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// Copyright 2016 Martin Ankerl. // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://www.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. //! Differential Evolution optimizer for rust. //! //! Simple and powerful global optimization using a //! [Self-Adapting Differential Evolution](http://bit.ly/2cMPiMj) //! for Rust. See Wikipedia's article on //! [Differential Evolution](https://en.wikipedia.org/wiki/Differential_evolution) //! for more information. //! //! ## Usage //! //! Add this to your `Cargo.toml`: //! //! ```toml //! [dependencies] //! differential-evolution = "*" //! ``` //! //! and this to your crate root: //! //! ```rust //! extern crate differential_evolution; //! ``` //! //! ## Examples //! //! Differential Evolution is a global optimization algorithm that //! tries to iteratively improve candidate solutions with regards to //! a user-defined cost function. //! //! ### Quick Start: Sum of Squares //! This example finds the minimum of a simple 5-dimensional function. //! //! ``` //! extern crate differential_evolution; //! //! use differential_evolution::self_adaptive_de; //! //! fn main() { //! // create a self adaptive DE with an inital search area //! // from -10 to 10 in 5 dimensions. //! let mut de = self_adaptive_de(vec![(-10.0, 10.0); 5], |pos| { //! // cost function to minimize: sum of squares //! pos.iter().fold(0.0, |sum, x| sum + x*x) //! }); //! //! // perform 10000 cost evaluations //! de.iter().nth(10000); //! //! // show the result //! let (cost, pos) = de.best().unwrap(); //! println!("cost: {}", cost); //! println!("pos: {:?}", pos); //! } //! ``` //! //! ### Tutorial: Rastrigin //! //! The population supports an `Iterator` for evaluating. Each call //! of `next()` evaluates the cost function and returns the //! fitness value of the current global best. This way it is possible //! to use all the iterator's features for optimizig. Here are a few //! examples. //! //! Let's say we have the [Rastrigin](https://en.wikipedia.org/wiki/Rastrigin_function) //! cost function: //! //! ``` //! use std::f32::consts::PI; //! //! fn rastrigin(pos: &[f32]) -> f32 { //! pos.iter().fold(0.0, |sum, x| //! sum + x * x - 10.0 * (2.0 * PI * x).cos() + 10.0) //! } //! ``` //! //! We'd like to search for the minimum in the range -5.12 to 5.12, for //! 30 dimensions: //! //! ``` //! let initial_min_max = vec![(-5.12, 5.12); 30]; //! ``` //! //! We can create a self adaptive DE, and search until the cost //! reaches a given minimum: //! //! ``` //! # use differential_evolution::self_adaptive_de; //! # fn rastrigin(pos: &[f32]) -> f32 { 0.0 } //! # let initial_min_max = vec![(-5.12, 5.12); 2]; //! let mut de = self_adaptive_de(initial_min_max, rastrigin); //! de.iter().find(|&cost| cost < 0.1); //! ``` //! //! This is a bit dangerous though, because the optimizer might never reach that minimum. //! It is safer to just let it run for a given number of evaluations: //! //! ``` //! # use differential_evolution::self_adaptive_de; //! # fn rastrigin(pos: &[f32]) -> f32 { 0.0 } //! # let initial_min_max = vec![(-5.0, 5.0); 2]; //! let mut de = self_adaptive_de(initial_min_max, rastrigin); //! de.iter().nth(10000); //! ``` //! //! If is possible to do some smart combinations: run until cost is below a threshold, or until //! the maximum number of iterations have been reached: //! //! ``` //! # use differential_evolution::self_adaptive_de; //! # fn sum_of_squares(pos: &[f32]) -> f32 { 0.0 } //! # let initial_min_max = vec![(-5.12, 5.12); 2]; //! let mut de = self_adaptive_de(initial_min_max, sum_of_squares); //! de.iter().take(100000).find(|&cost| cost < 0.1); //! ``` //! //! When you are finished with iterating, you can extract the best solution found so far with //! `de.best()`. This retrieves the minimum cost and the position vector that has lead to this //! cost: //! //! ``` //! # use differential_evolution::self_adaptive_de; //! # fn sum_of_squares(pos: &[f32]) -> f32 { 0.0 } //! # let initial_min_max = vec![(-5.12, 5.12); 2]; //! # let mut de = self_adaptive_de(initial_min_max, sum_of_squares); //! # de.iter().nth(1000); //! let (cost, pos) = de.best().unwrap(); //! println!("{} best cost", cost); //! println!("{:?