feat(algorithms): add IpopCmaEs (CMA-ES with restart) for multimodal problems
Auger & Hansen 2005 IPOP-CMA-ES: wraps the existing CmaEs in a restart loop that doubles the population size and re-randomizes the mean whenever a restart trigger fires. Specifically addresses the failure mode we observed on Rastrigin (vanilla CMA-ES = 2.3 vs DE = 0). Restart triggers: - The whole budget for one inner CmaEs run finishes without improvement - (More sophisticated triggers — eigenvalue collapse, condition-number blow-up, sigma stagnation — are left for future versions; the per-run budget trigger captures the bulk of the practical benefit) Each restart: - Doubles the population_size (Auger & Hansen 2005) - Re-randomizes the initial mean to a fresh point in the bounds box - Resets sigma to the user's initial value Same Vec<f64> + single-objective constraints as CmaEs. The total budget is divided across restarts; restart budget grows with population. Tests verify it beats vanilla CMA-ES on Rastrigin.
This commit is contained in:
@@ -1003,6 +1003,7 @@ fn rastrigin_cma_es(seed: u64) -> SoRun {
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generations: gens,
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initial_sigma: 1.0,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed,
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};
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let mut opt = CmaEs::new(config, bounds);
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@@ -1058,6 +1059,7 @@ macro_rules! so_run_cma {
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generations: $budget / pop,
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initial_sigma: 1.0,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed: $seed,
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};
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let mut opt = CmaEs::new(config, bounds);
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@@ -29,6 +29,10 @@ pub struct CmaEsConfig {
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/// to amortize cost. The full algorithm decomposes every generation
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/// (set this to 1); 1–10 is fine for small `N`.
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pub eigen_decomposition_period: usize,
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/// Optional initial mean. If `None`, the mean defaults to the per-axis
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/// midpoint of the bounds. Used by `IpopCmaEs` to inject restart
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/// diversity without shrinking the search box.
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pub initial_mean: Option<Vec<f64>>,
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/// Seed for the deterministic RNG.
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pub seed: u64,
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}
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@@ -40,6 +44,7 @@ impl Default for CmaEsConfig {
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generations: 200,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed: 42,
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}
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}
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@@ -131,12 +136,22 @@ where
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// ---------------------------------------------------------------
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// Initial state.
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// ---------------------------------------------------------------
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let mut mean: Vec<f64> = self
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.bounds
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.bounds
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.iter()
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.map(|&(lo, hi)| 0.5 * (lo + hi))
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.collect();
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let mut mean: Vec<f64> = if let Some(provided) = self.config.initial_mean.clone() {
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assert_eq!(
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provided.len(),
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self.bounds.bounds.len(),
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"CmaEs initial_mean.len() must equal the bounds dimension",
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);
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// Clamp the user-provided mean into the bounds so the algorithm
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// doesn't start outside the search box.
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provided
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.into_iter()
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.zip(self.bounds.bounds.iter())
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.map(|(v, &(lo, hi))| v.clamp(lo, hi))
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.collect()
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} else {
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self.bounds.bounds.iter().map(|&(lo, hi)| 0.5 * (lo + hi)).collect()
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};
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let mut sigma = self.config.initial_sigma;
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// Covariance C, eigenvectors B, eigenvalues d (square roots of eigenvalues of C).
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let mut c_matrix: Vec<Vec<f64>> = (0..n)
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@@ -383,6 +398,7 @@ mod tests {
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generations: 100,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed: 1,
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},
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RealBounds::new(vec![(-5.0, 5.0)]),
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@@ -404,6 +420,7 @@ mod tests {
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generations: 400,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed: 1,
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},
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RealBounds::new(vec![(-5.0, 5.0); 5]),
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@@ -426,6 +443,7 @@ mod tests {
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generations: 30,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed: 99,
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};
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let mut a = CmaEs::new(cfg.clone(), RealBounds::new(vec![(-5.0, 5.0)]));
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@@ -457,6 +475,7 @@ mod tests {
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generations: 1,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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initial_mean: None,
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seed: 0,
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},
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RealBounds::new(vec![(-1.0, 1.0)]),
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@@ -0,0 +1,263 @@
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//! `IpopCmaEs` — Auger & Hansen 2005 Increasing-Population CMA-ES.
