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//! # Local Search contains all of the implemented local search algorithms
//!
//! This module contains all of the implemented local search algorithms, which are:
//! - One step local search
//! - Simple local search
//! - Simple gain criteria search
//! - Simple mixed search
//! - Multi simple local search
//! - Multi simple gain criteria search
//! - Simple Particle Swarm Search
use crate::initial_points::generate_random_binary_point;
use crate::local_search_utils;
use crate::qubo::Qubo;
use crate::utils::get_best_point;
use ndarray::Array1;
use rayon::iter::{IntoParallelRefIterator, ParallelIterator};
use smolprng::{Algorithm, PRNG};
/// Given a QUBO and an integral initial point, run simple local search until the point converges or the step limit is hit.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // generate a random point inside with x in {0, 1}^10 with
/// let x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
///
/// // perform a simple local search starting at x_0
/// let x_sol = local_search::simple_local_search(&p, &x_0, 1000);
/// ```
pub fn simple_local_search(qubo: &Qubo, x_0: &Array1<usize>, max_steps: usize) -> Array1<usize> {
let mut x = x_0.clone();
let variables = (0..qubo.num_x()).collect();
let mut x_1 = local_search_utils::one_step_local_search_improved(qubo, &x, &variables);
let mut steps = 0;
while x_1 != x && steps <= max_steps {
x = x_1.clone();
// apply the local search to the selected variables
x_1 = local_search_utils::one_step_local_search_improved(qubo, &x, &variables);
steps += 1;
}
x_1
}
/// Given a QUBO and a vector of initial points, run local searches on each initial point and return all of the solutions.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // generate a random point inside with x in {0, 1}^10
/// let x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
/// let x_1 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
/// let x_2 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
///
/// let xs = vec![x_0, x_1, x_2];
///
/// // perform a multiple simple local search starting at x_0
/// let x_sols = local_search::multi_simple_local_search(&p, &xs);
/// ```
pub fn multi_simple_local_search(qubo: &Qubo, xs: &Vec<Array1<usize>>) -> Vec<Array1<usize>> {
// Given a vector of initial points, run simple local search on each of them
xs.par_iter()
.map(|x| simple_local_search(qubo, x, usize::MAX))
.collect()
}
/// Given a QUBO and a fractional or integral initial point, run a gain search until the point converges or the step limit is hit.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // generate a random point inside with x in {0, 1}^10
/// let x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
///
/// // perform a simple gain criteria search starting at x_0
/// let x_sol = local_search::simple_gain_criteria_search(&p, &x_0, 1000);
/// ```
pub fn simple_gain_criteria_search(
qubo: &Qubo,
x_0: &Array1<usize>,
max_steps: usize,
) -> Array1<usize> {
let mut x = x_0.clone();
let mut x_1 = local_search_utils::get_gain_criteria(qubo, &x);
let mut steps = 0;
while x_1 != x && steps <= max_steps {
x = x_1.clone();
x_1 = local_search_utils::get_gain_criteria(qubo, &x);
steps += 1;
}
x_1
}
/// Given a QUBO and a vector of initial points, run gain searches on each initial point and return all of the solutions.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // generate a random point inside with x in {0, 1}^10
/// let x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
/// let x_1 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
/// let x_2 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
///
/// let xs = vec![x_0, x_1, x_2];
///
/// // perform a multiple simple gain criteria search starting at x_0
/// let x_sols = local_search::multi_simple_gain_criteria_search(&p, &xs);
/// ```
pub fn multi_simple_gain_criteria_search(
qubo: &Qubo,
xs: &Vec<Array1<usize>>,
) -> Vec<Array1<usize>> {
// Given a vector of initial points, run simple local search on each of them
xs.par_iter()
.map(|x| simple_gain_criteria_search(qubo, x, 1000))
.collect()
}
/// Given a QUBO and a fractional or integral initial point, run a mixed search until the point converges or the step limit is hit.
/// This is a combination of local search and gain criteria search, where the gain criteria search is run on the local search.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // generate a random point inside with x in {0, 1}^10
/// let x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
///
/// // perform a simple mixed search starting at x_0
/// let x_sol = local_search::simple_mixed_search(&p, &x_0, 1000);
/// ```
pub fn simple_mixed_search(qubo: &Qubo, x_0: &Array1<usize>, max_steps: usize) -> Array1<usize> {
let mut x = x_0.clone();
let mut x_1 = local_search_utils::get_gain_criteria(qubo, &x);
let mut steps = 0;
let vars = (0..qubo.num_x()).collect();
while x_1 != x && steps <= max_steps {
x = x_1.clone();
x_1 = local_search_utils::one_step_local_search_improved(qubo, &x, &vars);
x_1 = local_search_utils::get_gain_criteria(qubo, &x_1);
steps += 1;
}
x_1
}
/// Performs a particle swarm search on a QUBO.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // perform particle swarm with 150 particles for 1000 iterations
/// let x_sol = local_search::particle_swarm_search(&p, 150, 1000, &mut prng);
/// ```
pub fn particle_swarm_search<T: Algorithm>(
qubo: &Qubo,
num_particles: usize,
max_steps: usize,
prng: &mut PRNG<T>,
) -> Array1<usize> {
// initialize the particles
let num_dim = qubo.num_x();
// generate random starting points
let mut particles: Vec<_> = (0..num_particles)
.map(|_| generate_random_binary_point(num_dim, prng, 0.5))
.collect();
// select all variables
let selected_vars = (0..num_dim).collect();
// say at each particular point that we will contract 10% of the variables
let num_contract = qubo.num_x() / 10 + 1;
// loop over the number of iterations
for _ in 0..max_steps {
// apply local search to each particle
particles = particles
.par_iter()
.map(|x| local_search_utils::one_step_local_search_improved(qubo, x, &selected_vars))
.collect();
// find the best particle
let best_particle = get_best_point(qubo, &particles);
// contract the particles towards the best particle
particles = particles
.iter()
.map(|x| local_search_utils::contract_point(&best_particle, x, num_contract))
.collect();
}
// find the best particle
get_best_point(qubo, &particles)
}
/// Performs a random search on a QUBO, where points are randomly generated and the best point is returned. This to
/// create a baseline to compare other algorithms against just random guesses.