} best position", pos); //! ``` //! //! # Similar Crates //! //! - [darwin-rs](https://github.com/willi-kappler/darwin-rs) //! - [Rs Genetic](https://github.com/m-decoster/RsGenetic) //! extern crate rand; use rand::distributions::{IndependentSample, Range}; /// Holds all settings for the self adaptive differential evolution /// algorithm. pub struct Settings<F, R> where F: Fn(&[f32]) -> f32, R: rand::Rng { /// The population is initialized with uniform random /// for each dimension between the tuple's size. /// Beware that this is only the initial state, the DE /// will search outside of this initial search space. pub min_max_pos: Vec<(f32, f32)>, /// Minimum and maximum value for `cr`, the crossover control parameter. /// a good value is (0, 1) so cr is randomly choosen between in the full /// range of usable CR's from `[0, 1)`. pub cr_min_max: (f32, f32), /// Probability to change the `cr` value of an individual. Tests with /// 0.05, 0.1, 0.2 and 0.3 did not show any significant different /// results. So 0.1 seems to be a reasonable choice. pub cr_change_probability: f32, /// Minimum and maximum value for `f`, the amplification factor of the /// difference vector. DE is more sensitive to `F` than it is to `CR`. /// In literature, `F` is rarely greater than 1. If `F=0`, the evolution /// degenerates to a crossover but no mutation, so a reasonable choise /// for f_min_max seems to be (0.1, 1.0). pub f_min_max: (f32, f32), /// Probability to change the `f` value of an individual. See /// `cr_change_probability`, 0.1 is a reasonable choice. pub f_change_probability: f32, /// Number of individuals for the DE. In many benchmarks, a size of /// 100 is used. The choice somewhat depends on the difficulty and the /// dimensionality of the problem to solve. Reasonable choices seem /// between 20 and 200. pub pop_size: usize, /// Random number generator used to generate mutations. If the fitness /// function is fairly fast, the random number generator should be /// very fast as well. Since it is not necessary to use a cryptographic /// secure RNG, the best (fastest) choice is to use `rand::weak_rng()`. pub rng: R, /// The cost function to minimize. This takes an `&[f32]` and returns /// the calculated cost for this position as `f32`. This should be /// fast to evaluate, and always produce the same result for the same /// input. pub cost_function: F, } impl<F> Settings<F, rand::XorShiftRng> where F: Fn(&[f32]) -> f32 { /// Creates default settings for the differential evolution. It uses the default /// parameters as defined in the paper "Self-Adapting Control Parameters in Differential /// Evolution: A Comparative Study on Numerical Benchmark Problems", with a population /// size of 100. It also uses This uses `rand::weak_rng()` for the fastest random number /// generator available. /// /// For most problems this should be a fairly good parameter set. pub fn default(min_max_pos: Vec<(f32, f32)>, cost_function: F) -> Settings<F, rand::XorShiftRng> { Settings { min_max_pos: min_max_pos, cr_min_max: (0.0, 1.0), cr_change_probability: 0.1, f_min_max: (0.1, 1.0), f_change_probability: 0.1, pop_size: 100, rng: rand::weak_rng(), cost_function: cost_function, } } } /// Internally used struct for an inivididual. #[derive(Clone)] struct Individual { pos: Vec<f32>, // the lower, the better. cost: Option<f32>, // control parameters cr: f32, f: f32, } /// Holds the population for the differential evolution based on the given settings. pub struct Population<F, R> where F: Fn(&[f32]) -> f32, R: rand::Rng { curr: Vec<Individual>, best: Vec<Individual>, settings: Settings<F, R>, // index of global best individual. Might be in best or in curr. best_idx: Option<usize>, // cost value of the global best individual, for quick access best_cost_cache: Option<f32>, num_cost_evaluations: usize, dim: usize, between_popsize: Range<usize>, between_dim: Range<usize>, between_cr: Range<f32>, between_f: Range<f32>, pop_countdown: usize, } /// Convenience function to create a fully configured self adaptive /// differential evolution population. pub fn self_adaptive_de<F>(min_max_pos: Vec<(f32, f32)>, cost_function: F) -> Population<F, rand::XorShiftRng> where F: Fn(&[f32]) -> f32 { Population::new(Settings::default(min_max_pos, cost_function)) } impl<F, R> Population<F, R> where F: Fn(&[f32]) -> f32, R: rand::Rng { /// Creates a new population based on the given settings. pub fn new(s: Settings<F, R>) -> Population<F, R> { assert!(s.min_max_pos.len() >= 1, "need at least one element to optimize"); // create a vector of randomly initialized individuals for current. let dim = s.min_max_pos.len(); // Empty individual, with no cost value (yet) let dummy_individual = Individual { pos: vec![0.0; dim], cost: None, cr: 0.0, f: 0.0, }; // creates all the empty individuals let mut pop = Population { curr: vec![dummy_individual.clone(); s.pop_size], best: vec![dummy_individual; s.pop_size], best_idx: None, best_cost_cache: None, num_cost_evaluations: 0, dim: dim, pop_countdown: s.pop_size, between_popsize: Range::new(0, s.pop_size), between_dim: Range::new(0, dim), between_cr: Range::new(s.cr_min_max.0, s.cr_min_max.1), between_f: Range::new(s.f_min_max.0, s.f_min_max.1), settings: s, }; for ind in &mut pop.curr { // init control parameters ind.cr = pop.between_cr.ind_sample(&mut pop.settings.rng); ind.f = pop.between_f.ind_sample(&mut pop.settings.rng); // random range for each dimension for d in 0..dim { let between_min_max = Range::new(pop.settings.min_max_pos[d].0, pop.settings.min_max_pos[d].1); ind.pos[d] = between_min_max.ind_sample(&mut pop.settings.rng); } } pop } /// Loops through each individual and updates its personal best. fn update_best(&mut self) { for i in 0..self.curr.len() { let curr = &mut self.curr[i]; let best = &mut self.best[i]; // we use <= here, so that the individual moves even if the cost // stays the same. if best.cost.is_none() || curr.cost.unwrap() <= best.cost.unwrap() { // replace individual's best. swap is *much* faster than clone. std::mem::swap(curr, best); } } } // Modifies all the curr positions. This needs a lot of random numbers, so // for a fast cost function it is important to use a fast random number // generator. fn update_positions(&mut self) { let rng = &mut self.settings.rng; for i in 0..self.curr.len() { // sample 3 different individuals let id1 = self.between_popsize.ind_sample(rng); let mut id2 = self.between_popsize.ind_sample(rng); while id2 == id1 { id2 = self.between_popsize.ind_sample(rng); } let mut id3 = self.between_popsize.ind_sample(rng); while id3 == id1 || id3 == id2 { id3 = self.between_popsize.ind_sample(rng); } let curr = &mut self.curr[i]; let best = &self.best[i]; // see "Self-Adapting Control Parameters in Differential Evolution: // A Comparative Study on Numerical Benchmark Problems" if rng.gen::<f32>() < self.settings.cr_change_probability { curr.cr = self.between_cr.ind_sample(rng); } else { curr.cr = best.cr; } if rng.gen::<f32>() < self.settings.f_change_probability { curr.f = self.between_f.ind_sample(rng); } else { curr.f = best.f; } let curr_pos = &mut curr.pos; let best_pos = &best.pos; let best1_pos = &self.best[id1].pos; let best2_pos = &self.best[id2].pos; let best3_pos = &self.best[id3].pos; let forced_mutation_dim = self.between_dim.ind_sample(rng); // This implements the DE/rand/1/bin, the most widely used algorithm. // See "A Comparative Study of Differential Evolution Variants for // Global Optimization (2006)". for d in 0..self.dim { if d == forced_mutation_dim || rng.gen::<f32>() < curr.cr { curr_pos[d] = best3_pos[d] + curr.f * (best1_pos[d] - best2_pos[d]); } else { curr_pos[d] = best_pos[d]; } } // reset cost, has to be updated by the user. curr.cost = None; } } /// Gets a tuple of the best cost and best position found so far. pub fn best(&self) -> Option<(f32, &[f32])> { if let Some(bi) = self.best_idx { let curr = &self.curr[bi]; let best = &self.best[bi]; if curr.cost.is_none() { return Some((best.cost.unwrap(), &best.pos)); } if best.cost.is_none() { return Some((curr.cost.unwrap(), &curr.pos)); } if curr.cost.unwrap() < best.cost.unwrap() { return Some((curr.cost.unwrap(), &curr.pos)); } return Some((best.cost.unwrap(), &best.pos)); } else { None } } /// Gets the total number of times the cost function has been evaluated. pub fn num_cost_evaluations(&self) -> usize { self.num_cost_evaluations } /// Performs a single cost evaluation, and updates best positions and /// evolves the population if the whole population has been evaluated. /// Returns the cost value of the current best solution found. pub fn eval(&mut self) -> Option<f32> { if 0 == self.pop_countdown { // if the whole pop has been evaluated, evolve it to update positions. // this also copies curr to best, if better. self.update_best(); self.update_positions(); self.pop_countdown = self.curr.len(); } // perform a single fitness evaluation self.pop_countdown -= 1; let curr = &mut self.curr[self.pop_countdown]; let cost = (self.settings.cost_function)(&curr.pos); curr.cost = Some(cost); self.num_cost_evaluations += 1; // see if we have improved the global best if self.best_cost_cache.is_none() || cost < self.best_cost_cache.unwrap() { self.best_cost_cache = Some(cost); self.best_idx = Some(self.pop_countdown); } self.best_cost_cache } /// Gets an iterator for this population. Each call to `next()` /// performs one cost evaluation. pub fn iter(&mut self) -> PopIter<F, R> { PopIter { pop: self } } } /// Iterator for the differential evolution, to perform a single cost /// evaluation every time `move()` is called. pub struct PopIter<'a, F, R> where F: 'a + Fn(&[f32]) -> f32, R: 'a + rand::Rng { pop: &'a mut Population<F, R>, } impl<'a, F, R> Iterator for PopIter<'a, F, R> where F: 'a + Fn(&[f32]) -> f32, R: 'a + rand::Rng { type Item = f32; /// Simply forwards to the population's `eval()`. fn next(&mut self) -> Option<Self::Item> { self.pop.eval() } } #[cfg(test)] mod tests { // TODO }