#### lp

This library helps the modeling of Linear Programming (LP) and Mixed Integer Programming (MIP) in OCaml.

It supports the model with not only linear terms, but also quadratic terms.

The model can be imported-from / exported-to CPLEX LP file format, which can be loaded by various solvers.

It also has direct interfaces to some solvers.

Currently supported are GLPK (GNU Linear Programming Kit) and Gurobi.

### Install

```
# optional but recommended to pin dev-repo
opam pin lp --dev-repo
opam pin lp-glpk --dev-repo
opam install lp lp-glpk
## If your application is based on js_of_ocaml:
opam pin lp-glpk-js --dev-repo
opam install lp-glpk-js
## If you have an access to Gurobi:
opam pin lp-gurobi --dev-repo
opam install lp-gurobi
```

### Example

A minimum example is shown below.

More detailed description can be found on wiki.

```
let x = Lp.var "x"
let y = Lp.var "y"
let problem =
let open Lp in
let obj = maximize (x ++ y) in
let c0 = x ++ (c 1.2 *~ y) <~ c 5.0 in
let c1 = (c 2.0 *~ x) ++ y <~ c 1.2 in
make obj [c0; c1]
let write () = Lp.write "my_problem.lp" problem
let solve () =
(* For other interfaces, use Lp_glpk_js or Lp_gurobi instead *)
match Lp_glpk.solve problem with
| Ok (obj, xs) ->
Printf.printf "Objective: %.2f\n" obj ;
Printf.printf "x: %.2f y: %.2f\n"
(Lp.PMap.find x xs) (Lp.PMap.find y xs)
| Error msg ->
print_endline msg
let () =
if Lp.validate problem then (write () ; solve ())
else print_endline "Oops, my problem is broken."
```

#### Notes on solver interfaces

Since lp-glpk is tested only on GLPK version 4.65 and 5+, something may fail on older versions.

lp-glpk-js is another interface to GLPK through glpk.js, that is useful for applications based on js_of_ocaml.

lp-gurobi is an interface to commercial solver Gurobi. To work with this, compile your application with

`-cclib -lgurobiXY`

flags, where XY is the version of Gurobi (e.g. 91).

### Documentation

High-level APIs have comments for odoc (or ocamldoc).

Generated docs can be found online or in docs directory.

### Development Status

Development is not quite active now because basic features are completed.

However, there are several TODOs.

Bug-reports, requests, or patches are always welcome via GitHub issues and pull requests.

#### Conformity to LP file format

Currently only basic features of LP file format are supported.

Yet to be supported are advanced features,

which are typically available on commercial solvers.

(There is no standard of LP file, though.)

##### supported

Single objective (linear and quadratic)

Constraints (linear and quadratic)

Bounds

Variable types (general and binary integers)

##### not-supported

Semi-continuous variables

Multi-objective

Lazy constraint

Special ordered set (SOS)

Piecewise-linear (PWL) objective and constraint

General Constraint

Scenario

### References

Some references to LP file format.

### License

md5=92a179cb5ff0feb598b9cc404779f6dc

sha512=c34ee01cc8ffa980b7e94a951179292a40df98fb4afa6d0d7bbeb6ae0a8d60c3fbfc031a634e2ee74236b493f38ee548bf22acfb6b5c47baccbbf2778ff89c7c