#linear-programming #linear-models #optimization #solver #formulation


A linear programming modeller written in Rust. This api helps to write LP model and use solver such as CBC, Gurobi, lp_solve, ...

9 releases

Uses old Rust 2015

0.5.0 Mar 1, 2021
0.4.3 Nov 5, 2020
0.4.2 Oct 14, 2019
0.4.0 Sep 26, 2019
0.3.0 Aug 7, 2017

#386 in Algorithms

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MIT license

2.5K SLoC


MIT license Build Status Gitter Github Actions This project provides a mathematical programming modeling library for Rust.

An optimization problem (e.g. an integer or linear programme) can be formulated using familiar Rust syntax (see examples), and written into a universal LP model format. This can then be processed by a mixed integer programming solver. Presently supported solvers that require a separate installation (see below the examples section) to be present at runtime of your lp_modeler-based project are:

Presently supported solvers that you can import as Rust crates (as optional features) are:

This project is inspired by COIN-OR PuLP which provides such a library for Python.


These examples present a formulation (in LP model format), and demonstrate the Rust code required to generate this formulation. Code can be found in tests/problems.rs.

Example 1 - Simple model


\ One Problem

  10 a + 20 b

Subject To
  c1: 500 a + 1200 b + 1500 c <= 10000
  c2: a - b <= 0

  a c b 


Rust code

extern crate lp_modeler;

use lp_modeler::solvers::{CbcSolver, SolverTrait};
use lp_modeler::dsl::*;
use lp_modeler::constraint;

fn main() {
    // Define problem variables
    let ref a = LpInteger::new("a");
    let ref b = LpInteger::new("b");
    let ref c = LpInteger::new("c");

    // Define problem and objective sense
    let mut problem = LpProblem::new("One Problem", LpObjective::Maximize);

    // Objective Function: Maximize 10*a + 20*b
    problem += 10.0 * a + 20.0 * b;

    // Constraint: 500*a + 1200*b + 1500*c <= 10000
    problem += constraint!(500*a + 1200*b + 1500*c <= 10000);

    // Constraint: a <= b
    problem += constraint!(a <= b);

    // Specify solver
    let solver = CbcSolver::new();

    // Run optimisation and process output hashmap
    match solver.run(&problem) {
        Ok(solution) => {
            println!("Status {:?}", solution.status);
            for (name, value) in solution.results.iter() {
                println!("value of {} = {}", name, value);
        Err(msg) => println!("{}", msg),

To generate the LP file which is shown above:


Example 2 - An Assignment model


This more complex formulation programmatically generates the expressions for the objective and constraints.

We wish to maximise the quality of the pairing between a group of men and women, based on their mutual compatibility score. Each man must be assigned to exactly one woman, and vice versa.

Compatibility Score Matrix
Abe Ben Cam
Deb 50 60 60
Eve 75 95 70
Fay 75 80 80

This problem is formulated as an Assignment Problem.

Rust code

extern crate lp_modeler;

use std::collections::HashMap;

use lp_modeler::dsl::*;
use lp_modeler::solvers::{SolverTrait, CbcSolver};

fn main() {
    // Problem Data
    let men = vec!["A", "B", "C"];
    let women = vec!["D", "E", "F"];
    let compatibility_score: HashMap<(&str, &str),f32> = vec![
        (("A", "D"), 50.0),
        (("A", "E"), 75.0),
        (("A", "F"), 75.0),
        (("B", "D"), 60.0),
        (("B", "E"), 95.0),
        (("B", "F"), 80.0),
        (("C", "D"), 60.0),
        (("C", "E"), 70.0),
        (("C", "F"), 80.0),

    // Define Problem
    let mut problem = LpProblem::new("Matchmaking", LpObjective::Maximize);

    // Define Variables
    let vars: HashMap<(&str,&str), LpBinary> =
            .flat_map(|&m| women.iter()
            .map(move |&w| {
                let key = (m,w);
                let value = LpBinary::new(&format!("{}_{}", m,w));
                (key, value)

    // Define Objective Function
    let obj_vec: Vec<LpExpression> = {
       vars.iter().map( |(&(m,w), bin)| {
           let &coef = compatibility_score.get(&(m, w)).unwrap();
           coef * bin
       } )
    problem += obj_vec.sum();

    // Define Constraints
    // - constraint 1: Each man must be assigned to exactly one woman
    for &m in &men{
        problem += sum(&women, |&w| vars.get(&(m,w)).unwrap() ).equal(1);

