From 071d1ee49846ffb77436f456bf0b167135d5d74c Mon Sep 17 00:00:00 2001 From: psmgeelen Date: Sat, 10 Feb 2018 09:41:46 +0100 Subject: [PATCH] Prototype for linear programming is done. We only need more examples of different CPLEX formats, specifically MOLP, big M, Q and ILP methods. --- figures/advanced_encoding.png | Bin 0 -> 52062 bytes figures/cplexformat.png | Bin 0 -> 23332 bytes figures/openfile.png | Bin 0 -> 30644 bytes figures/savefile.png | Bin 0 -> 18549 bytes glpkAPI.pdf | Bin 0 -> 205049 bytes linearprogramming.Rmd | 58 ++++++------ linearprogramming.nb.html | 160 +++++++++++++--------------------- report.txt | 38 ++++++++ sar.txt | 38 ++++++++ 9 files changed, 167 insertions(+), 127 deletions(-) create mode 100644 figures/advanced_encoding.png create mode 100644 figures/cplexformat.png create mode 100644 figures/openfile.png create mode 100644 figures/savefile.png create mode 100644 glpkAPI.pdf create mode 100644 report.txt create mode 100644 sar.txt diff --git a/figures/advanced_encoding.png b/figures/advanced_encoding.png new file mode 100644 index 0000000000000000000000000000000000000000..43fd0b5fe85353d44dab1ee33d6d4b799e5028f9 GIT binary patch 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CPLEX

In order to "just write down" the functions, we need to work with a particular format which is the "CPLEX". Its based on a more complicated engine that is used by big companies like IBM. R, of course, also provides a free alternative. The overal format is as follows. -

--Start-File--

-

Maximize

-

  obj: x1 + 2 x2 + 3 x3 + x4

-

Subject To

-

  c1: - x1 + x2 + x3 + 10 x4 <= 20

-

  c2: x1 - 3 x2 + x3 <= 30

-

  c3: x2 - 3.5 x4 = 0

-

Bounds

-

  0 <= x1 <= 40

-

  2 <= x4 <= 3

-

General

-

  x4

-

End

-

--End-File--

+![](figures/cplexformat.png) This link provides a concrete guide for the use of this format: http://lpsolve.sourceforge.net/5.0/CPLEX-format.htm -Note that this package also contains a free book from Fernandez that provide excellent examples for this method. The first template is provided on page 34. +Note that this package also contains a free book from Fernandez that provide excellent examples for this method. The first template is provided on page 34, which is excerpted above. + +

Workflow CPLEX

+ +The CPLEX format is based on ASCII coding. This coding is relates to how a file is stored. The workflow of creating a CPLEX file is a follows. You can create a new file in RStudio by clicking on the new file button. This will open a menu, select txt file. +![](figures/openfile.png) + +When everything has been entered in the correct CPLEX format, you can save the file by going on the menubar and clicking on the file button. +![](figures/savefile.png) + +From there you select the "Save file with encoding..." option. This will open another small screen with a few options of encoding, including ASCII. Select ASCII. After that you can select a path name for the file. Please note that if you save it as linear.programm.txt, you need to refer to it as such. In the examples above we used no extension (.txt, .doc, .docx, etc..) and therefore do not refer to one either in our commands. +

Required Packages

There are 3 packages required to run these linear programms
    -
  • lpSolve
  • -
  • lpSolveAPI
  • +
  • glpkAPI
  • Rglpk
So lets install those by executing the code below: ```{r} -install.packages("lpSolve") -install.packages("lpSolveAPI") +install.packages("glpkAPI") install.packages("Rglpk") ``` Having installed the requried packages, we can run the generic code for linear programming which is: ```{r} -library(lpSolveAPI) +library(glpkAPI) library(Rglpk) -x <- Rglpk_read_file("example_lp", type = "CPLEX_LP", ignore_first_row = FALSE, verbose = FALSE) +problem <- initProbGLPK(ptrtype = "glpk_prob") -solve <- Rglpk_solve_LP(x$objective, x$constraints[[1]], x$constraints[[2]], x$constraints[[3]], x$bounds, x$types, x$maximum) -``` +readLPGLPK(problem, "example_lp") + +solveSimplexGLPK(problem) + +printRangesGLPK(problem, fname = "report.txt") -Here the CPLEX object is 1) imported into R, 2) An optimum is calculated and 3) the results are retrieved. +file.show("report.txt") + +``` +In order to undestand the code above, I want to elaborate on what an API is. An API is an "Application Programming Interface". More simply put, its a way of communicating to other software. In order to use GLPK (GNU Linear Programming Kit), we need to create an object within this package. To do this we use the initProbGLPK, which initiates an empty object within the GLPK package. Note that this object is connected to R through an object in R, called "problem". More simply put: the "problem" object in R is the connection to the "glpk_prob" object in GLPK. These objects are in effect mirrors and connections. The read, solve and print commands dont require an object within R, since they are executed in the GLPK package. Due to the fact that the real calculations are not run in R, the sensitivty report cannot be displayed in the terminal either. For this reason a file.show command has been used, to open the file when the calculations are done. -

