K_MPSINFO   320   /* lp->mps_info */
#define LPX_K_MPSOBJ    321   /* lp->mps_obj */
#define LPX_K_MPSORIG   322   /* lp->mps_orig */
#define LPX_K_MPSWIDE   323   /* lp->mps_wide */
#define LPX_K_MPSFREE   324   /* lp->mps_free */
#define LPX_K_MPSSKIP   325   /* lp->mps_skip */
#define LPX_K_LPTORIG   326   /* lp->lpt_orig */
#define LPX_K_PRESOL    327   /* lp->presol */
#define LPX_K_BINARIZE  328   /* lp->binarize */
#define LPX_K_USECUTS   329   /* lp->use_cuts */
#define LPX_K_BFTYPE    330   /* lp->bfcp->type */
#define LPX_K_MIPGAP    331   /* lp->mip_gap */

#define LPX_C_COVER     0x01  /* mixed cover cuts */
#define LPX_C_CLIQUE    0x02  /* clique cuts */
#define LPX_C_GOMORY    0x04  /* Gomory's mixed integer cuts */
#define LPX_C_MIR       0x08  /* mixed integer rounding cuts */
#define LPX_C_ALL       0xFF  /* all cuts */

typedef struct
{     /* this structure contains results reported by the routines which
         checks Karush-Kuhn-Tucker conditions (for details see comments
         to those routines) */
      /*--------------------------------------------------------------*/
      /* xR - A * xS = 0 (KKT.PE) */
      double pe_ae_max;
      /* largest absolute error */
      int    pe_ae_row;
      /* number of row with largest absolute error */
      double pe_re_max;
      /* largest relative error */
      int    pe_re_row;
      /* number of row with largest relative error */
      int    pe_quality;
      /* quality of primal solution:
         'H' - high
         'M' - medium
         'L' - low
         '?' - primal solution is wrong */
      /*--------------------------------------------------------------*/
      /* l[k] <= x[k] <= u[k] (KKT.PB) */
      double pb_ae_max;
      /* largest absolute error */
      int    pb_ae_ind;
      /* number of variable with largest absolute error */
      double pb_re_max;
      /* largest relative error */
      int    pb_re_ind;
      /* number of variable with largest relative error */
      int    pb_quality;
      /* quality of primal feasibility:
         'H' - high
         'M' - medium
         'L' - low
         '?' - primal solution is infeasible */
      /*--------------------------------------------------------------*/
      /* A' * (dR - cR) + (dS - cS) = 0 (KKT.DE) */
      double de_ae_max;
      /* largest absolute error */
      int    de_ae_col;
      /* number of column with largest absolute error */
      double de_re_max;
      /* largest relative error */
      int    de_re_col;
      /* number of column with largest relative error */
      int    de_quality;
      /* quality of dual solution:
         'H' - high
         'M' - medium
         'L' - low
         '?' - dual solution is wrong */
      /*--------------------------------------------------------------*/
      /* d[k] >= 0 or d[k] <= 0 (KKT.DB) */
      double db_ae_max;
      /* largest absolute error */
      int    db_ae_ind;
      /* number of variable with largest absolute error */
      double db_re_max;
      /* largest relative error */
      int    db_re_ind;
      /* number of variable with largest relative error */
      int    db_quality;
      /* quality of dual feasibility:
         'H' - high
         'M' - medium
         'L' - low
         '?' - dual solution is infeasible */
      /*--------------------------------------------------------------*/
      /* (x[k] - bound of x[k]) * d[k] = 0 (KKT.CS) */
      double cs_ae_max;
      /* largest absolute error */
      int    cs_ae_ind;
      /* number of variable with largest absolute error */
      double cs_re_max;
      /* largest relative error */
      int    cs_re_ind;
      /* number of variable with largest relative error */
      int    cs_quality;
      /* quality of complementary slackness:
         'H' - high
         'M' - medium
         'L' - low
         '?' - primal and dual solutions are not complementary */
} LPXKKT;

#define lpx_create_prob _glp_lpx_create_prob
LPX *lpx_create_prob(void);
/* create problem object */

#define lpx_set_prob_name _glp_lpx_set_prob_name
void lpx_set_prob_name(LPX *lp, const char *name);
/* assign (change) problem name */

#define lpx_set_obj_name _glp_lpx_set_obj_name
void lpx_set_obj_name(LPX *lp, const char *name);
/* assign (change) objective function name */

