ml-direct

Direct - DIviding RECTangles algorithm.

The algorithm is intended to minimize real valued multivariate scalar fields over a hyper-rectangular region of N, theoretically the only prerequisite to achieve convergence is that the function must be continuous in the domain or at least continuous over a neighborhood of the global minimum.

Advanced example

import direct from 'ml-direct';

const options = {
  iterations: 50,
};

const lowerBoundaries = [-1, -1.5];
const upperBoundaries = [2, 6];

const predicted = direct(griewank, lowerBoundaries, upperBoundaries, options);

function griewank(x) {
  let d = x.length;
  let s = 0;
  let p = 1;
  for (let i = 0; i < d; i++) {
    s += Math.pow(x[i], 2) / Math.sqrt(4000);
    p *= Math.cos(x[i] / Math.sqrt(i + 1));
  }
  let result = s - p + 1;
  return result;
}

// predicted.minFunctionValue = 0;
// predicted.optima[0] = [0, 0]; This are the points where the function has minimum value

Installation

$ npm i ml-direct

Usage

import direct from 'ml-direct';

const options = {
  iterations: 25,
};

// for x we explore values between -5 and 4
// for y we explore values between -2 and 3

const lowerBoundaries = [-5, -2];
const upperBoundaries = [4, 3];

const quadratic = function (parameters) {
  let [x, y] = parameters;
  return Math.pow(x, 2) + Math.pow(y, 2);
};

const predicted = direct(quadratic, lowerBoundaries, upperBoundaries, options);

// predicted.minFunctionValue = 0;
// predicted.optima[0] = [0, 0];

API Documentation

References

• Jones, D. R., Perttunen, C. D., & Stuckman, B. E. (1993). Lipschitzian optimization without the Lipschitz constant. Journal of optimization Theory and Applications, 79(1), 157-181.

• Björkman, M., & Holmström, K. (1999). Global optimization using the DIRECT algorithm in Matlab.

• Preparata, F. P., & Shamos, M. I. (2012). Computational geometry: an introduction. Springer Science & Business Media.

License

MIT