Sensitivity Report

+

Examples

-Tornado graph would be kewl too +There are alot of concrete examples of how to write Linear Programs in CPLEX in the book that is also added to this zip file. The book is called "Linear Programming.pdf" There -To do: Sensitivity report, CPLEX formats for MOLP, ILP and big M methods, we need to test and formulate the ASCII issue +To do: Are there a couple of formats that we can steal from the book to cover the MOLP, ILP and LP principles? Maybe even Big M and stuff. \ No newline at end of file diff --git a/linearprogramming.nb.html b/linearprogramming.nb.html index 7b54fba..4ed82b0 100644 --- a/linearprogramming.nb.html +++ b/linearprogramming.nb.html @@ -173,64 +173,33 @@

Linear Programming 2.0

-

This notebook with give you a start in Linear Programming in R. Arseny and I have been working many hours to develop a workflow by which you can truly write down the functions and constraints, as you will for the exam. It is our belief that this will prepare more adequately for the exam and we hope to improve the overall “feel” of the course.

-

-CPLEX -

-

In order to “just write down” the functions, we need to work with a particular format which is the “CPLEX”. Its based on a more complicated engine that is used by big companies like IBM. R, of course, also provides a free alternative. The overal format is as follows.

-

-–Start-File– -

-

-Maximize -

-

-  obj: x1 + 2 x2 + 3 x3 + x4 -

-

-Subject To -

-

-  c1: - x1 + x2 + x3 + 10 x4 <= 20 -

-

-  c2: x1 - 3 x2 + x3 <= 30 -

-

-  c3: x2 - 3.5 x4 = 0 -

-

-Bounds -

-

-  0 <= x1 <= 40 -

-

-  2 <= x4 <= 3 -

-

-General -

-

-  x4 -

+This notebook with give you a start in Linear Programming in R. Arseny and I have been working many hours to develop a workflow by which you can truly write down the functions and constraints, as you will for the exam. It is our belief that this will prepare more adequately for the exam and we hope to improve the overall “feel” of the course.

-End

-–End-File–

-

This link provides a concrete guide for the use of this format: http://lpsolve.sourceforge.net/5.0/CPLEX-format.htm Note that this package also contains a free book from Fernandez that provide excellent examples for this method. The first template is provided on page 34.

+

+CPLEX +

+

In order to “just write down” the functions, we need to work with a particular format which is the “CPLEX”. Its based on a more complicated engine that is used by big companies like IBM. R, of course, also provides a free alternative. The overal format is as follows.

+
+ + +
+

This link provides a concrete guide for the use of this format: http://lpsolve.sourceforge.net/5.0/CPLEX-format.htm Note that this package also contains a free book from Fernandez that provide excellent examples for this method. The first template is provided on page 34, which is excerpted above.

+

+Workflow CPLEX +

+

The CPLEX format is based on ASCII coding. This coding is relates to how a file is stored. The workflow of creating a CPLEX file is a follows. You can create a new file in RStudio by clicking on the new file button. This will open a menu, select txt file.

+

When everything has been entered in the correct CPLEX format, you can save the file by going on the menubar and clicking on the file button.

+

From there you select the “Save file with encoding…” option. This will open another small screen with a few options of encoding, including ASCII. Select ASCII. After that you can select a path name for the file. Please note that if you save it as linear.programm.txt, you need to refer to it as such. In the examples above we used no extension (.txt, .doc, .docx, etc..) and therefore do not refer to one either in our commands.