#define lpx_set_obj_dir _glp_lpx_set_obj_dir
void lpx_set_obj_dir(LPX *lp, int dir);
/* set (change) optimization direction flag */

#define lpx_add_rows _glp_lpx_add_rows
int lpx_add_rows(LPX *lp, int nrs);
/* add new rows to problem object */

#define lpx_add_cols _glp_lpx_add_cols
int lpx_add_cols(LPX *lp, int ncs);
/* add new columns to problem object */

#define lpx_set_row_name _glp_lpx_set_row_name
void lpx_set_row_name(LPX *lp, int i, const char *name);
/* assign (change) row name */

#define lpx_set_col_name _glp_lpx_set_col_name
void lpx_set_col_name(LPX *lp, int j, const char *name);
/* assign (change) column name */

#define lpx_set_row_bnds _glp_lpx_set_row_bnds
void lpx_set_row_bnds(LPX *lp, int i, int type, double lb, double ub);
/* set (change) row bounds */

#define lpx_set_col_bnds _glp_lpx_set_col_bnds
void lpx_set_col_bnds(LPX *lp, int j, int type, double lb, double ub);
/* set (change) column bounds */

#define lpx_set_obj_coef _glp_lpx_set_obj_coef
void lpx_set_obj_coef(glp_prob *lp, int j, double coef);
/* set (change) obj. coefficient or constant term */

#define lpx_set_mat_row _glp_lpx_set_mat_row
void lpx_set_mat_row(LPX *lp, int i, int len, const int ind[],
      const double val[]);
/* set (replace) row of the constraint matrix */

#define lpx_set_mat_col _glp_lpx_set_mat_col
void lpx_set_mat_col(LPX *lp, int j, int len, const int ind[],
      const double val[]);
/* set (replace) column of the constraint matrix */

#define lpx_load_matrix _glp_lpx_load_matrix
void lpx_load_matrix(LPX *lp, int ne, const int ia[], const int ja[],
      const double ar[]);
/* load (replace) the whole constraint matrix */

#define lpx_del_rows _glp_lpx_del_rows
void lpx_del_rows(LPX *lp, int nrs, const int num[]);
/* delete specified rows from problem object */

#define lpx_del_cols _glp_lpx_del_cols
void lpx_del_cols(LPX *lp, int ncs, const int num[]);
/* delete specified columns from problem object */

#define lpx_delete_prob _glp_lpx_delete_prob
void lpx_delete_prob(LPX *lp);
/* delete problem object */

#define lpx_get_prob_name _glp_lpx_get_prob_name
const char *lpx_get_prob_name(LPX *lp);
/* retrieve problem name */

#define lpx_get_obj_name _glp_lpx_get_obj_name
const char *lpx_get_obj_name(LPX *lp);
/* retrieve objective function name */

#define lpx_get_obj_dir _glp_lpx_get_obj_dir
int lpx_get_obj_dir(LPX *lp);
/* retrieve optimization direction flag */

#define lpx_get_num_rows _glp_lpx_get_num_rows
int lpx_get_num_rows(LPX *lp);
/* retrieve number of rows */

#define lpx_get_num_cols _glp_lpx_get_num_cols
int lpx_get_num_cols(LPX *lp);
/* retrieve number of columns */

#define lpx_get_row_name _glp_lpx_get_row_name
const char *lpx_get_row_name(LPX *lp, int i);
/* retrieve row name */

#define lpx_get_col_name _glp_lpx_get_col_name
const char *lpx_get_col_name(LPX *lp, int j);
/* retrieve column name */

#define lpx_get_row_type _glp_lpx_get_row_type
int lpx_get_row_type(LPX *lp, int i);
/* retrieve row type */

#define lpx_get_row_lb _glp_lpx_get_row_lb
double lpx_get_row_lb(LPX *lp, int i);
/* retrieve row lower bound */

#define lpx_get_row_ub _glp_lpx_get_row_ub
double lpx_get_row_ub(LPX *lp, int i);
/* retrieve row upper bound */

#define lpx_get_row_bnds _glp_lpx_get_row_bnds
void lpx_get_row_bnds(LPX *lp, int i, int *typx, double *lb,
      double *ub);
/* retrieve row bounds */

