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// 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. //! * [Simulated Annealing](struct.SimulatedAnnealing.html) //! //! # References //! //! [0] [Wikipedia](https://en.wikipedia.org/wiki/Simulated_annealing) //! //! [1] S Kirkpatrick, CD Gelatt Jr, MP Vecchi. (1983). "Optimization by Simulated Annealing". //! Science 13 May 1983, Vol. 220, Issue 4598, pp. 671-680 //! DOI: 10.1126/science.220.4598.671 use crate::prelude::*; use argmin_codegen::ArgminSolver; use rand; use rand::Rng; /// Temperature functions for Simulated Annealing. /// /// Given the initial temperature `t_init` and the iteration number `i`, the current temperature /// `t_i` is given as follows: /// /// * `SATempFunc::TemperatureFast`: `t_i = t_init / i` /// * `SATempFunc::Boltzmann`: `t_i = t_init / ln(i)` /// * `SATempFunc::Exponential`: `t_i = t_init * 0.95^i` /// * `SATempFunc::Custom`: User provided temperature update function which must have the function /// signature `&Fn(init_temp: f64, iteration_number: u64) -> f64` pub enum SATempFunc { /// `t_i = t_init / i` TemperatureFast, /// `t_i = t_init / ln(i)` Boltzmann, /// `t_i = t_init * x^i` Exponential(f64), /// User-provided temperature function. The first parameter must be the current temperature and /// the second parameter must be the iteration number. Custom(Box<Fn(f64, u64) -> f64>), } /// Simulated Annealing /// /// # Example /// /// ``` /// extern crate argmin; /// extern crate rand; /// use argmin::prelude::*; /// use argmin::solver::simulatedannealing::{SATempFunc, SimulatedAnnealing}; /// use argmin::testfunctions::rosenbrock; /// use rand::prelude::*; /// use std::sync::{Arc, Mutex};; /// /// #[derive(Clone)] /// struct Rosenbrock { /// /// Parameter a, usually 1.0 /// a: f64, /// /// Parameter b, usually 100.0 /// b: f64, /// /// lower bound /// lower_bound: Vec<f64>, /// /// upper bound /// upper_bound: Vec<f64>, /// /// Random number generator. We use a `Arc<Mutex<_>>` here because `ArgminOperator` requires /// /// `self` to be passed as an immutable reference. This gives us thread safe interior /// /// mutability. /// rng: Arc<Mutex<SmallRng>>, /// } /// /// impl std::default::Default for Rosenbrock { /// fn default() -> Self { /// let lower_bound: Vec<f64> = vec![-5.0, -5.0]; /// let upper_bound: Vec<f64> = vec![5.0, 5.0]; /// Rosenbrock::new(1.0, 100.0, lower_bound, upper_bound) /// } /// } /// /// impl Rosenbrock { /// /// Constructor /// pub fn new(a: f64, b: f64, lower_bound: Vec<f64>, upper_bound: Vec<f64>) -> Self { /// Rosenbrock { /// a, /// b, /// lower_bound, /// upper_bound, /// rng: Arc::new(Mutex::new(SmallRng::from_entropy())), /// } /// } /// } /// /// impl ArgminOp for Rosenbrock { /// type Param= Vec<f64>; /// type Output = f64; /// type Hessian = (); /// /// fn apply(&self, param: &Vec<f64>) -> Result<f64, Error> { /// Ok(rosenbrock(param, self.a, self.b)) /// } /// /// /// This function is called by the annealing function /// fn modify(&self, param: &Vec<f64>, temp: f64) -> Result<Vec<f64>, Error> { /// let mut param_n = param.clone(); /// // Perform modifications to a degree proportional to the current temperature `temp`. /// for _ in 0..