Deb & Agrawal's standard real-valued crossover for NSGA-II. Takes two parents, returns two children; per dimension, with `per_variable_probability`, mixes the parents using a polynomial spread parameter \\(\\beta\\) drawn from a distribution controlled by `eta` (the distribution index — typical values 10–30, default 15). Children are clamped to per-variable bounds. Per-dim formula (Deb & Agrawal 1995): - `u ~ U[0, 1)` - `β = (2u)^(1/(η+1))` if `u ≤ 0.5` else `(1 / (2(1-u)))^(1/(η+1))` - `c1 = 0.5·((1+β)·p1 + (1-β)·p2)`, `c2 = 0.5·((1-β)·p1 + (1+β)·p2)` This is the simple compute-then-clamp form; the bounds-aware β formulation from the full paper is left as a future refinement. Tests cover: two children for two parents, output lengths preserved, all variables clamped to bounds, and per_variable_probability=0 returns the parents unchanged.
heuropt
A practical Rust toolkit for implementing heuristic single-objective, multi-objective, and many-objective optimization algorithms.
heuropt is not a research framework full of abstract machinery — it is a
small set of concrete types, a handful of simple traits, and a few reference
algorithms. The goal: an entry-level Rust engineer can define a problem, run a
built-in optimizer, or implement a new optimizer without learning any
framework concepts.
Installation
[dependencies]
heuropt = "0.1"
# Optional features:
# - "serde": derive Serialize/Deserialize on the core data types.
# - "parallel": evaluate populations across rayon's thread pool.
# Seeded runs stay bit-identical to serial mode.
# heuropt = { version = "0.1", features = ["serde", "parallel"] }
Define a problem
use heuropt::prelude::*;
struct SchafferN1;
impl Problem for SchafferN1 {
type Decision = Vec<f64>;
fn objectives(&self) -> ObjectiveSpace {
ObjectiveSpace::new(vec![
Objective::minimize("f1"),
Objective::minimize("f2"),
])
}
fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
let v = x[0];
Evaluation::new(vec![v * v, (v - 2.0).powi(2)])
}
}
Run NSGA-II
use heuropt::prelude::*;
# struct SchafferN1;
# impl Problem for SchafferN1 {
# type Decision = Vec<f64>;
# fn objectives(&self) -> ObjectiveSpace {
# ObjectiveSpace::new(vec![Objective::minimize("f1"), Objective::minimize("f2")])
# }
# fn evaluate(&self, x: &Vec<f64>) -> Evaluation {
# Evaluation::new(vec![x[0] * x[0], (x[0] - 2.0).powi(2)])
# }
# }
let initializer = RealBounds::new(vec![(-5.0, 5.0)]);
let variation = GaussianMutation { sigma: 0.2 };
let config = Nsga2Config { population_size: 60, generations: 80, seed: 42 };
let mut optimizer = Nsga2::new(config, initializer, variation);
let result = optimizer.run(&SchafferN1);
println!("Pareto front size: {}", result.pareto_front.len());
See examples/toy_nsga2.rs for the full version.
Implement a custom optimizer
A new optimizer is just an implementation of Optimizer<P>:
use heuropt::prelude::*;
struct MyOptimizer { /* state */ }
impl<P> Optimizer<P> for MyOptimizer
where
P: Problem<Decision = Vec<f64>>,
{
fn run(&mut self, problem: &P) -> OptimizationResult<P::Decision> {
// Generate candidates.
// Evaluate them with `problem.evaluate(...)`.
// Keep the best, or maintain a Pareto archive.
// Return an OptimizationResult.
# OptimizationResult::new(
# Population::new(Vec::new()),
# Vec::new(),
# None,
# 0,
# 0,
# )
}
}
A complete worked example is in examples/custom_optimizer.rs.
Current algorithms
RandomSearch— sample-evaluate-keep baseline.Paes— a small (1+1) Pareto Archived Evolution Strategy.Nsga2— the canonical Pareto-based evolutionary algorithm.DifferentialEvolution— DE/rand/1/bin for single-objective real-valued problems.
Plus reusable utilities: pareto_compare, pareto_front, best_candidate,
non_dominated_sort, crowding_distance, ParetoArchive, and the metrics
spacing and hypervolume_2d.
Design philosophy
- Concrete data, small trait surface.
Problem,Optimizer,Initializer,Variationare the only traits a user interacts with day-to-day. Everything else is plain structs. - No type hell. No trait objects in the core path, no GATs, no HRTBs in
user-facing APIs, no generic-RNG plumbing —
Rngis a single concrete type alias. - Readable algorithms. Built-ins are written for clarity, not maximum
abstraction reuse.
RandomSearchis the recommended file to read before writing your own optimizer. - One crate first. No premature splitting into
-core/-algorithms/-operators. Split later if the crate grows. - Panic on programmer error. Invalid configuration panics with a clear
message in v1; the API may grow
Result-returning variants later if the base API proves useful.
See docs/heuropt_tech_design_spec.md for the full design rationale.
License
MIT.