#define lpx_get_col_type _glp_lpx_get_col_type
int lpx_get_col_type(LPX *lp, int j);
/* retrieve column type */

#define lpx_get_col_lb _glp_lpx_get_col_lb
double lpx_get_col_lb(LPX *lp, int j);
/* retrieve column lower bound */

#define lpx_get_col_ub _glp_lpx_get_col_ub
double lpx_get_col_ub(LPX *lp, int j);
/* retrieve column upper bound */

#define lpx_get_col_bnds _glp_lpx_get_col_bnds
void lpx_get_col_bnds(LPX *lp, int j, int *typx, double *lb,
      double *ub);
/* retrieve column bounds */

#define lpx_get_obj_coef _glp_lpx_get_obj_coef
double lpx_get_obj_coef(LPX *lp, int j);
/* retrieve obj. coefficient or constant term */

#define lpx_get_num_nz _glp_lpx_get_num_nz
int lpx_get_num_nz(LPX *lp);
/* retrieve number of constraint coefficients */

#define lpx_get_mat_row _glp_lpx_get_mat_row
int lpx_get_mat_row(LPX *lp, int i, int ind[], double val[]);
/* retrieve row of the constraint matrix */

#define lpx_get_mat_col _glp_lpx_get_mat_col
int lpx_get_mat_col(LPX *lp, int j, int ind[], double val[]);
/* retrieve column of the constraint matrix */

#define lpx_create_index _glp_lpx_create_index
void lpx_create_index(LPX *lp);
/* create the name index */

#define lpx_find_row _glp_lpx_find_row
int lpx_find_row(LPX *lp, const char *name);
/* find row by its name */

#define lpx_find_col _glp_lpx_find_col
int lpx_find_col(LPX *lp, const char *name);
/* find column by its name */

#define lpx_delete_index _glp_lpx_delete_index
void lpx_delete_index(LPX *lp);
/* delete the name index */

#define lpx_scale_prob _glp_lpx_scale_prob
void lpx_scale_prob(LPX *lp);
/* scale problem data */

#define lpx_unscale_prob _glp_lpx_unscale_prob
void lpx_unscale_prob(LPX *lp);
/* unscale problem data */

#define lpx_set_row_stat _glp_lpx_set_row_stat
void lpx_set_row_stat(LPX *lp, int i, int stat);
/* set (change) row status */

#define lpx_set_col_stat _glp_lpx_set_col_stat
void lpx_set_col_stat(LPX *lp, int j, int stat);
/* set (change) column status */

#define lpx_std_basis _glp_lpx_std_basis
void lpx_std_basis(LPX *lp);
/* construct standard initial LP basis */

#define lpx_adv_basis _glp_lpx_adv_basis
void lpx_adv_basis(LPX *lp);
/* construct advanced initial LP basis */

#define lpx_cpx_basis _glp_lpx_cpx_basis
void lpx_cpx_basis(LPX *lp);
/* construct Bixby's initial LP basis */

#define lpx_simplex _glp_lpx_simplex
int lpx_simplex(LPX *lp);
/* easy-to-use driver to the simplex method */

#define lpx_exact _glp_lpx_exact
int lpx_exact(LPX *lp);
/* easy-to-use driver to the exact simplex method */

#define lpx_get_status _glp_lpx_get_status
int lpx_get_status(LPX *lp);
/* retrieve generic status of basic solution */

#define lpx_get_prim_stat _glp_lpx_get_prim_stat
int lpx_get_prim_stat(LPX *lp);
/* retrieve primal status of basic solution */

#define lpx_get_dual_stat _glp_lpx_get_dual_stat
int lpx_get_dual_stat(LPX *lp);
/* retrieve dual status of basic solution */

#define lpx_get_obj_val _glp_lpx_get_obj_val
double lpx_get_obj_val(LPX *lp);
/* retrieve objective value (basic solution) */

#define lpx_get_row_stat _glp_lpx_get_row_stat
int lpx_get_row_stat(LPX *lp, int i);
/* retrieve row status (basic solution) */

#define lpx_get_row_prim _glp_lpx_get_row_prim
double lpx_get_row_prim(LPX *lp, int i);
/* retrieve row primal value (basic solution) */

#define lpx_get_row_dual _glp_lpx_get_row_dual
double lpx_get_row_dual(LPX *lp, int i);
/* retrieve row dual value (basic solution) */

