## glpk

GNU Linear Programming Kit (GLPK).

## TOC »

## Usage

(require-extension glpk)

## Documentation

GLPK is a package for solving linear programming and mixed integer programming problems.

The Chicken GLPK library provides a Scheme interface to a large subset of the GLPK procedures for problem setup and solving. Below is a list of procedures that are included in this egg, along with brief descriptions. This egg has been tested with GLPK version 4.28.

### Problem constructors and predicates

`lpx:empty-problem:: () -> LPX`procedureThis procedure creates a new problem that has no rows or columns.

`lpx:make-problem:: DIR * PBOUNDS * XBOUNDS * OBJCOEFS * CONSTRAINTS * [ORDER] -> LPX`procedureThis procedure creates a new problem with the specified parameters.

- Argument
`DIR`specifies the optimization direction flag. It can be one of`'maximize`or`'minimize`. - Argument
`PBOUNDS`is a list that specifies the type and bounds for each row of the problem object. Each element of this list can take one of the following forms:

'(unbounded) Free (unbounded) variable, `-Inf <= x <= +Inf`'(lower-bound LB) Variable with lower bound, `LB <= x <= +Inf`'(upper-bound UB) Variable with upper bound, `-Inf <= x <= UB`'(double-bounded LB UB) Double-bounded variable, `LB <= x <= UB`'(fixed LB UB) Fixed variable, `LB = x = UB`- Argument
`XBOUNDS`is a list that specifies the type and bounds for each column (structural variable) of the problem object. Each element of this list can take one of the forms described for parameter`PBOUNDS`. - Argument
`OBJCOEFS`is a list that specifies the objective coefficients for each column (structural variable). This list must be of the same length as`XBOUNDS`. - Argument
`OBJCOEFS`is a list that specifies the objective coefficients for each column (structural variable). - Argument
`CONSTRAINTS`is an SRFI-4`f64vector`that represents the problem's constraint matrix (in row-major or column-major order). - Optional argument
`ORDER`specifies the element order of the constraints matrix. It can be one of`'row-major`or`'column-major`.

- Argument

`lpx?:: OBJECT -> BOOL`procedureReturns true if the given object was created by

`lpx:empty-problem`or`lpx:make-problem`, false otherwise.

### Problem accessors and modifiers

`lpx:set-problem-name:: LPX * NAME -> LPX`procedureSets problem name.

`lpx:get-problem-name:: LPX -> NAME`procedureReturns the name of the given problem.

`lpx:set-direction:: LPX * DIR -> LPX`procedureSpecifies the optimization direction flag, which can be one of

`'maximize`or`'minimize`.

`lpx:get-direction:: LPX -> DIR`procedureReturns the optimization direction for the given problem.

`lpx:set-class:: LPX * CLASS -> LPX`procedureSets problem class (linear programming or mixed-integer programming. Argument

`CLASS`can be one of`'lp`or`'mip`.

`lpx:get-class:: LPX -> CLASS`procedureReturns the problem class.

`lpx:add-rows:: LPX * N -> LPX`procedureThis procedure adds

`N`rows (constraints) to the given problem. Each new row is initially unbounded and has an empty list of constraint coefficients.

`lpx:add-columns:: LPX * N -> LPX`procedureThis procedure adds

`N`columns (structural variables) to the given problem.

`lpx:set-row-name:: LPX * I * NAME -> LPX`procedureSets the name of row

`I`.

`lpx:set-column-name:: LPX * J * NAME -> LPX`procedureSets the name of column

`J`.

`lpx:get-row-name:: LPX * I -> NAME`procedureReturns the name of row

`I`.

`lpx:get-column-name:: LPX * J -> NAME`procedureReturns the name of column

`J`.

`lpx:get-num-rows:: LPX -> N`procedureReturns the current number of rows in the given problem.

`lpx:get-num-columns:: LPX -> N`procedureReturns the current number of columns in the given problem.

