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lp-modeler

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.

Usage

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

Formulation

\ One Problem

Maximize
  10 a + 20 b

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

Generals
  a c b 

End

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:

problem.write_lp("problem.lp")

Example 2 - An Assignment model

Formulation

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
AbeBenCam
Deb506060
Eve759570
Fay758080

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),
    ].into_iter().collect();

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

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

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

COIN-OR Cbc

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

GLPK

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

Gurobi

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

Changelog

0.5.0

0.4.3

0.4.2

0.4.1

0.4.0

0.3.3

0.3.3

0.3.1

0.3.0

Contributors

Main contributor

All contributions :heart:

Further work