#define lpx_get_row_info _glp_lpx_get_row_info
void lpx_get_row_info(LPX *lp, int i, int *tagx, double *vx,
      double *dx);
/* obtain row solution information */

#define lpx_get_col_stat _glp_lpx_get_col_stat
int lpx_get_col_stat(LPX *lp, int j);
/* retrieve column status (basic solution) */

#define lpx_get_col_prim _glp_lpx_get_col_prim
double lpx_get_col_prim(LPX *lp, int j);
/* retrieve column primal value (basic solution) */

#define lpx_get_col_dual _glp_lpx_get_col_dual
double lpx_get_col_dual(glp_prob *lp, int j);
/* retrieve column dual value (basic solution) */

#define lpx_get_col_info _glp_lpx_get_col_info
void lpx_get_col_info(LPX *lp, int j, int *tagx, double *vx,
      double *dx);
/* obtain column solution information (obsolete) */

#define lpx_get_ray_info _glp_lpx_get_ray_info
int lpx_get_ray_info(LPX *lp);
/* determine what causes primal unboundness */

#define lpx_check_kkt _glp_lpx_check_kkt
void lpx_check_kkt(LPX *lp, int scaled, LPXKKT *kkt);
/* check Karush-Kuhn-Tucker conditions */

#define lpx_warm_up _glp_lpx_warm_up
int lpx_warm_up(LPX *lp);
/* "warm up" LP basis */

#define lpx_eval_tab_row _glp_lpx_eval_tab_row
int lpx_eval_tab_row(LPX *lp, int k, int ind[], double val[]);
/* compute row of the simplex table */

#define lpx_eval_tab_col _glp_lpx_eval_tab_col
int lpx_eval_tab_col(LPX *lp, int k, int ind[], double val[]);
/* compute column of the simplex table */

#define lpx_transform_row _glp_lpx_transform_row
int lpx_transform_row(LPX *lp, int len, int ind[], double val[]);
/* transform explicitly specified row */

#define lpx_transform_col _glp_lpx_transform_col
int lpx_transform_col(LPX *lp, int len, int ind[], double val[]);
/* transform explicitly specified column */

#define lpx_prim_ratio_test _glp_lpx_prim_ratio_test
int lpx_prim_ratio_test(LPX *lp, int len, const int ind[],
      const double val[], int how, double tol);
/* perform primal ratio test */

#define lpx_dual_ratio_test _glp_lpx_dual_ratio_test
int lpx_dual_ratio_test(LPX *lp, int len, const int ind[],
      const double val[], int how, double tol);
/* perform dual ratio test */

#define lpx_interior _glp_lpx_interior
int lpx_interior(LPX *lp);
/* easy-to-use driver to the interior point method */

#define lpx_ipt_status _glp_lpx_ipt_status
int lpx_ipt_status(LPX *lp);
/* retrieve status of interior-point solution */

#define lpx_ipt_obj_val _glp_lpx_ipt_obj_val
double lpx_ipt_obj_val(LPX *lp);
/* retrieve objective value (interior point) */

#define lpx_ipt_row_prim _glp_lpx_ipt_row_prim
double lpx_ipt_row_prim(LPX *lp, int i);
/* retrieve row primal value (interior point) */

#define lpx_ipt_row_dual _glp_lpx_ipt_row_dual
double lpx_ipt_row_dual(LPX *lp, int i);
/* retrieve row dual value (interior point) */

#define lpx_ipt_col_prim _glp_lpx_ipt_col_prim
double lpx_ipt_col_prim(LPX *lp, int j);
/* retrieve column primal value (interior point) */

#define lpx_ipt_col_dual _glp_lpx_ipt_col_dual
double lpx_ipt_col_dual(LPX *lp, int j);
/* retrieve column dual value (interior point) */

#define lpx_set_class _glp_lpx_set_class
void lpx_set_class(LPX *lp, int klass);
/* set problem class */

#define lpx_get_class _glp_lpx_get_class
int lpx_get_class(LPX *lp);
/* determine problem klass */

#define lpx_set_col_kind _glp_lpx_set_col_kind
void lpx_set_col_kind(LPX *lp, int j, int kind);
/* set (change) column kind */

#define lpx_get_col_kind _glp_lpx_get_col_kind
int lpx_get_col_kind(LPX *lp, int j);
/* retrieve column kind */

