Zitzler & Künzli 2004 IBEA: replaces Pareto-rank + crowding fitness
with a single scalar fitness derived from a binary quality indicator
(here, the additive ε-indicator). Loses no information at three or
more objectives the way crowding distance does.
Algorithm:
- For every (i, j) pair compute I(i, j) = max_k (f_k(i) - f_k(j)) on
minimization-oriented objectives.
- Fitness F(i) = -Σ_{j≠i} exp(-I(j, i) / κ).
- Each generation: combine parents + offspring, iteratively remove the
lowest-F member (cleanly recomputing the contribution of the dropped
member from each surviving member's fitness) until population_size
remain.
- Parent selection: binary tournament on F (higher wins).
Bounds-aware operators recommended (SBX + PolyMut).
Tests: produces a non-empty front on Schaffer N.1, deterministic
reruns, panic on `population_size == 0`.
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 — see LICENSE.
Changelog
See CHANGELOG.md.