feat(nsgaii): add NSGA-II multi-objective optimization solver

README.md

@@ -118,6 +118,7 @@ argmin is designed to simplify the implementation of optimization algorithms and
 - Nelder-Mead method
 - Simulated Annealing
 - Particle Swarm Optimization
+- NSGA-II
 
 ### External solvers compatible with argmin
 

crates/argmin/src/core/mod.rs

@@ -47,7 +47,10 @@ pub use executor::Executor;
 pub use float::ArgminFloat;
 pub use kv::{KvValue, KV};
 pub use parallelization::{SendAlias, SyncAlias};
-pub use problem::{CostFunction, Gradient, Hessian, Jacobian, LinearProgram, Operator, Problem};
+pub use problem::{
+    CostFunction, Gradient, Hessian, Jacobian, LinearProgram, MultiObjectiveCostFunction, Operator,
+    Problem,
+};
 pub use result::OptimizationResult;
 pub use solver::Solver;
 pub use state::{IterState, LinearProgramState, PopulationState, State};

crates/argmin/src/core/problem.rs

@@ -381,6 +381,49 @@ pub trait CostFunction {
     bulk!(cost, Self::Param, Self::Output);
 }
 
+/// Defines the computation of multiple objective functions for multi-objective optimization.
+///
+/// This trait is used by multi-objective optimization algorithms to evaluate multiple conflicting 
+/// objectives simultaneously.
+///
+/// # Example
+///
+/// ```
+/// use argmin::core::{MultiObjectiveCostFunction, Error};
+///
+/// struct BiObjectiveProblem {}
+///
+/// impl MultiObjectiveCostFunction for BiObjectiveProblem {
+///     type Param = Vec<f64>;
+///     type Output = Vec<f64>;
+///
+///     /// Compute two objectives
+///     fn objectives(&self, param: &Self::Param) -> Result<Self::Output, Error> {
+///         let f1 = param[0].powi(2) + param[1].powi(2);
+///         let f2 = (param[0] - 1.0).powi(2) + (param[1] - 1.0).powi(2);
+///         Ok(vec![f1, f2])
+///     }
+///
+///     fn num_objectives(&self) -> usize {
+///         2
+///     }
+/// }
+/// ```
+pub trait MultiObjectiveCostFunction {
+    /// Type of the parameter vector
+    type Param;
+    /// Type of the return value (typically a vector of objective values)
+    type Output;
+
+    /// Compute all objective functions
+    fn objectives(&self, param: &Self::Param) -> Result<Self::Output, Error>;
+
+    /// Returns the number of objectives
+    fn num_objectives(&self) -> usize;
+
+    bulk!(objectives, Self::Param, Self::Output);
+}
+
 /// Defines the computation of the gradient.
 ///
 /// # Example

crates/argmin/src/core/result.rs

@@ -15,7 +15,7 @@ use std::fmt;
 /// Consists of the problem and the final state of the solver.
 /// Both can be accessed via deconstructing or via the methods
 /// [`problem`](`OptimizationResult::problem`) and [`state`](`OptimizationResult::state`).
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct OptimizationResult<O, S, I> {
     /// Problem
     pub problem: Problem<O>,

crates/argmin/src/solver/mod.rs

@@ -15,6 +15,8 @@ pub mod linesearch;
 pub mod neldermead;
 pub mod newton;
 #[cfg(feature = "rand")]
+pub mod nsgaii;
+#[cfg(feature = "rand")]
 pub mod particleswarm;
 pub mod quasinewton;
 #[cfg(feature = "rand")]