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```//! This module contains multi-objective functions

use crate::{FixedDimensional, NDimensional, UnConstrained, Constrained, MultiObjective, Bounded};

/// This is the Chankong-Haimes function.
///
/// The function is borrowed from [here](https://en.wikipedia.org/wiki/Test_functions_for_optimization).
/// This function is specificaly 2 dimensional, and has a Pareto fron that looks like this:
///
pub struct ChankongHaimes {}

impl FixedDimensional for ChankongHaimes {
const D: usize = 2;
}

impl Bounded for ChankongHaimes {
const BOUNDS: (f64, f64) = (-20.0, 20.0);
}

impl Constrained for ChankongHaimes {
const NH: usize = 0;
const NG: usize = 2;

fn equality_constraints(_x: Vec<f64>) -> Vec<f64> {
vec![0.0; Self::NH]
}

fn inequality_constraints(x: Vec<f64>) -> Vec<f64> {
let mut fx: Vec<f64> = vec![0.0; Self::NG];
fx[0] = x[0].powi(2) + x[1].powi(2) - 225.0;
fx[1] = x[0] - 3.0*x[1] + 10.0;
fx
}
}

impl MultiObjective for ChankongHaimes {
const NF: usize = 2;

fn f(x: Vec<f64>) -> Vec<f64> {
Self::check_input(x.clone());
let mut fx: Vec<f64> = vec![0.0; Self::NF];
fx[0] = 2.0 + (x[0] - 2.0).powi(2) - (x[1] - 1.0).powi(2);
fx[1] = 9.0*x[0] - (x[1] - 1.0).powi(2);
fx
}
}

#[cfg(test)]
mod chankong_haimes_tests {
use super::{ChankongHaimes as F, MultiObjective, Constrained, FixedDimensional};

#[test]
fn check_zero() {
let x = vec![0.0; F::D];
F::f(x.clone());
F::equality_constraints(x.clone());
F::inequality_constraints(x);
assert!(true);
}

#[test]
fn check_one() {
let x = vec![0.0; F::D];
F::f(x.clone());
F::equality_constraints(x.clone());
F::inequality_constraints(x);
assert!(true);
}
}

/// This is the Fonseca-Fleming function.
///
/// The function is borrowed from [here](https://en.wikipedia.org/wiki/Test_functions_for_optimization).
/// Although the function accepts a vector with an arbitrary number of inputs, this is what the
/// Pareto front looks like in 2D:
///
pub struct FonsecaFlemming {}

impl NDimensional for FonsecaFlemming {}
impl UnConstrained for FonsecaFlemming {}

impl Bounded for FonsecaFlemming {
const BOUNDS: (f64, f64) = (-4.0, 4.0);
}

impl MultiObjective for FonsecaFlemming {
const NF: usize = 2;

fn f(x: Vec<f64>) -> Vec<f64> {
let mut fx: Vec<f64> = vec![0.0; Self::NF];
let n = x.len();
let mut sumxminus: f64 = 0.0;
let mut sumxplus: f64 = 0.0;
let nsqrt = (n as f64).sqrt();
for xi in x {
sumxminus += (xi - 1.0/nsqrt).powi(2);
sumxplus += (xi + 1.0/nsqrt).powi(2);
}
fx[0] = 1.0 - (-sumxminus).exp();
fx[1] = 1.0 - (-sumxplus).exp();
fx
}
}

#[cfg(test)]
mod flemingfonseca_tests {
use super::{FonsecaFlemming as F, NDimensional, MultiObjective};

#[test]
fn check_zero() {
F::f(vec![0.0; F::LOW_D]);
F::f(vec![0.0; F::HIGH_D]);
assert!(true);
}

#[test]
fn check_one() {
F::f(vec![1.0; F::LOW_D]);
F::f(vec![1.0; F::HIGH_D]);
assert!(true);
}
}

/// This is the Viennet function.
///
/// The function is borrowed from [here](https://en.wikipedia.org/wiki/Test_functions_for_optimization).
/// This function is specifically 2 dimensional, and has a Pareto fron that looks like this:
///

pub struct Viennet {}

impl UnConstrained for Viennet {}

impl FixedDimensional for Viennet {
const D: usize = 2;
}

impl Bounded for Viennet {
const BOUNDS: (f64, f64) = (-3.0, 3.0);
}

impl MultiObjective for Viennet {
const NF: usize = 3;

fn f(x: Vec<f64>) -> Vec<f64> {
Self::check_input(x.clone());
let mut fx: Vec<f64> = vec![0.0; Self::NF];
let x2y2 = x[0].powi(2) + x[1].powi(2);
fx[0] = 0.5*x2y2 + x2y2.sin();
fx[1] = (3.0*x[0] - 2.0*x[1] + 4.0).powi(2)/8.0 + (x[0] - x[1] + 1.0).powi(2)/27.0 + 15.0;
fx[2] = 1.0/(x2y2 + 1.0) - 1.1*(-x2y2).exp();
fx
}
}

#[cfg(test)]
mod viennet_tests {
use super::{Viennet as F, MultiObjective, FixedDimensional};

#[test]
fn check_zero() {
let x = vec![0.0; F::D];
F::f(x.clone());
assert!(true);
}

#[test]
fn check_one() {
let x = vec![0.0; F::D];
F::f(x.clone());
assert!(true);
}
}```