#define lpx_get_num_int _glp_lpx_get_num_int
int lpx_get_num_int(LPX *lp);
/* retrieve number of integer columns */

#define lpx_get_num_bin _glp_lpx_get_num_bin
int lpx_get_num_bin(LPX *lp);
/* retrieve number of binary columns */

#define lpx_integer _glp_lpx_integer
int lpx_integer(LPX *lp);
/* easy-to-use driver to the branch-and-bound method */

#define lpx_intopt _glp_lpx_intopt
int lpx_intopt(LPX *lp);
/* easy-to-use driver to the branch-and-bound method */

#define lpx_mip_status _glp_lpx_mip_status
int lpx_mip_status(LPX *lp);
/* retrieve status of MIP solution */

#define lpx_mip_obj_val _glp_lpx_mip_obj_val
double lpx_mip_obj_val(LPX *lp);
/* retrieve objective value (MIP solution) */

#define lpx_mip_row_val _glp_lpx_mip_row_val
double lpx_mip_row_val(LPX *lp, int i);
/* retrieve row value (MIP solution) */

#define lpx_mip_col_val _glp_lpx_mip_col_val
double lpx_mip_col_val(LPX *lp, int j);
/* retrieve column value (MIP solution) */

#define lpx_check_int _glp_lpx_check_int
void lpx_check_int(LPX *lp, LPXKKT *kkt);
/* check integer feasibility conditions */

#define lpx_reset_parms _glp_lpx_reset_parms
void lpx_reset_parms(LPX *lp);
/* reset control parameters to default values */

#define lpx_set_int_parm _glp_lpx_set_int_parm
void lpx_set_int_parm(LPX *lp, int parm, int val);
/* set (change) integer control parameter */

#define lpx_get_int_parm _glp_lpx_get_int_parm
int lpx_get_int_parm(LPX *lp, int parm);
/* query integer control parameter */

#define lpx_set_real_parm _glp_lpx_set_real_parm
void lpx_set_real_parm(LPX *lp, int parm, double val);
/* set (change) real control parameter */

#define lpx_get_real_parm _glp_lpx_get_real_parm
double lpx_get_real_parm(LPX *lp, int parm);
/* query real control parameter */

#define lpx_read_mps _glp_lpx_read_mps
LPX *lpx_read_mps(const char *fname);
/* read problem data in fixed MPS format */

#define lpx_write_mps _glp_lpx_write_mps
int lpx_write_mps(LPX *lp, const char *fname);
/* write problem data in fixed MPS format */

#define lpx_read_bas _glp_lpx_read_bas
int lpx_read_bas(LPX *lp, const char *fname);
/* read LP basis in fixed MPS format */

#define lpx_write_bas _glp_lpx_write_bas
int lpx_write_bas(LPX *lp, const char *fname);
/* write LP basis in fixed MPS format */

#define lpx_read_freemps _glp_lpx_read_freemps
LPX *lpx_read_freemps(const char *fname);
/* read problem data in free MPS format */

#define lpx_write_freemps _glp_lpx_write_freemps
int lpx_write_freemps(LPX *lp, const char *fname);
/* write problem data in free MPS format */

#define lpx_read_cpxlp _glp_lpx_read_cpxlp
LPX *lpx_read_cpxlp(const char *fname);
/* read problem data in CPLEX LP format */

#define lpx_write_cpxlp _glp_lpx_write_cpxlp
int lpx_write_cpxlp(LPX *lp, const char *fname);
/* write problem data in CPLEX LP format */

#define lpx_read_model _glp_lpx_read_model
LPX *lpx_read_model(const char *model, const char *data,
      const char *output);
/* read LP/MIP model written in GNU MathProg language */

#define lpx_print_prob _glp_lpx_print_prob
int lpx_print_prob(LPX *lp, const char *fname);
/* write problem data in plain text format */

#define lpx_print_sol _glp_lpx_print_sol
int lpx_print_sol(LPX *lp, const char *fname);
/* write LP problem solution in printable format */

#define lpx_print_sens_bnds _glp_lpx_print_sens_bnds
int lpx_print_sens_bnds(LPX *lp, const char *fname);
/* write bounds sensitivity information */

#define lpx_print_ips _glp_lpx_print_ips
int lpx_print_ips(LPX *lp, const char *fname);
/* write interior point solution in printable format */