Required Packages

There are 3 packages required to run these linear programms

  • -lpSolve -
  • -
  • -lpSolveAPI +glpkAPI
  • Rglpk @@ -238,76 +207,69 @@

    So lets install those by executing the code below:

    - -
    install.packages("lpSolve")
    + +
    install.packages("glpkAPI")
    - -
    Installing package into 㤼㸱C:/Users/Qnect/Documents/R/win-library/3.4㤼㸲
    -(as 㤼㸱lib㤼㸲 is unspecified)
    -trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.4/lpSolve_5.6.13.zip'
    -Content type 'application/zip' length 733314 bytes (716 KB)
    -downloaded 716 KB
    - - -
    package ‘lpSolve’ successfully unpacked and MD5 sums checked
    -
    -The downloaded binary packages are in
    -    C:\Users\Qnect\AppData\Local\Temp\RtmpesSfrf\downloaded_packages
    - - -
    install.packages("lpSolveAPI")
    - - -
    Installing package into 㤼㸱C:/Users/Qnect/Documents/R/win-library/3.4㤼㸲
    -(as 㤼㸱lib㤼㸲 is unspecified)
    -trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.4/lpSolveAPI_5.5.2.0-17.zip'
    -Content type 'application/zip' length 1044053 bytes (1019 KB)
    -downloaded 1019 KB
    - - -
    package ‘lpSolveAPI’ successfully unpacked and MD5 sums checked
    -
    -The downloaded binary packages are in
    -    C:\Users\Qnect\AppData\Local\Temp\RtmpesSfrf\downloaded_packages
    + +
    Error in install.packages : Updating loaded packages
    install.packages("Rglpk")
    - -
    Installing package into 㤼㸱C:/Users/Qnect/Documents/R/win-library/3.4㤼㸲
    -(as 㤼㸱lib㤼㸲 is unspecified)
    -trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.4/Rglpk_0.6-3.zip'
    -Content type 'application/zip' length 957907 bytes (935 KB)
    -downloaded 935 KB
    - - -
    package ‘Rglpk’ successfully unpacked and MD5 sums checked
    -
    -The downloaded binary packages are in
    -    C:\Users\Qnect\AppData\Local\Temp\RtmpesSfrf\downloaded_packages
    + +
    Error in install.packages : Updating loaded packages

    Having installed the requried packages, we can run the generic code for linear programming which is:

    - -
    library(lpSolveAPI)
    +
    +
    library(glpkAPI)
     library(Rglpk)
    -x <- Rglpk_read_file("example_lp", type = "CPLEX_LP", ignore_first_row = FALSE, verbose = FALSE)
    -solve <- Rglpk_solve_LP(x$objective, x$constraints[[1]], x$constraints[[2]], x$constraints[[3]], x$bounds, x$types, x$maximum)
    +problem <- initProbGLPK(ptrtype = "glpk_prob") +readLPGLPK(problem, "example_lp")
    + + +
    Reading problem data from `example_lp'...
    +example_lp:12: warning: missing final end of line
    +3 rows, 4 columns, 9 non-zeros
    +One variable is integer
    +12 lines were read
    + 0
    + + +
    solveSimplexGLPK(problem)
    + + +
    [1]GLPK Simplex Optimizer, v4.47
    + 03 rows, 4 columns, 9 non-zeros
    +      0: obj =  2.000000000e+000  infeas = 7.000e+000 (1)
    +*     2: obj =  2.300000000e+001  infeas = 0.000e+000 (0)
    +*     4: obj =  1.252083333e+002  infeas = 0.000e+000 (0)
    +OPTIMAL SOLUTION FOUND
    + + +
    printRangesGLPK(problem, fname = "report.txt")
    + + +
    Write sensitivity analysis report to `report.txt'...[1]
    + 0
    + + +
    file.show("report.txt")
    -

    Here the CPLEX object is 1) imported into R, 2) An optimum is calculated and 3) the results are retrieved.

    +

    In order to undestand the code above, I want to elaborate on what an API is. An API is an “Application Programming Interface”. More simply put, its a way of communicating to other software. In order to use GLPK (GNU Linear Programming Kit), we need to create an object within this package. To do this we use the initProbGLPK, which initiates an empty object within the GLPK package. Note that this object is connected to R through an object in R, called “problem”. More simply put: the “problem” object in R is the connection to the “glpk_prob” object in GLPK. These objects are in effect mirrors and connections. The read, solve and print commands dont require an object within R, since they are executed in the GLPK package. Due to the fact that the real calculations are not run in R, the sensitivty report cannot be displayed in the terminal either. For this reason a file.show command has been used, to open the file when the calculations are done.