`lpx:set-row-bounds:: LPX * I * BOUNDS -> LPX`procedureSets bounds for row

`I`in the given problem. Argument`BOUNDS`specifies the type and bounds for the specified row. It can take one of the following forms:'(unbounded) Free (unbounded) variable, `-Inf <= x <= +Inf`'(lower-bound LB) Variable with lower bound, `LB <= x <= +Inf`'(upper-bound UB) Variable with upper bound, `-Inf <= x <= UB`'(double-bounded LB UB) Double-bounded variable, `LB <= x <= UB`'(fixed LB UB) Fixed variable, `LB = x = UB`

`lpx:set-column-bounds:: LPX * J * BOUNDS -> LPX`procedureSets bounds for column

`J`in the given problem. Argument`BOUNDS`specifies the type and bounds for the specified column. It can take one of the following forms:'(unbounded) Free (unbounded) variable, `-Inf <= x <= +Inf`'(lower-bound LB) Variable with lower bound, `LB <= x <= +Inf`'(upper-bound UB) Variable with upper bound, `-Inf <= x <= UB`'(double-bounded LB UB) Double-bounded variable, `LB <= x <= UB`'(fixed LB UB) Fixed variable, `LB = x = UB`

`lpx:set-objective-coefficient:: LPX * J * COEF -> LPX`procedureSets the objective coefficient at column

`J`(structural variable).

`lpx:set-column-kind:: LPX * J * KIND -> LPX`procedureSets the kind of column

`J`(structural variable). Argument`KIND`can be one of the following:'iv integer variable 'cv continuous variable

`lpx:load-constraint-matrix:: LPX * F64VECTOR * NROWS * NCOLS [* ORDER] -> LPX`procedureLoads the constraint matrix for the given problem. The constraints matrix is represented as an SRFI-4

`f64vector`(in row-major or column-major order). Optional argument`ORDER`specifies the element order of the constraints matrix. It can be one of`'row-major`or`'column-major`.

`lpx:get-column-primals:: LPX -> F64VECTOR`procedureReturns the primal values of all structural variables (columns).

`lpx:get-objective-value:: LPX -> NUMBER`procedureReturns the current value of the objective function.

### Problem control parameters

The procedures in this section retrieve or set control parameters of GLPK problem object. If a procedure is invoked only with a problem object as an argument, it will return the value of its respective control parameter. If it is invoked with an additional argument, that argument is used to set a new value for the control parameter.

`lpx:message_level:: LPX [ * (none | error | normal | full)] -> LPX | VALUE`procedureLevel of messages output by solver routines.

`lpx:scaling:: LPX [ * (none | equilibration | geometric-mean | geometric-mean+equilibration)] -> LPX | VALUE`procedureScaling option.

`lpx:use_dual_simplex:: LPX [ * BOOL] -> LPX | VALUE`procedureDual simplex option.

`lpx:pricing:: LPX [ * (textbook | steepest-edge)] -> LPX | VALUE`procedurePricing option (for both primal and dual simplex).

`lpx:solution_rounding:: LPX [ * BOOL] -> LPX | VALUE`procedureSolution rounding option.

`lpx:iteration_limit:: LPX [ * INT] -> LPX | VALUE`procedureSimplex iteration limit.

`lpx:iteration_count:: LPX [ * INT] -> LPX | VALUE`procedureSimplex iteration count.

`lpx:branching_heuristic:: LPX [ * (first | last | driebeck+tomlin)] -> LPX | VALUE`procedureBranching heuristic option (for MIP only).

`lpx:backtracking_heuristic:: LPX [ * (dfs | bfs | best-projection | best-local-bound)] -> LPX | VALUE`procedureBacktracking heuristic option (for MIP only).

`lpx:use_presolver:: LPX [ * BOOL] -> LPX | VALUE`procedureUse the LP presolver.

`lpx:relaxation:: LPX [ * REAL] -> LPX | VALUE`procedureRelaxation parameter used in the ratio test.

`lpx:time_limit:: LPX [ * REAL] -> LPX | VALUE`procedureSearching time limit, in seconds.

### Scaling & solver procedures

`lpx:scale-problem:: LPX -> LPX`procedureThis procedure performs scaling of of the constraints matrix in order to improve its numerical properties.