#define lpx_print_mip _glp_lpx_print_mip
int lpx_print_mip(LPX *lp, const char *fname);
/* write MIP problem solution in printable format */

#define lpx_is_b_avail _glp_lpx_is_b_avail
int lpx_is_b_avail(LPX *lp);
/* check if LP basis is available */

#define lpx_write_pb _glp_lpx_write_pb
int lpx_write_pb(LPX *lp, const char *fname, int normalized,
      int binarize);
/* write problem data in (normalized) OPB format */

#define lpx_main _glp_lpx_main
int lpx_main(int argc, const char *argv[]);
/* stand-alone LP/MIP solver */

#ifdef __cplusplus
}
#endif

#endif

/* eof */


ファイブマン

Re: LP緩和による近時問題の実装について

#4

投稿記事 by ファイブマン » 14年前

コード:

# libglpk.la - a libtool library file
# Generated by libtool (GNU libtool 1.3087 2008-08-02) 2.2.7a
#
# Please DO NOT delete this file!
# It is necessary for linking the library.

# The name that we can dlopen(3).
dlname='libglpk.so.0'

# Names of this library.
library_names='libglpk.so.0.24.0 libglpk.so.0 libglpk.so'

# The name of the static archive.
old_library='libglpk.a'

# Linker flags that can not go in dependency_libs.
inherited_linker_flags=''

# Libraries that this one depends upon.
dependency_libs=' -lm'

# Names of additional weak libraries provided by this library
weak_library_names=''

# Version information for libglpk.
current=24
age=24
revision=0

# Is this an already installed library?
installed=yes

# Should we warn about portability when linking against -modules?
shouldnotlink=no

# Files to dlopen/dlpreopen
dlopen=''
dlpreopen=''

# Directory that this library needs to be installed in:
libdir='/usr/local/lib'
ドキュメントは載せられませんでした。これは作成において影響を及ぼしてしまうでしょうか。
また、この課題ですが、今日中、または明日の朝あたりまでに完成というのは無理難題でしょうか。
厚かましいですが、御回答宜しくお願いします。

アバター
bitter_fox
記事: 607
登録日時: 15年前
住所: 大阪府

Re: LP緩和による近時問題の実装について

#5

投稿記事 by bitter_fox » 14年前

ファイブマン さんが書きました:すみません。ヘッダファイルと共有ライブラリ、ドキュメントが他にあるのを書き込むのを忘れてました。長くなるのでまずヘッダファイルを書き込み、次に共有ライブラリ、ドキュメントを書き込みます。

コード:

/* glpk.h */

/***********************************************************************
*  This code is part of GLPK (GNU Linear Programming Kit).
*
*  Copyright (C) 2000,01,02,03,04,05,06,07,08,2009 Andrew Makhorin,
*  Department for Applied Informatics, Moscow Aviation Institute,
*  Moscow, Russia. All rights reserved. E-mail: <mao@mai2.rcnet.ru>.
*
*  GLPK is free software: you can redistribute it and/or modify it
*  under the terms of the GNU General Public License as published by
*  the Free Software Foundation, either version 3 of the License, or
*  (at your option) any later version.
*
*  GLPK is distributed in the hope that it will be useful, but WITHOUT
*  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
*  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
*  License for more details.
*
*  You should have received a copy of the GNU General Public License
*  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
GLPKとはライブラリだったんですか。何らかの実装を行わなければならない物と勘違いしておりました。
ファイブマン さんが書きました: 資料をもとにLP緩和による重みつき集合被服問題の近似アルゴリズムを実装しなさい。

資料: glpk.c

コード:

#include<glpk.h>
 
int main(int argc, char *argv[])
{
glp_prob *lp;
int ia[6], ja[6];
double ar[6], z, x1, x2;
 
lp = glp_create_prob();
glp_set_obj_dir(lp, GLP_MAX);
glp_add_cols(lp, 2);
glp_set_obj_coef(lp, 1, 1.0);
glp_set_obj_coef(lp, 2, 1.0);
glp_set_col_bnds(lp, 1, GLP_LO, 0.0, 0.0);
glp_set_col_bnds(lp, 2, GLP_LO, 0.0, 0.0);
 
