1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
// Copyright 2018 Stefan Kroboth // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or // http://opensource.org/licenses/MIT>, at your option. This file may not be // copied, modified, or distributed except according to those terms. //! # Ackley test function //! //! Defined as //! //! `f(x_1, x_2, ..., x_n) = - a * exp( -b \sqrt{\frac{1}{d}\sum_{i=1}^n x_i^2 ) - //! exp( \frac{1}{d} cos(c * x_i) ) + a + exp(1)` //! //! where `x_i \in [-32.768, 32.768]` and usually `a = 10`, `b = 0.2` and `c = 2*pi` //! //! The global minimum is at `f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0`. use num::{Float, FromPrimitive}; use std::f64::consts::PI; use std::iter::Sum; /// Ackley test function /// /// Defined as /// /// `f(x_1, x_2, ..., x_n) = - a * exp( -b \sqrt{\frac{1}{d}\sum_{i=1}^n x_i^2 ) - /// exp( \frac{1}{d} cos(c * x_i) ) + a + exp(1)` /// /// where `x_i \in [-32.768, 32.768]` and usually `a = 10`, `b = 0.2` and `c = 2*pi` /// /// The global minimum is at `f(x_1, x_2, ..., x_n) = f(0, 0, ..., 0) = 0`. pub fn ackley<T: Float + FromPrimitive + Sum>(param: &[T]) -> T { ackley_param( param, T::from_f64(20.0).unwrap(), T::from_f64(0.2).unwrap(), T::from_f64(2.0 * PI).unwrap(), ) } /// Ackley test function /// /// The same as `ackley`; however, it allows to set the parameters a, b and c. pub fn ackley_param<T: Float + FromPrimitive + Sum>(param: &[T], a: T, b: T, c: T) -> T { let num1 = T::from_f64(1.0).unwrap(); let n = T::from_usize(param.len()).unwrap(); -a * (-b * ((num1 / n) * param.iter().map(|x| x.powi(2)).sum()).sqrt()).exp() - ((num1 / n) * param.iter().map(|x| (c * *x).cos()).sum()).exp() + a + num1.exp() } mod tests { #[test] fn test_ackley_optimum() { // There seem to be numerical problems which is why the epsilons are multiplied with a // factor. Not sure if this is acceptable... assert!(::ackley(&[0.0_f32, 0.0_f32, 0.0_f32]).abs() < ::std::f32::EPSILON * 10_f32); assert!(::ackley(&[0.0_f64, 0.0_f64, 0.0_f64]).abs() < ::std::f64::EPSILON * 3_f64); } #[test] fn test_parameters() { assert!( ::ackley(&[0.0_f64, 0.0_f64, 0.0_f64]).abs() == ::ackley_param( &[0.0_f64, 0.0_f64, 0.0_f64], 20.0, 0.2, 2.0 * ::std::f64::consts::PI ).abs() ); } }