    -Sensitivity Report +Examples

    -

    Tornado graph would be kewl too

    -

    To do: Sensitivity report, CPLEX formats for MOLP, ILP and big M methods, we need to test and formulate the ASCII issue

    +

    There are alot of concrete examples of how to write Linear Programs in CPLEX in the book that is also added to this zip file. The book is called “Linear Programming.pdf” There

    +

    To do: Are there a couple of formats that we can steal from the book to cover the MOLP, ILP and LP principles? Maybe even Big M and stuff.

    -
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    +
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    diff --git a/report.txt b/report.txt new file mode 100644 index 0000000..6e89af6 --- /dev/null +++ b/report.txt @@ -0,0 +1,38 @@ +GLPK 4.47 - SENSITIVITY ANALYSIS REPORT Page 1 + +Problem: +Objective: obj = 125.2083333 (MAXimum) + + No. Row name St Activity Slack Lower bound Activity Obj coef Obj value at Limiting + Marginal Upper bound range range break point variable +------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------ + 1 c1 NU 20.00000 . -Inf -2.00000 -1.64583 89.00000 x4 + 1.64583 20.00000 22.00000 +Inf 128.50000 x4 + + 2 c2 NU 30.00000 . -Inf 28.00000 -1.35417 122.50000 x4 + 1.35417 30.00000 52.00000 +Inf 155.00000 x4 + + 3 c3 NS . . . -.50000 -Inf 123.00000 x4 + 4.41667 . 5.50000 +Inf 149.50000 x4 + +GLPK 4.47 - SENSITIVITY ANALYSIS REPORT Page 2 + +Problem: +Objective: obj = 125.2083333 (MAXimum) + + No. Column name St Activity Obj coef Lower bound Activity Obj coef Obj value at Limiting + Marginal Upper bound range range break point variable +------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------ + 1 x1 NU 40.00000 1.00000 . 29.00000 -.29167 111.00000 x4 + 1.29167 40.00000 41.00000 +Inf 126.50000 x4 + + 2 x2 BS 10.20833 2.00000 . 7.00000 -2.42857 80.00000 x1 + . +Inf 10.50000 11.28571 220.00000 c2 + + 3 x3 BS 20.62500 3.00000 . 19.50000 .59259 75.55556 c2 + . +Inf 22.00000 13.33333 338.33333 x1 + + 4 x4 BS 2.91667 1.00000 2.00000 . -14.50000 80.00000 x1 + . 3.00000 4.44444 33.50000 220.00000 c2 + +End of report diff --git a/sar.txt b/sar.txt new file mode 100644 index 0000000..6e89af6 --- /dev/null +++ b/sar.txt @@ -0,0 +1,38 @@ +GLPK 4.47 - SENSITIVITY ANALYSIS REPORT Page 1 + +Problem: +Objective: obj = 125.2083333 (MAXimum) + + No. Row name St Activity Slack Lower bound Activity Obj coef Obj value at Limiting + Marginal Upper bound range range break point variable +------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------ + 1 c1 NU 20.00000 . -Inf -2.00000 -1.64583 89.00000 x4 + 1.64583 20.00000 22.00000 +Inf 128.50000 x4 + + 2 c2 NU 30.00000 . -Inf 28.00000 -1.35417 122.50000 x4 + 1.35417 30.00000 52.00000 +Inf 155.00000 x4 + + 3 c3 NS . . . -.50000 -Inf 123.00000 x4 + 4.41667 . 5.50000 +Inf 149.50000 x4 + +GLPK 4.47 - SENSITIVITY ANALYSIS REPORT Page 2 + +Problem: +Objective: obj = 125.2083333 (MAXimum) + + No. Column name St Activity Obj coef Lower bound Activity Obj coef Obj value at Limiting + Marginal Upper bound range range break point variable +------ ------------ -- ------------- ------------- ------------- ------------- ------------- ------------- ------------ + 1 x1 NU 40.00000 1.00000 . 29.00000 -.29167 111.00000 x4 + 1.29167 40.00000 41.00000 +Inf 126.50000 x4 + + 2 x2 BS 10.20833 2.00000 . 7.00000 -2.42857 80.00000 x1 + . +Inf 10.50000 11.28571 220.00000 c2 + + 3 x3 BS 20.62500 3.00000 . 19.50000 .59259 75.55556 c2 + . +Inf 22.00000 13.33333 338.33333 x1 + + 4 x4 BS 2.91667 1.00000 2.00000 . -14.50000 80.00000 x1 + . 3.00000 4.44444 33.50000 220.00000 c2 + +End of report