glp_add_rows(lp, 3);
glp_set_row_bnds(lp, 1, GLP_UP, 0, 10.0);
glp_set_row_bnds(lp, 2, GLP_UP, 0, 12.0);
glp_set_row_bnds(lp, 3, GLP_UP, 0, 16.0);
ia[1] = 1, ja[1] = 1, ar[1] = 1.0;
ia[1] = 1, ja[1] = 2, ar[1] = 2.0;
ia[1] = 2, ja[1] = 1, ar[1] = 2.0;
ia[1] = 2, ja[1] = 2, ar[1] = 1.0;
ia[1] = 3, ja[1] = 2, ar[1] = 4.0;
glp_load_matrix(lp, 5, ia, ja, ar);
 
glp_simplex(lp, NULL);
z = glp_get_obj_val(lp);
x1 = glp_get_col_prim(lp, 1);
x2 = glp_get_col_prim(lp, 2);
printf("\n");
printf("z = %g; x1 = %g; x2 = %g\n", z, x1, x2);
glp_delete_prob(lp);
return 0; 
}
これをもとに何を実装すればよいのでしょう?

ファイブマン

Re: LP緩和による近時問題の実装について

#6

投稿記事 by ファイブマン » 14年前

肝心な問題を忘れていましたね.すみません.
以下,問題です.

線形計画問題(Linear Programming)

maximize x_1 + x_2
s.t. x_1 + x_2 <= 10
2x_1 + x_2 <= 12
4x_2 <= 16
0 <=x_1, 0 <=x_2

ファイブマン

Re: LP緩和による近時問題の実装について

#7

投稿記事 by ファイブマン » 14年前

いまさらですが,タイトルの近似問題が誤って近時になっていました.すみませ
ん,そして先ほどの返信に書くのを忘れていました.
回答宜しくお願いします.

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bitter_fox
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Re: LP緩和による近時問題の実装について

#8

投稿記事 by bitter_fox » 14年前

ファイブマン さんが書きました:肝心な問題を忘れていましたね.すみません.
以下,問題です.

線形計画問題(Linear Programming)

maximize x_1 + x_2
s.t. x_1 + x_2 <= 10
2x_1 + x_2 <= 12
4x_2 <= 16
0 <=x_1, 0 <=x_2

コード:

glp_prob *lp;
 
lp = glp_create_prob();
glp_set_obj_dir(lp, GLP_MAX);
glp_add_cols(lp, 2);
glp_set_obj_coef(lp, 1, 1.0);
glp_set_col_bnds(lp, 1, GLP_LO, 0.0, 0.0);
 
glp_set_row_bnds(lp, 1, GLP_UP, 0, 10.0);
glp_load_matrix(lp, 5, ia, ja, ar);
 
glp_simplex(lp, NULL);
z = glp_get_obj_val(lp);
x1 = glp_get_col_prim(lp, 1);
glp_delete_prob(lp);
これらの関数が既にライブラリとして提供されていて、main関数もあるのであればこれ以上実装するものが無くないですか?

LPやGLPKについても専門的に学んでおらず、コメントが無くmainで何をやっているのかもよく分からないので、ちょっと厳しいです。

ファイブマン

Re: LP緩和による近時問題の実装について

#9

投稿記事 by ファイブマン » 14年前

bitter_fox さんが書きました: これらの関数が既にライブラリとして提供されていて、main関数もあるのであればこれ以上実装するものが無くないですか?
課題内容には,これを”参考に”とあるんですよねぇ.むしろそのまんまということなのですかね?

そして,これをsolaris上でコンパイルしたのですが,どうもうまくいきません.
(ヘッダもライブラリも同じディレクトリにあるのに)資料の指示通り,コンパイルは

%gcc -I/export/home/teachers/thoriyam/include(/export...はヘッダファイルのあるディレクトリ)
%gcc -L/export/home/teachers/thoriyam/lib(/export...はライブラリのあるディレクトリ)
%gcc -R/export/home/teachers/thoriyam/lib(/export...はライブラリのあるディレクトリ)
%gcc -lglpk -lm glpk(ソースファイル名).c

これを毎回やるのは面倒なのでMakefileを利用するとよいらしいのですがまだ作り方を習得していないので,この長いコンパイルをしようと思ったのですが,
%gcc: no input files
と出てしまい,うまく動きません.
間違いなくそこにファイルは存在し,さらに一応ソースファイルと同じディレクトリにコピーしてそこにおいて
%gcc -I./
等で試してみたのですがそれでも
%gcc: no input filesと出てしまいます.

この原因はなんでしょうか.

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