HiGHS Solver Engine

HiGHS is high-performance mathematical optimization software developed at the University of Edinburgh. It is widely recognized as the state-of-the-art open-source solver for Linear Programming (LP), Mixed-Integer Programming (MIP), and Convex Quadratic Programming (QP).

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Key Features in WaSHI

• Built-in & Zero-Config: Bundled directly with @ohtaman/washi. No separate peer dependency or compilation required.
• Permissive MIT License: 100% commercially friendly.
• Web Worker Multithreading: Automatically offloads intensive solving to background Web Workers in browser environments to avoid freezing the UI thread.
• Fast WASM Execution: Emscripten-compiled 32-bit WASM runs at near-native speed.

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Supported Problem Classes

1. Linear Programming (LP)

Solves continuous problems via Primal and Dual Simplex algorithms or Interior Point (IPM) methods:

const model = new Model({ solver: "highs" });
const x = model.continuous("x", { lb: 0 });
const y = model.continuous("y", { lb: 0 });
model.objective(maximize(expr`10 * ${x} + 6 * ${y}`));
model.constraint(c`${x} + ${y} <= 100`);
await model.solve();

2. Mixed-Integer Linear Programming (MIP)

Solves discrete problems using Branch-and-Bound and cutting plane techniques:

const count = model.integer("count", { lb: 0, ub: 50 });

3. Convex Quadratic Programming (QP)

Solves quadratic objective functions subject to linear constraints:

// Minimize risk/variance uniformly using expr:
model.objective(minimize(expr`0.5 * ${x}^2 + 0.5 * ${y}^2`));

// Or programmatically with .mul():
// const quadObj = x.mul(x).mul(0.5).add(y.mul(y).mul(0.5));
// model.objective(minimize(quadObj));

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Solver Options

Pass solver options into model.solve():

await model.solve({
  timeLimit: 60.0,       // Maximum solve time in seconds
  mipGap: 0.001,         // Terminate when within 0.1% of global optimality
  verbose: true,         // Output internal simplex / branch-and-bound logs
});

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Worker Configuration in Browsers

By default in browsers, WaSHI spawns a dedicated Web Worker to execute HiGHS in the background.

If you need to run synchronously on the main thread (or in environments where Web Workers are prohibited):

const model = new Model({
  solver: "highs",
  solverOptions: {
    useWorker: false,
  },
});