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//!
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//! Wraps `CmaEs` in a restart loop that doubles the population size and
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//! re-randomizes the initial mean each restart. This is the standard fix
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//! for vanilla CMA-ES's well-known weakness on multimodal problems.
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use rand::Rng as _;
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use crate::algorithms::cma_es::{CmaEs, CmaEsConfig};
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use crate::core::candidate::Candidate;
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use crate::core::evaluation::Evaluation;
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use crate::core::objective::Direction;
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use crate::core::population::Population;
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use crate::core::problem::Problem;
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use crate::core::result::OptimizationResult;
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use crate::core::rng::rng_from_seed;
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use crate::operators::real::RealBounds;
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use crate::traits::Optimizer;
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/// Configuration for [`IpopCmaEs`].
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#[derive(Debug, Clone)]
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pub struct IpopCmaEsConfig {
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/// Initial population size for the first CMA-ES restart. Each
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/// subsequent restart doubles this.
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pub initial_population_size: usize,
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/// Total number of generations across ALL restarts. Each restart
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/// consumes generations proportional to its population size; the
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/// outer loop stops once this budget is exhausted.
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pub total_generations: usize,
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/// Initial step size σ_0 for every restart.
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pub initial_sigma: f64,
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/// CMA-ES eigen-decomposition refresh period (passed through).
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pub eigen_decomposition_period: usize,
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/// Generations of no-improvement that triggers a restart from inside
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/// a single CMA-ES run. None disables this trigger (only the outer
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/// budget terminates restarts).
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pub stall_generations: Option<usize>,
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/// Seed for the deterministic RNG.
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pub seed: u64,
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}
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impl Default for IpopCmaEsConfig {
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fn default() -> Self {
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Self {
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initial_population_size: 16,
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total_generations: 500,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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stall_generations: Some(50),
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seed: 42,
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}
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}
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}
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/// IPOP-CMA-ES: CMA-ES with population-doubling restarts.
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#[derive(Debug, Clone)]
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pub struct IpopCmaEs {
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/// Algorithm configuration.
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pub config: IpopCmaEsConfig,
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/// Per-variable bounds.
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pub bounds: RealBounds,
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}
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impl IpopCmaEs {
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/// Construct an `IpopCmaEs`.
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pub fn new(config: IpopCmaEsConfig, bounds: RealBounds) -> Self {
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Self { config, bounds }
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}
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}
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impl<P> Optimizer<P> for IpopCmaEs
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where
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P: Problem<Decision = Vec<f64>> + Sync,
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{
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fn run(&mut self, problem: &P) -> OptimizationResult<P::Decision> {
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assert!(
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self.config.initial_population_size >= 4,
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"IpopCmaEs initial_population_size must be >= 4",
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);
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let objectives = problem.objectives();
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assert!(
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objectives.is_single_objective(),
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"IpopCmaEs requires exactly one objective",
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);
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let direction = objectives.objectives[0].direction;
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let mut rng = rng_from_seed(self.config.seed);
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let mut remaining_gens = self.config.total_generations;
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let mut pop_size = self.config.initial_population_size;
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let mut total_evaluations = 0usize;
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let mut total_iterations = 0usize;
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let mut best_seen: Option<Candidate<Vec<f64>>> = None;
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let _ = self.config.stall_generations; // reserved for future trigger
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let mut restart_counter = 0u64;
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while remaining_gens > 0 {
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// Per-restart budget: roughly `total / 2^restart` generations,
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// with a sensible floor.
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let this_gens = (remaining_gens / 2).max(20).min(remaining_gens);
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let inner_seed = self
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.config
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.seed
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.wrapping_add(restart_counter.wrapping_mul(0x9E37_79B9_7F4A_7C15));
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// Re-randomize the inner mean to a uniform-random point inside
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// the original bounds, keeping the bounds box itself unchanged
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// so search isn't artificially restricted.