(temp.floor() as u64 + 1) { /// // Compute random index of the parameter vector using the supplied random number /// // generator. /// let mut rng = self.rng.lock().unwrap(); /// let idx = (*rng).gen_range(0, param.len()); /// /// // Compute random number in [0.01, 0.01]. /// let val = 0.01 * (*rng).gen_range(-1.0, 1.0); /// /// // modify previous parameter value at random position `idx` by `val` /// let tmp = param[idx] + val; /// /// // check if bounds are violated. If yes, project onto bound. /// if tmp > self.upper_bound[idx] { /// param_n[idx] = self.upper_bound[idx]; /// } else if tmp < self.lower_bound[idx] { /// param_n[idx] = self.lower_bound[idx]; /// } else { /// param_n[idx] = param[idx] + val; /// } /// } /// Ok(param_n) /// } /// } /// /// fn run() -> Result<(), Error> { /// // Define bounds /// let lower_bound: Vec<f64> = vec![-5.0, -5.0]; /// let upper_bound: Vec<f64> = vec![5.0, 5.0]; /// /// // Define cost function /// let operator = Rosenbrock::new(1.0, 100.0, lower_bound, upper_bound); /// /// // definie inital parameter vector /// let init_param: Vec<f64> = vec![1.0, 1.2]; /// /// // Define initial temperature /// let temp = 15.0; /// /// // Set up simulated annealing solver /// let mut solver = SimulatedAnnealing::new(operator, init_param, temp)?; /// /// // Optional: Define temperature function (defaults to `SATempFunc::TemperatureFast`) /// solver.temp_func(SATempFunc::Boltzmann); /// /// // Optional: Attach a logger /// solver.add_logger(ArgminSlogLogger::term()); /// /// ///////////////////////// /// // Stopping criteria // /// ///////////////////////// /// /// // Optional: Set maximum number of iterations (defaults to `std::u64::MAX`) /// solver.set_max_iters(1_000); /// /// // Optional: Set target cost function value (defaults to `std::f64::NEG_INFINITY`) /// solver.set_target_cost(0.0); /// /// // Optional: stop if there was no new best solution after 100 iterations /// solver.stall_best(100); /// /// // Optional: stop if there was no accepted solution after 100 iterations /// solver.stall_accepted(100); /// /// ///////////////////////// /// // Reannealing // /// ///////////////////////// /// /// // Optional: Reanneal after 100 iterations (resets temperature to initial temperature) /// solver.reannealing_fixed(100); /// /// // Optional: Reanneal after no accepted solution has been found for 50 iterations /// solver.reannealing_accepted(50); /// /// // Optional: Start reannealing after no new best solution has been found for 80 iterations /// solver.reannealing_best(80); /// /// ///////////////////////// /// // Run solver // /// ///////////////////////// /// /// solver.run()?; /// /// // Wait a second (lets the logger flush everything before printing again) /// std::thread::sleep(std::time::Duration::from_secs(1)); /// /// // Print result /// println!("{:?}", solver.result()); /// Ok(()) /// } /// /// fn main() { /// if let Err(ref e) = run() { /// println!("{} {}", e.as_fail(), e.backtrace()); /// std::process::exit(1); /// } /// } /// ``` /// /// # References /// /// [0] [Wikipedia](https://en.wikipedia.org/wiki/Simulated_annealing) /// /// [1] S Kirkpatrick, CD Gelatt Jr, MP Vecchi. (1983). "Optimization by Simulated Annealing". /// Science 13 May 1983, Vol. 220, Issue 4598, pp. 671-680 /// DOI: 10.1126/science.220.4598.671 #[derive(ArgminSolver)] #[log("initial_temperature" => "self.init_temp")] #[log("stall_iter_accepted_limit" => "self.stall_iter_accepted_limit")] #[log("stall_iter_best_limit" => "self.stall_iter_best_limit")] #[log("reanneal_fixed" => "self.reanneal_fixed")] #[log("reanneal_accepted" => "self.reanneal_accepted")] #[log("reanneal_best" => "self.reanneal_best")] pub struct SimulatedAnnealing<O> where O: ArgminOp<Output = f64>, { /// Initial temperature init_temp: f64, /// which temperature function? temp_func: SATempFunc, /// Number of iterations used for the caluclation of temperature. This is needed for /// reannealing! temp_iter: u64, /// Iterations since the last accepted solution stall_iter_accepted: u64, /// Stop if stall_iter_accepted