`lpx:simplex:: LPX -> STATUS`procedureThis procedure solves the given LP problem using the simplex method. It can return one of the following status codes:

LPX_E_OK the LP problem has been successfully solved LPX_E_BADB Unable to start the search, because the initial basis specified in the problem object is invalid--the number of basic (auxiliary and structural) variables is not the same as the number of rows in the problem object. LPX_E_SING Unable to start the search, because the basis matrix corresponding to the initial basis is singular within the working precision. LPX_E_COND Unable to start the search, because the basis matrix corresponding to the initial basis is ill-conditioned, i.e. its condition number is too large. LPX_E_BOUND Unable to start the search, because some double-bounded (auxiliary or structural) variables have incorrect bounds. LPX_E_FAIL The search was prematurely terminated due to the solver failure. LPX_E_OBJLL The search was prematurely terminated, because the objective function being maximized has reached its lower limit and continues decreasing (the dual simplex only). LPX_E_OBJUL The search was prematurely terminated, because the objective function being minimized has reached its upper limit and continues increasing (the dual simplex only). LPX_E_ITLIM The search was prematurely terminated, because the simplex iteration limit has been exceeded. LPX_E_TMLIM The search was prematurely terminated, because the time limit has been exceeded. LPX_E_NOPFS The LP problem instance has no primal feasible solution (only if the LP presolver is used). LPX_E_NODFS The LP problem instance has no dual feasible solution (only if the LP presolver is used).

`lpx:integer:: LPX -> STATUS`procedureSolves an MIP problem using the branch-and-bound method.

## Examples

;; ;; Two Mines Linear programming example from ;; ;; http://people.brunel.ac.uk/~mastjjb/jeb/or/basicor.html#twomines ;; ;; Two Mines Company ;; ;; The Two Mines Company owns two different mines that produce an ore ;; which, after being crushed, is graded into three classes: high, ;; medium and low-grade. The company has contracted to provide a ;; smelting plant with 12 tons of high-grade, 8 tons of medium-grade ;; and 24 tons of low-grade ore per week. The two mines have different ;; operating characteristics as detailed below. ;; ;; Mine Cost per day ($'000) Production (tons/day) ;; High Medium Low ;; X 180 6 3 4 ;; Y 160 1 1 6 ;; ;; Production (tons/week) ;; High Medium Low ;; Contract 12 8 24 ;; ;; How many days per week should each mine be operated to fulfill the ;; smelting plant contract? ;; (require-extension srfi-4) (require-extension glpk) ;; (1) Unknown variables ;; ;; x = number of days per week mine X is operated ;; y = number of days per week mine Y is operated ;; ;; (2) Constraints ;; ;; ;; * ore production constraints - balance the amount produced with ;; the quantity required under the smelting plant contract ;; ;; High 6x + 1y >= 12 ;; Medium 3x + 1y >= 8 ;; Low 4x + 6y >= 24 ;; ;; (3) Objective ;; ;; The objective is to minimise cost which is given by 180x + 160y. ;; ;; minimise 180x + 160y ;; subject to ;; 6x + y >= 12 ;; 3x + y >= 8 ;; 4x + 6y >= 24 ;; x <= 5 ;; y <= 5 ;; x,y >= 0 ;; ;; (4) Auxiliary variables (rows) ;; ;; p = 6x + y ;; q = 3x + y ;; r = 4x + 6y ;; ;; 12 <= p < +inf ;; 8 <= q < +inf ;; 24 <= r < +inf (define pbounds `((lower-bound 12) (lower-bound 8) (lower-bound 24))) ;; (5) Structural variables (columns) ;; ;; 0 <= x <= 5 ;; 0 <= y <= 5 (define xbounds `((double-bounded 0 5) (double-bounded 0 5))) ;; (6) Objective coefficients: 180, 160 (define objcoefs (list 180 160)) ;; Constraints matrix (in row-major order) ;; ;; 6 1 ;; 3 1 ;; 4 6 (define constraints (f64vector 6 1 3 1 4 6)) ;; Create the problem definition & run the solver (let ((lpp (lpx:make-problem 'minimize pbounds xbounds objcoefs constraints))) (lpx:scale-problem lpp) (lpx:use_presolver lpp #t) (let ((status (lpx:simplex lpp))) (print "solution status = " status) (print "objective value = " (lpx:get-objective-value lpp)) (print "primals = " (lpx:get-column-primals lpp))))

## About this egg

### Author

### Version history

- 1.4
- Using assert in unit test
- 1.3
- Documentation converted to wiki format
- 1.2
- Ported to Chicken 4
- 1.1
- Added chicken-glpk.h to file manifest
- 1.0
- Initial release

### License

Copyright 2008-2011 Ivan Raikov and the Okinawa Institute of Science and Technology This program 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. This program 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. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>.