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https://github.com/neil-lindquist/linear-programming
A Common Lisp library for solving linear programming problems
https://github.com/neil-lindquist/linear-programming
common-lisp linear-programming
Last synced: about 2 months ago
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A Common Lisp library for solving linear programming problems
- Host: GitHub
- URL: https://github.com/neil-lindquist/linear-programming
- Owner: neil-lindquist
- License: mit
- Created: 2019-06-22T03:56:02.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2023-12-02T20:31:41.000Z (about 1 year ago)
- Last Synced: 2024-05-02T22:12:25.305Z (8 months ago)
- Topics: common-lisp, linear-programming
- Language: Common Lisp
- Homepage: https://neil-lindquist.github.io/linear-programming/
- Size: 341 KB
- Stars: 108
- Watchers: 5
- Forks: 4
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
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README
# Common Lisp Linear Programming
[](https://github.com/neil-lindquist/linear-programming/actions/workflows/ci.yml)
[](https://coveralls.io/github/neil-lindquist/linear-programming?branch=master)
[](https://github.com/neil-lindquist/linear-programming/releases)
[](https://neil-lindquist.github.io/linear-programming/)
This is a Common Lisp library for solving linear programming problems.
It's designed to provide a high-level and ergonomic API for specifying linear programming problems as lisp expressions.
The core library is implemented purely in Common Lisp with only a few community-standard libraries as dependencies (ASDF, Alexandria, Iterate).
However, the solver is designed to support alternative backends without any change to the user's code.
Currently, there is a [backend for the GNU Linear Programming Kit (GLPK)](https://github.com/neil-lindquist/linear-programming-glpk).
## Installation
The linear-programming library is avalible in both the main Quicklisp distribution and Ultralisp, so it can loaded with with `(ql:quickload :linear-programming)`.
You can check that it works by running `(asdf:test-system :linear-programming)`.
If you are not using Quicklisp, place this repository, Alexandria, and Iterate somewhere where ASDF can find them.
Then, it can be loaded with `(asdf:load-system :linear-programming)` and tested as above.
## Usage
See [neil-lindquist.github.io/linear-programming/](https://neil-lindquist.github.io/linear-programming/) for further documentation.
Consider the following linear programming problem.
> maximize x + 4y + 3z
> such that
> * 2x + y ≤ 8
> * y + z ≤ 7
> * x, y, z ≥ 0
First, the problem needs to be specified.
Problems are specified with a simple DSL, as described in the [syntax reference](https://neil-lindquist.github.io/linear-programming/linear-problem-syntax).
```common-lisp
(use-package :linear-programming)
(defvar problem (parse-linear-problem '(max (= w (+ x (* 4 y) (* 3 z))))
'((<= (+ (* 2 x) y) 8)
(<= (+ y z) 7))))
```
Once the problem is created, it can be solved with the simplex method.
```common-lisp
(defvar solution (solve-problem problem))
```
Finally, the optimal tableau can be inspected to get the resulting objective function, decision variables, and reduced-costs (i.e. the shadow prices for the variable's lower bounds).
```common-lisp
(format t "Objective value solution: ~A~%" (solution-variable solution 'w))
(format t "x = ~A (reduced cost: ~A)~%" (solution-variable solution 'x) (solution-reduced-cost solution 'x))
(format t "y = ~A (reduced cost: ~A)~%" (solution-variable solution 'y) (solution-reduced-cost solution 'y))
(format t "z = ~A (reduced cost: ~A)~%" (solution-variable solution 'z) (solution-reduced-cost solution 'z))
;; ==>
;; Objective value solution: 57/2
;; x = 1/2 (reduced cost: 0)
;; y = 7 (reduced cost: 0)
;; z = 0 (reduced cost: 1/2)
```
Alternatively, the `with-solution-variables` and `with-solved-problem` macros simplify some steps and binds the solution variables in their bodies.
```common-lisp
(with-solution-variables (w x y z) solution
(format t "Objective value solution: ~A~%" w)
(format t "x = ~A (reduced cost: ~A)~%" x (reduced-cost x))
(format t "y = ~A (reduced cost: ~A)~%" y (reduced-cost y))
(format t "z = ~A (reduced cost: ~A)~%" z (reduced-cost z)))
;; ==>
;; Objective value solution: 57/2
;; x = 1/2 (reduced cost: 0)
;; y = 7 (reduced cost: 0)
;; z = 0 (reduced cost: 1/2)
(with-solved-problem ((max (= w (+ x (* 4 y) (* 3 z))))
(<= (+ (* 2 x) y) 8)
(<= (+ y z) 7))
(format t "Objective value solution: ~A~%" w)
(format t "x = ~A (reduced cost: ~A)~%" x (reduced-cost x))
(format t "y = ~A (reduced cost: ~A)~%" y (reduced-cost y))
(format t "z = ~A (reduced cost: ~A)~%" z (reduced-cost z)))
;; ==>
;; Objective value solution: 57/2
;; x = 1/2 (reduced cost: 0)
;; y = 7 (reduced cost: 0)
;; z = 0 (reduced cost: 1/2)
```