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mathopt

A JavaScript library of mathematical optimization methods.

Overview

  • Works on browsers and NodeJS.
  • Tested on these browsers:
    • TODO

Installation

Install manually by adding to your HTML file:

<script src="/path/to/mathopt/index.js"></script>

Install with npm:

$ npm install --save mathopt

Install with component:

$ component install jakutis/mathopt

Install with bower:

$ bower install --save mathopt

API

See a demonstration of examples (source code in "examples" subfolder).

.basicPSO

Basic Particle Swarm Optimization method finds the global minimum of a given numerical function using particle swarm paradigm.

Implements the algorithm that is described in an article "Particle swarm optimization" by James Kennedy and Russel Eberhart that is published in proceedings of IEEE International Conference on Neural Networks, 1995.

The default parameters are taken from an article "The Particle Swarm - Explosion, Stability, and Convergence in a Multidimensional Complex Space" by Maurice Clerck and James Kennedy that is published in IEEE Transactions on Evolutionary Computation (2002, issue #1 of volume #6).

All particles are initialized with the position specified in initialPosition option. Initial velocities are sampled from U(0, 2).

var cornfield = function(x, y) {
    return Math.abs(x - 100) + Math.abs(y - 100);
};

// basic usage
// prints "Minimum found at TODO"
console.log('Minimum found at ', mathopt.basicPSO(cornfield));

// demonstration of all the options
mathopt.basicPSO(function(x) {
    return cornfield(x[0], x[1]);
}, {
    // default: 21
    particles: 50,

    // default: inferred from the given function; when specified - the given function must accept a vector
    dimensions: 2,

    // default: [0, 0]
    initialPosition: [5, 5],

    // default: 0.01
    idleSpeed: 0.1,

    // default: 0.7298
    inertia: 0.7,

    // default: 2.9922/2
    localAcceleration: 1.5,

    // default: 2.9922/2
    globalAcceleration: 1.5,

    // default: `function(i, p, v, pbest, best, cb) { cb && setTimeout(cb, 0); }`
    // when onstop is null, cb argument is not passed
    oniteration: function(iteration, positions, velocities, bestpositions, bestparticle, cb) {
        console.log(iteration, bestpositions);
        cb && setTimeout(cb, 0);
    },

    // default: null
    // when set, switches to asynchronous behavior:
    // - .basicPSO does not return anything
    // - oniteration receives a `cb` callback
    onstop: function(min) {
        // prints "Minimum found at x=TODO, y=TODO, after TODO iterations"
        console.log('Minimum found at x=' + min[0] + ', y=' + min[1] + ' after ' + min.iterations + ' iterations');
    }
});

Development

TODO