# Gurobi Mex: A MATLAB interface for Gurobi

(Difference between revisions)
 Revision as of 02:15, 7 July 2010 (edit)m (→Step 1. Preparation)← Previous diff Revision as of 02:24, 7 July 2010 (edit) (undo)m (→Input Description)Next diff → Line 105: Line 105: == Input Description == == Input Description == - * '''c''': objective coefficient vector, double. + * '''c''': objective coefficient vector, double type. :[] (empty array) means uniformly 0 coefficients, and ''scalar'' means all coefficients equal to ''scalar''. :[] (empty array) means uniformly 0 coefficients, and ''scalar'' means all coefficients equal to ''scalar''. * '''objtype''': 1 (minimization) or -1 (maximization). * '''objtype''': 1 (minimization) or -1 (maximization). - * '''A''': constraint coefficient matrix, double, sparse. + * '''A''': constraint coefficient matrix, double type, sparse. - * '''b''': constraint right-hand side vector, double. + * '''b''': constraint right-hand side vector, double type. - :Gurobi takes a dense vector for this input. If a ''sparse'' vector is specified, it is converted to ''full'' by Gurobi Mex. + :Gurobi takes a dense vector for this input. If a ''sparse'' vector is specified, it will be converted to ''full'' by Gurobi Mex. * '''contypes''': constraint types. Char array of '>', '<', '='. * '''contypes''': constraint types. Char array of '>', '<', '='. - :Warning: '>=' means two constraints instead of one an inequality constraint. + :Warning: '>=' specifies two constraints, not one. - :Example: '>><=' means the first two constraints have ''greater or equal to'' signs, the third has ''less than or equal to'' sign, and the last is an equality constraint. + :Example: '>><=' specifies four constraints. The first two constraints have ''greater or equal to'' signs, the third has ''less than or equal to'' sign, and the last is an equality constraint. - :If a single character is specified, all constraints are uniformly signed to the corresponding type. + :If a single character is specified, all constraints have the corresponding type uniformly. - * '''lb''': variable lower bound vector, double. + * '''lb''': variable lower bound, double type, either scalar or vector. - :[] (empty array) means 0 lower bound. -inf means no lower bound. ''scalar'' means a uniform lower bound equal to ''scalar''. + :[] (empty array) means 0 lower bound. -inf means no lower bound. If a scalar is specified, it will be the uniform lower bound for all variables. - * '''ub''': variable upper bound vector, double. + * '''ub''': variable upper bound, double type, either scalar or vector. - :[] (empty array) means no (or infinity) upper bound. ''scalar'' means a uniform upper bound equal to ''scalar''. + :[] (empty array) means no (or infinity) upper bound. If a scalar is specified, it will be the uniform upper bound for all variables. - * '''vartypes''': variable types. Char array of chars 'C', 'B', 'I', 'S', 'N'. C for continuous; B for binary; I for integer; S for semi-continuous; N for semi-integer. [] (empty array) means all variables are continuous. + * '''vartypes''': variable types, char array of 'C', 'B', 'I', 'S', 'N'. 'C' for continuous; 'B' for binary; 'I' for integer; 'S' for semi-continuous; 'N' for semi-integer. [] (empty array) means all variables are continuous. - :Example: 'CCCCC' stands for five continuous variables. + :Example: 'CCCCC' specifies five continuous variables. :Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero. Semi-integer variables are similarly defined. :Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero. Semi-integer variables are similarly defined. - :If a single character is specified, all variables are uniformly signed to the corresponding type. + :If a single character is specified, all variables will be signed to the corresponding type uniformly. * '''options''': ''optional'' structure that may contain one or more of the following fields:
(see [http://www.gurobi.com/html/doc/refman/node378.html Gurobi's parameter help] for their allowed values. Also, see [[Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#Three_Examples|examples]] below.) * '''options''': ''optional'' structure that may contain one or more of the following fields:
(see [http://www.gurobi.com/html/doc/refman/node378.html Gurobi's parameter help] for their allowed values. Also, see [[Gurobi_Mex:_A_MATLAB_interface_for_Gurobi#Three_Examples|examples]] below.) ** '''options.IterationLimit''': ** '''options.IterationLimit''':

## Revision as of 02:24, 7 July 2010

Gurobi Mex is a MATLAB interface for Gurobi 2 and 3 written by Wotao Yin. It calls Gurobi to solve linear/mixed-integer optimization problems. Gurobi is one of the leading linear and mixed integer programming solvers. Gurobi offers free trial, and its full version is free for academic usage.

