linprog

Idea is to provide wrapper for most performant opensource optimization tools that are available. This shard is about linear and mixed integer optimization. According to http://plato.asu.edu/bench.html CLP is pretty good for linear programming, and other projects of COIN-OR (CBC and IPOPT) are fine for nonlinear.

CoinMP is decribed as simple API for CLP and CBC (just what I need!), but appears to be buggy and obsolete.

SYMPHONY looks easy enough to use and to distribute.

1. SYMPHONY works, but require few patches to be easily wrappable (namely extern C to disable mangling and #define printf to disable console spam). I've created fork https://github.com/konovod/SYMPHONY with patches
2. It is distributed under EPL1.0 that is incompatible with GPL, but otherwise pretty permissive.

Installation

1. Install COIN-OR SYMPHONY from package manager to get all dependencies
2. git clone https://github.com/konovod/SYMPHONY
3. configure && make
4. copy SYMPHONY/SYMPHONY/src/.libs/libSym.so.0.0.0 to /usr/lib, create symlink /usr/lib/libSym.so.1 pointing to it

Alternatively: you can use installation instructions for the upstream version: https://github.com/coin-or/SYMPHONY Master already has extern C fix but will spam some messages to console.

Usage

require "linalg"
require "linprog"

# linear programming
# x - solution, f - objective value
x, f = Symphony.lpsolve(
  # c - objective function
  c: LA::GMat.new([[0, -1]]),
  # a_ub - left part of inequalities
  a_ub: LA::GMat.new([[-1, 1], [3, 2], [2, 3]]),
  # b_ub - right part of inequalities
  b_ub: LA::GMat.new([[1, 12, 12]]).t,
  # a_eq, b_eq - left and right parts of equalities, can be skipped if empty
  # bounds - constraints to variables
  bounds: {Symphony::Constraint.none, Symphony::Constraint.new(-3.0, Float64::INFINITY)})
pp x, f

# constraint can be same for all vars
x, f = Symphony.lpsolve(
  c: LA::GMat.new([[0, -1]]),
  a_ub: LA::GMat.new([[-1, 1], [3, 2], [2, 3]]),
  b_ub: LA::GMat.new([[1, 12, 12]]).t,
  bounds: Symphony::Constraint.positive)
pp x, f

# tasks can use equalities, inequalities or both
x, f = Symphony.lpsolve(
  c: LA::Mat.row([1, 7, 4, 2, 3, 5]),
  a_eq: LA::GMat.new([
    [1, 1, 1, 0, 0, 0],
    [0, 0, 0, 1, 1, 1],
    [1, 0, 0, 1, 0, 0],
    [0, 1, 0, 0, 1, 0],
    [0, 0, 1, 0, 0, 1],
  ]),
  b_eq: LA::Mat.column([30, 20, 15, 25, 10]))
pp x, f

# integer and mixed integer programming
x, f = Symphony.lpsolve(
  c: LA::GMat.new([[0, -1]]),
  a_ub: LA::GMat.new([[-1, 1], [3, 2], [2, 3]]),
  b_ub: LA::GMat.new([[1, 12, 12]]).t,
  bounds: {Symphony::Constraint.integer, Symphony::Constraint.new(0.0, 6.0, integer: true)})
pp x, f

# there is also more complex interface that allows to save\load problems, but it's WIP, check spec dir for it

Roadmap:

• warmstarting
• sensitivity analysis
• access to solver parameters
• way to reset solver properly or otherwise avoid memory leak
• sparse matrix support
• DSL for problems creation