GLPK Solver Engine

The GNU Linear Programming Kit (GLPK) is a long-standing, robust simplex and interior-point solver package intended for solving large-scale linear programming (LP) and mixed integer programming (MIP).

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Installation

GLPK is provided as an optional peer dependency via glpk.js:

npm install glpk.js

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Licensing Consideration (GPL-3.0)

GLPK is licensed under the GNU General Public License v3.0 (GPL-3.0).

• Because WaSHI is MIT-licensed, glpk.js is never bundled statically in the core package.
• It is dynamically imported only if you explicitly register or invoke @ohtaman/washi/solvers/glpk.
• Ensure your project's distribution requirements comply with the GPL-3.0 license when shipping products that bundle GLPK.

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Basic Usage

import { Model, expr, maximize } from "@ohtaman/washi";
import "@ohtaman/washi/solvers/glpk";

const model = new Model({ solver: "glpk" });

const x = model.continuous("x", { lb: 0, ub: 10 });
const y = model.continuous("y", { lb: 0, ub: 20 });

model.objective(maximize(expr`3 * ${x} + 2 * ${y}`));
model.constraint(expr`${x} + ${y} <= 15`, "cap");

await model.solve();

console.log("GLPK Status:", model.status);
console.log("Objective:", model.objectiveValue);

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Result Semantics & Status Mapping

Solver Statuses

GLPK return codes are mapped strictly to WaSHI SolverStatus:

• GLP_OPT (5) $\to$ "Optimal"
• GLP_FEAS (2) $\to$ "Feasible" (feasible MIP incumbent found)
• GLP_INFEAS (3) / GLP_NOFEAS (4) $\to$ "Infeasible"
• GLP_UNBND (6) $\to$ "Unbounded"
• GLP_UNDEF (1) and unrecognized/missing statuses $\to$ "Unknown" (never misclassified as "Optimal")

Solution Availability

• Variable values (model.values, var.value) and objective values (model.objectiveValue) are exposed only when a valid primal solution is available ("Optimal" or "Feasible").
• For unsuccessful or non-optimal solves (Infeasible, Unbounded, Unknown, Error), model.objectiveValue is null and variable values remain null without fabricating fake all-zero solutions.

Differences Between LP and MIP

• Linear Programming (LP): Solved using the simplex algorithm. Dual values (shadow prices via constraint.dual) and slacks are populated for optimal solutions.
• Mixed-Integer Programming (MIP): Solved using the branch-and-cut algorithm. Produces integer-feasible primal variable solutions; dual values are mathematically undefined for discrete optimization and omitted.