cl-glpk

A Common Lisp library for solving linear programs.

Portability

CL-GLPK should work on any Lisp/OS/machine combination, as long as CFFI, Trivial-Garbage, Iterate, and GLPK work.

CL-GLPK has been tested on SBCL 1.0.2 / Mac OS X (10.4) / PPC and CCL trunk / Mac OS X (10.6) / x86-64.

Quick Introduction

Load the ASDF system. The low-level FFI bindings are implicitly documented by the GLPK manual. For the (partial) high-level API, see examples/sample.lisp. The highest-level API allows you to express linear programs like:

(make-linear-program
 :maximize (+ (* 10 x1) (* 6 x2) (* 4 x3))
 :subject-to ((<= (+ x1 x2 x3) 100)
              (<= (+ (* 4 x2) (* 10 x1) (* 5 x3)) 600)
              (<= (+ (* 2 x1) (* 2 x2) (* 6 x3)) 300))
 :bounds ((>= x3 10)))

Any of the :BOUNDS constraints could be in the :SUBJECT-TO list instead, but I'm not yet sure what impact that will have on performance, so until I can identify (and if necessary, prevent) that, I pull my variable bounds into a separate parameter.

Then you can solve the program and get results with

(simplex *)
(format t "z = ~a, x1 = ~a, x2 = ~a, x3 = ~a~%"
        (objective-value **)
        (column-primal-value ** 1)
        (column-primal-value ** 2)
        (column-primal-value ** 3))

There are still a lot of improvements to build into this high-level API before it's really complete.

Instead of the macro you can also use the underlying functional interface compute-linear-program.

The created object representing the linear program must be destroyed subsequently with destroy-linear-program. This ensures that all data structures are correctly deallocated when they are no longer needed, and not wait till GC time.

One can use the macro with-linear-program to handle object creation/destruction:

(with-linear-program (lp (:maximize (+ (* 10 x1) (* 6 x2) (* 4 x3))
                          :subject-to ((<= (+ x1 x2 x3) 100)
                                       (<= (+ (* 4 x2) (* 10 x1) (* 5 x3)) 600)
                                       (<= (+ (* 2 x1) (* 2 x2) (* 6 x3)) 300))
                          :bounds ((>= x3 10))))
   (simplex lp)
   (format t "z = ~a, x1 = ~a, x2 = ~a, x3 = ~a~%"
        (objective-value **)
        (column-primal-value ** 1)
        (column-primal-value ** 2)
        (column-primal-value ** 3)))

License

BSD sans advertising clause (see file COPYING)

TODO List

Write more examples

Write some tests

Improve error handling

Currently error handling is done by either (ERROR ...) or (ASSERT ...).

Extend High Level API

Make up a DSL (similar to GLPK's MPS files, but lispier)

This is partially completed in make-linear-program/compute-linear-problem.

Complete FFI bindings

Memory management

Linear problem FFI objects are properly freed by way of attaching a finalizer to their CLOS counterpart. Replacing the constraints of a linear problem CLOS object will free the memory used by replaced constraints (glp_load_matrix will do this on the C side).

valeryz / cl-glpk