    // - constraint 2: Each woman must be assigned to exactly one man
    for &w in &women{
        problem += sum(&men, |&m| vars.get(&(m,w)).unwrap() ).equal(1);

    // Run Solver
    let solver = CbcSolver::new();
    let result = solver.run(&problem);

    // Compute final objective function value
    // (terminate if error, or assign status & variable values)
    assert!(result.is_ok(), result.unwrap_err());
    let (status, results) = result.unwrap();
    let mut obj_value = 0f32;
    for (&(m, w), var) in &vars{
        let obj_coef = compatibility_score.get(&(m, w)).unwrap();
        let var_value = results.get(&var.name).unwrap();

        obj_value += obj_coef * var_value;

    // Print output
    println!("Status: {:?}", status);
    println!("Objective Value: {}", obj_value);
    for (var_name, var_value) in &results{
        let int_var_value = *var_value as u32;
        if int_var_value == 1{
            println!("{} = {}", var_name, int_var_value);

This code computes the objective function value and processes the output to print the chosen pairing of men and women:

Status: Optimal
Objective Value: 230
B_E = 1
C_D = 1
A_F = 1

installing external solvers

installing conda (package manager)

If you want the latest release version of Cbc, Gurobi or GLPK, the easiest cross-platform installation pathway should be via conda. Importantly, this does not require admin rights on the system you want to install it on. All you need to do is install conda. Once this is done, use the respective conda command for the solver you want to use (see below).


latest release (via conda)

To get the latest Cbc release for your system with conda (installation see above), use this command:

conda create -n coin-or-cbc -c conda-forge coin-or-cbc

Then activating the newly created environment will make the cbc executable available:

conda activate coin-or-cbc

latest release (via coinbrew)

To get the latest Cbc release, including the . We recommend using COIN-OR's coinbrew, as described here: https://coin-or.github.io/user_introduction#building-from-source

latest commit (via coinbrew)

To get the very latest Cbc version, including unreleased bug fixes, you will need to build it from source. We recommend using COIN-OR's coinbrew, as described here: https://coin-or.github.io/user_introduction#building-from-source


recent release (via conda)

To get a recent release of GLPK for your system with conda, use this command:

conda create -n glpk -c conda-forge glpk

Then activating the newly created environment will make the glpsol executable available:

conda activate glpk


latest release (via conda)

To use Gurobi, you need to have a valid license key and have it in a location that Gurobi can find it. Once you have a valid license, you can get the latest Gurobi release for your system with conda, use this command:

conda create -n gurobi -c gurobi gurobi

Then activating the newly created environment will make the gurobi_cl executable available:

conda activate gurobi



  • Add a native minilp impl to call the Rust native solver minilp
  • Changed coin_cbc-based NativeCbcSolver to an optional feature
  • Fix adding upper bounds to NativeCbc
  • Add a coinstraint!() macro
  • Add AddAssign, SubAssign and MulAssign traits
  • Reworked various internal functions to remove recursions (fixes related stack overflows)
  • Add install infos for the solvers to the docs


  • Add a native coin-or impl (NativeCBCSolver) to call CoinOR CBC trough the C API.


  • Fix incorrect simplification of (expr-c1)+c2


  • Fix failed cbc parsing on infeasible solution


  • Improve modules

    • Remove maplit dependency
    • All the features to write expressions and constraints are put into dsl module
    • use lp_modeler::dsl::* is enough to write a system
    • use lp_modeler::solvers::* is always used to choose a solver
  • Add a sum() method for vector of LpExpression/Into<LpExpression> instead of lp_sum() function

  • Add a sum() function used in the form:

    problem += sum(&vars, |&v| v * 10.0) ).le(10.0);


  • Fix and improve error message for GLPK solution parsing
  • Format code with rust fmt


  • Add new examples in documentation
  • Improve 0.0 comparison


  • Add distributive property (ex: 3 * (a + b + 2) = 3*a + 3*b + 6)
  • Add trivial rules (ex: 3 * a * 0 = 0 or 3 + 0 = 3)
  • Add commutative property to simplify some computations
  • Support for GLPK


  • Functional lib with simple algebra properties


Main contributor

All contributions ❤️

Further work

  • Parse and provide the objective value
  • Config for lp_solve and CPLEX
  • It would be great to use some constraint for binary variables such as
    • a && b which is the constraint a + b = 2
    • a || b which is the constraint a + b >= 1
    • a <=> b which is the constraint a = b
    • a => b which is the constraint a <= b
    • All these cases are easy with two constraints but more complex with expressions
    • ...


~20K SLoC