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//! Whitley test function
use ndarray::Array1;
/// Whitley function - challenging multimodal function
/// Global minimum: f(x) = 0 at x = (1, 1, ..., 1)
/// Bounds: x_i in [-10.24, 10.24]
pub fn whitley(x: &Array1<f64>) -> f64 {
let n = x.len();
let mut sum = 0.0;
for i in 0..n {
for j in 0..n {
let xi = x[i];
let xj = x[j];
let term = 100.0 * (xi.powi(2) - xj).powi(2) + (1.0 - xj).powi(2);
sum += term.powi(2) / 4000.0 - term.cos() + 1.0;
}
}
sum
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_whitley_known_properties() {
// Test some properties of the Whitley function
use ndarray::Array1;
// Test the known global optimum
let x_global = Array1::from(vec![1.0, 1.0]);
let f_global = whitley(&x_global);
// Should be 0 at the global optimum
assert!(
f_global.abs() < 1e-10,
"Global optimum value not as expected: {}",
f_global
);
// Test that function is always non-negative (based on its construction)
let test_points = vec![
vec![0.0, 0.0],
vec![2.0, 2.0],
vec![-5.0, 3.0],
vec![10.0, -10.0],
];
for point in test_points {
let x = Array1::from(point.clone());
let f = whitley(&x);
assert!(
f >= 0.0,
"Function should be non-negative at {:?}: {}",
point,
f
);
assert!(
f.is_finite(),
"Function should be finite at {:?}: {}",
point,
f
);
}
// Test boundary behavior
let x_boundary = Array1::from(vec![10.24, -10.24]);
let f_boundary = whitley(&x_boundary);
assert!(
f_boundary >= 0.0,
"Function at boundary should be non-negative"
);
assert!(
f_boundary.is_finite(),
"Function at boundary should be finite"
);
}
}