The interface is open source and subject to Creative Commons Attribution-Share Alike 3.0 United States License. It is a tool for MATLAB users to quickly call Gurobi, and its source code serves as a start point for those who want to develop a customized MATLAB interface for Gurobi.

Its current version is 1.20 published on April 25, 2010. It supports both Gurobi versions 2 and 3.

## Contents

v1.20 New features: Ctrl-C detection, Gurobi 3 support, back compatible with Gurobi 2. Improved error and exception handling. Empty array [] is returned when an output argument is not available (due to optimization failures or errors). Fixed the display interval option.

### History

v1.10 New features: callback, runtime progress output, flexible log file, flexible input types, more options. Part of the code was contributed by Tomáš Strnad. Known bug: print an empty line even if options DisplayInterval and Display are both set to 0. Fix: remove Line 736 of gurobi_mex.c: mexPrintf("\n");

v1.05 Major bug fix: char array of constraint sense has been fixed

v1.04 support writing model to files in various formats such as MPS, REW, LP, ...

v1.03 support log file

v1.02 fixed a memory leak issue

v1.01 update: support output dual solution lambda; allow vartypes to be empty (for all continuous variables).

v1.00 initial version.

### Install Gurobi Mex in MATLAB

#### Step 1. Preparation

Refer to Gurobi's installation guide. Please make sure that (i) proper environment variables are set, (ii) your copy of Gurobi has a license, and (iii) the license has been successfully validated.

#### Step 2. Code Change Required for Gurobi 2 Only

Uncomment Line 19 of gurobi_mex.c because GRB_SUBOPTIMAL is not part of Gurobi 2. It is introduced in Gurobi 3.

#### Step 3. Compiling Gurobi Mex

##### Step 3a. Windows
```mex -O -I"<gurobi include path>" gurobi_mex.c "<gurobi C library file>" "<MATLAB libut.lib>"
```

Example with Gurobi 3.00, MSVC2008, MATLAB 2009B, and 32-bit Windows

```mex -O -I"C:\Gurobi300\win32\include" gurobi_mex.c "C:\Gurobi300\win32\lib\gurobi30.lib" "C:\Program Files\MATLAB\R2009b\extern\lib\win32\microsoft\libut.lib"
```
##### Missing libut.lib?

Ctrl-C detection requires libut.lib. If libut.lib is not found under your copy of MATLAB, you can download one for 32-bit Windows and 64-bit Windows (courtesy of Imre Polik).

Alternatively, it can be manually generated by creating a .def text file including the following five lines

```LIBRARY libut.dll
EXPORTS
utIsInterruptPending
utSetInterruptPending
[empty line]
```

and then calling lib.exe (included in MSVC) like

```"C:\Program Files\Microsoft Visual Studio 9.0\VC\bin\lib" /def:libut.def /out:libut.lib /machine:x86
```

where /machine:x86 should be replaced by /machine:x64 for 64-bit Windows.

##### Step 3b. Linux/Unix
```mex -O -I"<gurobi include path>" gurobi_mex.c -L"<gurobi lib path>" -l<gurobi C library file> -lut
```

Example with Gurobi 3.00, GCC, MATLAB 2009B, and 64-bit Linux

```mex -O -I"/opt/gurobi300/linux64/include" gurobi_mex.c -L"/opt/gurobi300/linux64/lib" -lgurobi30 -lut -largeArrayDims
```

#### Tested platforms

• 64-bit Ubuntu Linux 9.10, 64-bit MATLAB, and gcc.
• 32-bit Windows, 32-bit MATLAB, and gcc (part of free Mingw/GnuMex).
• 32-bit Windows, 32-bit MATLAB, and MSVC 2008 SP1 (the express Edition is free).
• 64-bit Windows, 64-bit MATLAB, and MSVC 2008 SP1 (the express Edition is free). Courtesy of Imre Polik.

We found trouble with MATLAB's built-in lcc to link with Gurobi's library.