///
/// Example:
/// ``` rust
/// use hercules::qubo::Qubo;
/// use smolprng::{PRNG, JsfLarge};
/// use hercules::{initial_points, utils};
/// use hercules::local_search;
///
/// // generate a random QUBO
/// let mut prng = PRNG {
/// generator: JsfLarge::default(),
/// };
/// let p = Qubo::make_random_qubo(10, &mut prng, 0.5);
///
/// // perform random search with 1000 points
/// let x_sol = local_search::random_search(&p, 1000, &mut prng);
/// ```
pub fn random_search<T: Algorithm>(
qubo: &Qubo,
num_points: usize,
prng: &mut PRNG<T>,
) -> Array1<usize> {
// set up an initial best point and objective
let mut best_point = generate_random_binary_point(qubo.num_x(), prng, 0.5);
let mut best_objective = qubo.eval_usize(&best_point);
// loop over the number of points
for _ in 0..num_points {
// generate a new point and evaluate it
let new_point = generate_random_binary_point(qubo.num_x(), prng, 0.5);
let new_obj = qubo.eval_usize(&new_point);
// if the new point is better, update the best point
if new_obj <= best_objective {
best_point = new_point;
best_objective = new_obj;
}
}
best_point
}
#[cfg(test)]
mod tests {
use crate::local_search::*;
use crate::qubo::Qubo;
use crate::tests::{make_solver_qubo, make_test_prng};
use crate::{initial_points, local_search_utils};
use ndarray::Array1;
use sprs::CsMat;
#[test]
fn test_opt_criteria() {
let p = make_solver_qubo();
let mut prng = make_test_prng();
let mut x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
x_0 = local_search_utils::get_gain_criteria(&p, &x_0);
println!("{:?}", p.eval_usize(&x_0));
}
#[test]
fn test_multi_opt_heuristics() {
let p = make_solver_qubo();
let mut prng = make_test_prng();
let mut xs = initial_points::generate_random_binary_points(p.num_x(), 10, &mut prng);
xs = multi_simple_gain_criteria_search(&p, &xs);
let min_obj = crate::tests::get_min_obj(&p, &xs);
println!("{:?}", min_obj);
}
#[test]
fn test_mixed_search() {
let p = make_solver_qubo();
let mut prng = make_test_prng();
let mut xs = initial_points::generate_random_binary_points(p.num_x(), 10, &mut prng);
xs = xs
.par_iter()
.map(|x| simple_mixed_search(&p, &x, 1000))
.collect();
let min_obj = crate::tests::get_min_obj(&p, &xs);
println!("{min_obj:?}");
}
#[test]
fn test_particle_swarm() {
let p = make_solver_qubo();
let mut prng = make_test_prng();
let x = particle_swarm_search(&p, 5, 100, &mut prng);
println!("{:?}", p.eval_usize(&x));
}
#[test]
fn compare_methods() {
let p = make_solver_qubo();
let mut prng = make_test_prng();
let x_0 = initial_points::generate_random_binary_point(p.num_x(), &mut prng, 0.5);
let max_iter = p.num_x();
let x_pso = particle_swarm_search(&p, 100, max_iter, &mut prng);
let x_mixed = simple_mixed_search(&p, &x_0, max_iter);
let x_gain = simple_gain_criteria_search(&p, &x_0, max_iter);
let x_opt = simple_local_search(&p, &x_0, max_iter);
let x_rand = random_search(&p, 100, &mut prng);
println!(
"PSO: {:?}, MIXED: {:?}, GAIN: {:?}, 1OPT: {:?}, Rand: {:?} ",
p.eval_usize(&x_pso),
p.eval_usize(&x_mixed),
p.eval_usize(&x_gain),
p.eval_usize(&x_opt),
p.eval_usize(&x_rand)
);
}
#[test]
fn qubo_heuristics() {
let eye = CsMat::eye(3);
let p = Qubo::new(eye);
let x_0 = Array1::from_vec(vec![1, 0, 1]);
let x_1 = simple_local_search(&p, &x_0, 10);
print!("{:?}", x_1);
}
#[test]
fn qubo_multi_heuristics() {
let eye = CsMat::eye(3);
let p = Qubo::new(eye);
let x_0 = Array1::from_vec(vec![1, 0, 1]);
let x_1 = Array1::from_vec(vec![0, 1, 0]);
let x_2 = Array1::from_vec(vec![1, 1, 1]);
let xs = vec![x_0, x_1, x_2];
let x_3 = multi_simple_local_search(&p, &xs);
print!("{:?}", x_3);
}
}