exceedes this number stall_iter_accepted_limit: u64, /// Iterations since the last best solution was found stall_iter_best: u64, /// Stop if stall_iter_best exceedes this number stall_iter_best_limit: u64, /// Reanneal after this number of iterations is reached reanneal_fixed: u64, /// Similar to `iter`, but will be reset to 0 when reannealing is performed reanneal_iter_fixed: u64, /// Reanneal after no accepted solution has been found for `reanneal_accepted` iterations reanneal_accepted: u64, /// Similar to `stall_iter_accepted`, but will be reset to 0 when reannealing is performed reanneal_iter_accepted: u64, /// Reanneal after no new best solution has been found for `reanneal_best` iterations reanneal_best: u64, /// Similar to `stall_iter_best`, but will be reset to 0 when reannealing is performed reanneal_iter_best: u64, /// current temperature cur_temp: f64, /// previous cost prev_cost: f64, /// random number generator rng: rand::prelude::ThreadRng, /// base base: ArgminBase<O>, } impl<O> SimulatedAnnealing<O> where O: ArgminOp<Output = f64>, { /// Constructor /// /// Parameters: /// /// * `cost_function`: cost function /// * `init_param`: initial parameter vector /// * `init_temp`: initial temperature pub fn new( cost_function: O, init_param: <O as ArgminOp>::Param, init_temp: f64, ) -> Result<Self, Error> { let prev_cost = cost_function.apply(&init_param)?; if init_temp <= 0_f64 { Err(ArgminError::InvalidParameter { text: "initial temperature".to_string(), } .into()) } else { Ok(SimulatedAnnealing { init_temp, temp_func: SATempFunc::TemperatureFast, temp_iter: 0u64, stall_iter_accepted: 0u64, stall_iter_accepted_limit: std::u64::MAX, stall_iter_best: 0u64, stall_iter_best_limit: std::u64::MAX, reanneal_fixed: std::u64::MAX, reanneal_iter_fixed: 0, reanneal_accepted: std::u64::MAX, reanneal_iter_accepted: 0, reanneal_best: std::u64::MAX, reanneal_iter_best: 0, cur_temp: init_temp, prev_cost, rng: rand::thread_rng(), base: ArgminBase::new(cost_function, init_param), }) } } /// Set temperature function to one of the options in `SATempFunc`. pub fn temp_func(&mut self, temperature_func: SATempFunc) -> &mut Self { self.temp_func = temperature_func; self } /// The optimization stops after there has been no accepted solution after `iter` iterations pub fn stall_accepted(&mut self, iter: u64) -> &mut Self { self.stall_iter_accepted_limit = iter; self } /// The optimization stops after there has been no new best solution after `iter` iterations pub fn stall_best(&mut self, iter: u64) -> &mut Self { self.stall_iter_best_limit = iter; self } /// Start reannealing after `iter` iterations pub fn reannealing_fixed(&mut self, iter: u64) -> &mut Self { self.reanneal_fixed = iter; self } /// Start reannealing after no accepted solution has been found for `iter` iterations pub fn reannealing_accepted(&mut self, iter: u64) -> &mut Self { self.reanneal_accepted = iter; self } /// Start reannealing after no new best solution has been found for `iter` iterations pub fn reannealing_best(&mut self, iter: u64) -> &mut Self { self.reanneal_best = iter; self } /// Acceptance function /// /// Any solution which satisfies `next_cost < prev_cost` will be accepted. Solutions worse than /// the previous one are accepted with a probability given as: /// /// `1 / (1 + exp((next_cost - prev_cost) / current_temperature))`, /// /// which will always be between 0 and 0.5. fn accept(&mut self, next_param: &<O as ArgminOp>::Param, next_cost: f64) -> (bool, bool) { let prob: f64 = self.rng.gen(); let mut new_best = false; let accepted = if (next_cost < self.prev_cost) || (1.0 / (1.0 + ((next_cost - self.prev_cost) / self.cur_temp).exp()) > prob) { // If yes, update the parameter vector for the next iteration. self.prev_cost = next_cost; self.set_cur_param(next_param.clone()); // In case the new solution is better than the current best, update best as well. if next_cost < self.best_cost() { new_best = true; self.set_best_cost(next_cost); self.set_best_param(next_param.clone()); } true } else { false }; (accepted, new_best) } /// Update the temperature based on the current iteration number. /// /// Updates are performed based on specific update functions. See `SATempFunc` for details. fn update_temperature(&mut self) { self.cur_temp = match self.temp_func { SATempFunc::TemperatureFast => self.init_temp / ((self.temp_iter + 1) as f64), SATempFunc::Boltzmann => self.init_temp / ((self.temp_iter + 1) as f64).ln(), SATempFunc::Exponential(x) => self.init_temp * x.powf((self.temp_iter + 1) as f64), SATempFunc::Custom(ref func) => func(self.init_temp, self.temp_iter), }; } /// Perform annealing fn anneal(&mut self) -> Result<<O as ArgminOp>::Param, Error> { let tmp = self.cur_param(); let cur_temp = self.cur_temp; self.modify(&tmp, cur_temp) } /// Perform reannealing fn reanneal(&mut self) -> (bool, bool, bool) { let out = ( self.reanneal_iter_fixed >= self.reanneal_fixed, self.reanneal_iter_accepted >= self.reanneal_accepted, self.reanneal_iter_best >= self.reanneal_best, ); if out.0 || out.1 || out.2 { self.reanneal_iter_fixed = 0; self.reanneal_iter_accepted = 0; self.reanneal_iter_best = 0; self.cur_temp = self.init_temp; self.temp_iter = 0; } out } /// Update the stall iter variables fn update_stall_and_reanneal_iter(&mut self, accepted: bool, new_best: bool) { self.stall_iter_accepted = if accepted { 0 } else { self.stall_iter_accepted + 1 }; self.reanneal_iter_accepted = if accepted { 0 } else { self.reanneal_iter_accepted + 1 }; self.stall_iter_best = if new_best { 0 } else { self.stall_iter_best + 1 }; self.reanneal_iter_best = if new_best { 0 } else { self.reanneal_iter_best + 1 }; } } impl<O> ArgminIter for SimulatedAnnealing<O> where O: ArgminOp<Output = f64>, { type Param = <O as ArgminOp>::Param; type Output = <O as ArgminOp>::Output; type Hessian = <O as ArgminOp>::Hessian; /// Perform one iteration of SA algorithm fn next_iter(&mut self) -> Result<ArgminIterData<Self::Param>, Error> { // Careful: The order in here is *very* important, even if it may not seem so. Everything // is linked to the iteration number, and getting things mixed up will lead to strange // behaviour. None of these strange behaviour is dangerous, but still. // Make a move let new_param = self.anneal()?; // Evaluate cost function with new parameter vector let new_cost = self.apply(&new_param)?; // Decide whether new parameter vector should be accepted. // If no, move on with old parameter vector. let (accepted, new_best) = self.accept(&new_param, new_cost); // Update stall iter variables self.update_stall_and_reanneal_iter(accepted, new_best); let (r_fixed, r_accepted, r_best) = self.reanneal(); // Update temperature for next iteration. self.temp_iter += 1; // Todo: this variable may not be necessary (temp_iter does the same?) self.reanneal_iter_fixed += 1; self.update_temperature(); let mut out = ArgminIterData::new(new_param, new_cost); out.add_kv(make_kv!( "t" => self.cur_temp; "new_be" => new_best; "acc" => accepted; "st_i_be" => self.stall_iter_best; "st_i_ac" => self.stall_iter_accepted; "ra_i_fi" => self.reanneal_iter_fixed; "ra_i_be" => self.reanneal_iter_best; "ra_i_ac" => self.reanneal_iter_accepted; "ra_fi" => r_fixed; "ra_be" => r_best; "ra_ac" => r_accepted; )); Ok(out) } }