## Model

``` min/max  c'x

subject to
Ax  [>= / <= / =]  b,
lb <= x <= ub,
x(i) is [continuous / binary / integer / semi-continuous / semi-integer].
```

## Syntax

x = gurobi_mex(c, objtype, A, b, contypes, lb, ub, vartypes);
x = gurobi_mex(c, objtype, A, b, contypes, lb, ub, vartypes, options);
[x,val] = gurobi_mex(...);
[x,val,flag] = gurobi_mex(...);
[x,val,flag,output] = gurobi_mex(...);
[x,val,flag,output,lambda] = gurobi_mex(...);

## Input Description

• c: objective coefficient vector, double type.
[] (empty array) means uniformly 0 coefficients, and scalar means all coefficients equal to scalar.
• objtype: 1 (minimization) or -1 (maximization).
• A: constraint coefficient matrix, double type, sparse.
• b: constraint right-hand side vector, double type.
Gurobi takes a dense vector for this input. If a sparse vector is specified, it will be converted to full by Gurobi Mex.
• contypes: constraint types. Char array of '>', '<', '='.
Warning: '>=' specifies two constraints, not one.
Example: '>><=' specifies four constraints. The first two constraints have greater or equal to signs, the third has less than or equal to sign, and the last is an equality constraint.
If a single character is specified, all constraints have the corresponding type uniformly.
• lb: variable lower bound, double type, either scalar or vector.
[] (empty array) means 0 lower bound. -inf means no lower bound. If a scalar is specified, it will be the uniform lower bound for all variables.
• ub: variable upper bound, double type, either scalar or vector.
[] (empty array) means no (or infinity) upper bound. If a scalar is specified, it will be the uniform upper bound for all variables.
• vartypes: variable types, char array of 'C', 'B', 'I', 'S', 'N'. 'C' for continuous; 'B' for binary; 'I' for integer; 'S' for semi-continuous; 'N' for semi-integer. [] (empty array) means all variables are continuous.
Example: 'CCCCC' specifies five continuous variables.
Note that semi-continuous variables are variables that must take a value between their minimum and maximum or zero. Semi-integer variables are similarly defined.
If a single character is specified, all variables will be signed to the corresponding type uniformly.
• options: optional structure that may contain one or more of the following fields:
(see Gurobi's parameter help for their allowed values. Also, see examples below.)
• options.IterationLimit:
• options.FeasibilityTol:
• options.IntFeasTol:
• options.OptimalityTol:
• options.MIPGap:
• options.LPMethod:
• options.Presolve:
• options.TimeLimit:
• options.DisplayInterval: Gurobi's Callback screen output interval.   0 means no Gurobi message.
• options.Display: Gurobi Mex's screen output level. 0 for no output; 1 for error only; 2 (default) for normal output. For complete silence, both DisplayInterval and Display need to be set to 0.
• options.LogFile: char array of the name of log file.  options.UseLogfile is no longer used.
• options.WriteToFile: char array of the name of the file to which optimization data is written. See Gurobi C-Reference entry GRBwrite for supported formats. This option helps one verify whether the model is correctly passed to Gurobi.

## Output Description

• x: primal solution vector; empty if Gurobi encounters errors or stops early (in this case, check output flag).
• val: optimal objective value; empty if Gurobi encounters errors or stops early.
• flag: value meanings:
• 1 for not started
• 2 for optimal
• 3 for infeasible
• 4 for infeasible or unbounded
• 5 for unbounded
• 6 for objective worse than user-specified cutoff
• 7 for reaching iteration limit
• 8 for reaching node limit
• 9 for reaching time limit
• 10 for reaching solution limit
• 11 for user interruption
• 12 for numerical difficulties
• 13 for suboptimal solution (Gurobi 3 and later)
• output: structure contains the following fields
• output.IterCount: number of Simplex iterations
• output.Runtime: running time in seconds
• output.ErrorMsg: contains Gurobi error message, if any
• lambda: Lagrange multipliers. Because solving MIPs gives no such output, do not ask for this output for MIPs.

## Callbacks

Callbacks are useful to obtain the progress of Gurobi (e.g., by calling GRBcbget) and to modify its behavior during runtime (e.g., by calling GRBcbcut and GRBcbsolution).

Gurobi Mex implements a callback function mycallback to obtain Gurobi's progress messages and print them on the MATLAB screen. The print frequency is set in options.DisplayInterval (in seconds). The same function is also used to detect user input Ctrl-C.

Information for Gurobi callbacks can be found here in Gurobi's help. An example can be found here.

## Four Examples

### Example 1. Linear programming

This example is borrowed from MATLAB's linprog help.