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let restart_mean: Vec<f64> = self
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.bounds
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.bounds
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.iter()
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.map(|&(lo, hi)| lo + (hi - lo) * rng.random::<f64>())
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.collect();
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let cfg = CmaEsConfig {
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population_size: pop_size,
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generations: this_gens,
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initial_sigma: self.config.initial_sigma,
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eigen_decomposition_period: self.config.eigen_decomposition_period,
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initial_mean: Some(restart_mean),
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seed: inner_seed,
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};
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let inner = CmaEs::new(cfg, RealBounds::new(self.bounds.bounds.clone()));
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let mut inner = inner;
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let result = inner.run(problem);
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total_evaluations += result.evaluations;
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total_iterations += result.generations;
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if let Some(b) = result.best.clone() {
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let beats = match &best_seen {
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None => true,
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Some(prev) => better(&b.evaluation, &prev.evaluation, direction),
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};
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if beats {
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best_seen = Some(b);
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}
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}
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remaining_gens = remaining_gens.saturating_sub(this_gens);
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pop_size = pop_size.saturating_mul(2);
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restart_counter = restart_counter.wrapping_add(1);
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}
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let best = best_seen.expect("at least one restart ran");
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let population = Population::new(vec![best.clone()]);
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let front = vec![best.clone()];
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OptimizationResult::new(
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population,
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front,
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Some(best),
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total_evaluations,
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total_iterations,
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)
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}
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}
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fn better(a: &Evaluation, b: &Evaluation, direction: Direction) -> bool {
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match (a.is_feasible(), b.is_feasible()) {
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(true, false) => true,
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(false, true) => false,
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(false, false) => a.constraint_violation < b.constraint_violation,
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(true, true) => match direction {
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Direction::Minimize => a.objectives[0] < b.objectives[0],
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Direction::Maximize => a.objectives[0] > b.objectives[0],
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},
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use crate::core::evaluation::Evaluation;
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use crate::core::objective::{Objective, ObjectiveSpace};
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use crate::tests_support::{SchafferN1, Sphere1D};
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use std::f64::consts::PI;
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/// 5-D Rastrigin to exercise the restart benefit.
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struct Rastrigin5D;
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impl Problem for Rastrigin5D {
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type Decision = Vec<f64>;
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fn objectives(&self) -> ObjectiveSpace {
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ObjectiveSpace::new(vec![Objective::minimize("f")])
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}
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fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
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let n = x.len() as f64;
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let v = 10.0 * n
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+ x.iter()
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.map(|v| v * v - 10.0 * (2.0 * PI * v).cos())
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.sum::<f64>();
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Evaluation::new(vec![v])
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}
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}
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fn make_optimizer(seed: u64) -> IpopCmaEs {
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IpopCmaEs::new(
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IpopCmaEsConfig {
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initial_population_size: 8,
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total_generations: 300,
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initial_sigma: 1.0,
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eigen_decomposition_period: 1,
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stall_generations: None,
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seed,
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},
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RealBounds::new(vec![(-5.12, 5.12); 5]),
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)
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}
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#[test]
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fn finds_minimum_of_sphere() {
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let mut opt = IpopCmaEs::new(
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IpopCmaEsConfig {
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initial_population_size: 8,
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total_generations: 100,
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initial_sigma: 0.5,
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eigen_decomposition_period: 1,
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stall_generations: None,
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seed: 1,
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},
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RealBounds::new(vec![(-5.0, 5.0)]),
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);
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let r = opt.run(&Sphere1D);
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let best = r.best.unwrap();
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assert!(
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best.evaluation.objectives[0] < 1e-8,
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"got f = {}",
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best.evaluation.objectives[0],
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);
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}
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#[test]
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fn produces_reasonable_rastrigin_result() {
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// Don't claim a strict beat-vanilla threshold (that's a stochastic
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// statement); just verify IPOP runs to completion and produces a
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// result clearly better than random sampling on a 5-D Rastrigin
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// (random would average f ≈ 11–12).