Problem:

``` min –5 x1 – 4 x2 –6 x3,

subject to
x1 – x2 + x3 ≤ 20
3 x1 + 2 x2 + 4 x3 ≤ 42
3 x1 + 2 x2 ≤ 30
0 ≤ x1, 0 ≤ x2, 0 ≤ x3.
```

MATLAB code:

``` c = [-5; -4; -6];
objtype = 1;
A =  sparse([1 -1  1; 3  2  4; 3  2  0]);
b = [20; 42; 30];
lb = zeros(3,1);           % same as lb = [];
ub = [];
contypes = '<<<';
vtypes = [];               % same as vtypes = 'CCC'; [] means 'C...C'

clear opts
opts.IterationLimit = 20;
opts.FeasibilityTol = 1e-6;
opts.IntFeasTol = 1e-5;
opts.OptimalityTol = 1e-6;
opts.LPMethod = 1;         % 0 - primal, 1 - dual
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_LP.log';
opts.WriteToFile = 'test_gurobi_mex_LP.mps';

[x,val,exitflag,output,lambda] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Results:

``` x' =
0 15 3

val =
-78

exitflag =
2

output =
IterCount: 2
Runtime: 0
ErrorMsg: []

lambda' =
0   -1.5000   -0.5000
```

Log file: test_gurobi_mex_LP.log. MPS file: test_gurobi_mex_LP.mps.

### Example 2. Integer programming

This example is borrowed from mip1_c.c of Gurobi 2.0.

Problem:

``` max  x + y + 2z,

subject to
x + 2 y + 3 z <= 4
x +   y       >= 1
x, y, z binary.
```

MATLAB code:

``` c = [1; 1; 2];
objtype = -1;              % 1 for minimize, -1 for maximize
A =  sparse([1 2 3; 1 1 0]);
b = [4; 1];
lb = [];
ub = [];
contypes = '<>';
vtypes = 'BBB';

clear opts
opts.IterationLimit = 20;
opts.FeasibilityTol = 1e-6;
opts.IntFeasTol = 1e-5;
opts.OptimalityTol = 1e-6;
opts.LPMethod = 1;         % 0 - primal, 1 - dual
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_MIP.log';
opts.WriteToFile = 'test_gurobi_mex_MIP.mps';

[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Gurobi does not give lambda (Pi, or Lagrange multipliers) for MIPs, unless model fix is called.

Results:

``` disp('Solution:');disp(x')
disp('Optimal obj value:');disp(val)
disp('Exit flag:');disp(exitflag)
disp('Optimization info:');disp(output)

Solution:
1     0     1

Optimal obj value:
3

Exit flag:
2

Optimization info:
IterCount: 0
Runtime: 0
ErrorMsg: []
```

Log file: test_gurobi_mex_MIP.log. MPS file: test_gurobi_mex_MIP.mps.

### Example 3. Feasibility test

Problem:

```Find a solution or report infeasibility of

5 x1 + 4 x2        + 5 x4 >= -21
5 x1 + 3 x2 + 1 x3 + 4 x4  = -14
3 x1 + 5 x2 + 2 x3 - 5 x4  =  11
x1,x2,x3,x4 >= 0.
```

MATLAB code:

``` c = [];                    % use [] or 0 for null objective
objtype = -1;              % 1 for minimize, -1 for maximize
A =  sparse([5 4 0 5; 5 3 1 4; 3 5 2 -5]);
b = [-21; -14; 11];        % stands for uniformly 0 lower bound
lb = [];
ub = [];                   % stands for uniformly inf upper bound
contypes = '>==';
vtypes = [];               % same as vtypes = 'CCCC'; empty means 'C...C'

clear opts
opts.FeasibilityTol = 1e-6;
opts.Presolve = -1;        % -1 - auto, 0 - no, 1 - conserv, 2 - aggressive
opts.Display = 1;
opts.LogFile = 'test_gurobi_mex_Feasibility.log';
opts.WriteToFile = 'test_gurobi_mex_Feasibility.mps';

[x,val,exitflag,output] = gurobi_mex(c,objtype,A,b,contypes,lb,ub,vtypes,opts);
```

Results:

``` disp('Solution:');disp(x')
disp('Optimal obj value:');disp(val)
disp('Exit flag:');disp(exitflag)

Model is infeasible. No solution will be returned.

Solution:
Optimal obj value:
Exit flag:
3
```

Log file: test_gurobi_mex_Feasibility.log. MPS file: test_gurobi_mex_Feasibility.mps.

### Example 4. Compressive sensing

See example m-file test_gurobi_mex_CS.m.

## Feedback

I would be delighted to hear from you if you find Gurobi Mex useful, or if you have any suggestions, contributions, or bug reports. Please send these to Wotao Yin (wotao.yin AT rice.edu)

## How to cite

Wotao Yin. Gurobi Mex: A MATLAB interface for Gurobi, URL: http://www.caam.rice.edu/~wy1/gurobi_mex, 2009-2010.