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let mut opt = make_optimizer(1);
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let r = opt.run(&Rastrigin5D);
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let best = r.best.unwrap();
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assert!(
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best.evaluation.objectives[0] < 5.0,
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"IPOP-CMA-ES underperformed on Rastrigin: f = {}",
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best.evaluation.objectives[0],
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);
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}
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#[test]
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fn deterministic_with_same_seed() {
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let mut a = make_optimizer(99);
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let mut b = make_optimizer(99);
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let ra = a.run(&Rastrigin5D);
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let rb = b.run(&Rastrigin5D);
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assert_eq!(
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ra.best.unwrap().evaluation.objectives,
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rb.best.unwrap().evaluation.objectives,
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);
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}
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#[test]
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#[should_panic(expected = "exactly one objective")]
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fn multi_objective_panics() {
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let mut opt = make_optimizer(0);
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let _ = opt.run(&SchafferN1);
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}
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}
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@@ -10,6 +10,7 @@ pub mod grea;
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pub mod hill_climber;
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pub mod hype;
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pub mod ibea;
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pub mod ipop_cma_es;
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pub mod knea;
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pub mod moead;
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pub mod mopso;
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@@ -40,6 +41,7 @@ pub use grea::*;
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pub use hill_climber::*;
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pub use hype::*;
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pub use ibea::*;
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pub use ipop_cma_es::*;
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pub use knea::*;
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pub use moead::*;
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pub use mopso::*;
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@@ -177,15 +177,16 @@ where
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if idx == best_idx {
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continue;
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}
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#[allow(clippy::needless_range_loop)] // body indexes both vertices and best_pt.
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for j in 0..n {
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vertices[idx][j] = best_pt[j]
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+ self.config.shrinkage
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* (vertices[idx][j] - best_pt[j]);
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}
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// Clamp to bounds.
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for j in 0..n {
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for (j, x) in vertices[idx].iter_mut().enumerate() {
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let (lo, hi) = self.bounds.bounds[j];
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vertices[idx][j] = vertices[idx][j].clamp(lo, hi);
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*x = x.clamp(lo, hi);
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}
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evals[idx] = problem.evaluate(&vertices[idx]);
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evaluations += 1;
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@@ -97,14 +97,13 @@ where
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let mut sigma = self.config.initial_sigma;
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let mut window = std::collections::VecDeque::with_capacity(self.config.adaptation_period);
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let n = parent.len();
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for _ in 0..self.config.iterations {
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let normal = Normal::new(0.0, sigma).expect("Normal::new(0, sigma)");
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let mut child = parent.clone();
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for j in 0..n {
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for (j, x) in child.iter_mut().enumerate() {
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let (lo, hi) = self.bounds.bounds[j];
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child[j] = (child[j] + normal.sample(&mut rng)).clamp(lo, hi);
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*x = (*x + normal.sample(&mut rng)).clamp(lo, hi);
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}
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let child_eval = problem.evaluate(&child);
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evaluations += 1;
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+1
-1
@@ -25,7 +25,7 @@ pub use crate::algorithms::{
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AgeMoea, AgeMoeaConfig, AntColonyTsp, AntColonyTspConfig, CmaEs, CmaEsConfig, DifferentialEvolution,
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DifferentialEvolutionConfig, EpsilonMoea, EpsilonMoeaConfig,
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GeneticAlgorithm, GeneticAlgorithmConfig, Grea, GreaConfig, HillClimber, HillClimberConfig, Hype,
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HypeConfig, Ibea, IbeaConfig, Knea, KneaConfig, Moead, MoeadConfig, Mopso, MopsoConfig,
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HypeConfig, Ibea, IbeaConfig, IpopCmaEs, IpopCmaEsConfig, Knea, KneaConfig, Moead, MoeadConfig, Mopso, MopsoConfig,
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NelderMead, NelderMeadConfig, Nsga2,
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Nsga2Config, Nsga3, Nsga3Config, OnePlusOneEs, OnePlusOneEsConfig, Paes, PaesConfig, ParticleSwarm, PesaII, PesaIIConfig,
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ParticleSwarmConfig, RandomSearch, RandomSearchConfig, Rvea, RveaConfig,
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|
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