heuropt 0.11.0

A practical Rust toolkit for heuristic single-, multi-, and many-objective optimization.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198

//! Pareto dominance enum and pairwise dominance comparison.

use crate::core::evaluation::Evaluation;
use crate::core::objective::{Direction, ObjectiveSpace};

#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};

/// The Pareto relationship between two evaluations.
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum Dominance {
    /// `a` dominates `b`.
    Dominates,
    /// `a` is dominated by `b`.
    DominatedBy,
    /// Neither dominates the other.
    NonDominated,
    /// All objective values are equal after orientation conversion.
    Equal,
}

/// Pareto-compare two evaluations under the given objective space.
///
/// Behavior (spec §9.2):
///
/// 1. Feasible candidates dominate infeasible candidates.
/// 2. If both are infeasible, the candidate with smaller
///    `constraint_violation` dominates.
/// 3. Otherwise compare objective values after converting both to
///    minimization orientation via [`ObjectiveSpace::as_minimization`].
///
/// # Example
///
/// ```
/// use heuropt::prelude::*;
///
/// let s = ObjectiveSpace::new(vec![
///     Objective::minimize("f1"),
///     Objective::minimize("f2"),
/// ]);
/// let a = Evaluation::new(vec![1.0, 1.0]);
/// let b = Evaluation::new(vec![2.0, 2.0]);
/// assert_eq!(pareto_compare(&a, &b, &s), Dominance::Dominates);
/// assert_eq!(pareto_compare(&b, &a, &s), Dominance::DominatedBy);
/// ```
pub fn pareto_compare(a: &Evaluation, b: &Evaluation, objectives: &ObjectiveSpace) -> Dominance {
    let a_feasible = a.is_feasible();
    let b_feasible = b.is_feasible();
    match (a_feasible, b_feasible) {
        (true, false) => return Dominance::Dominates,
        (false, true) => return Dominance::DominatedBy,
        (false, false) => {
            return if a.constraint_violation < b.constraint_violation {
                Dominance::Dominates
            } else if a.constraint_violation > b.constraint_violation {
                Dominance::DominatedBy
            } else {
                Dominance::Equal
            };
        }
        (true, true) => {}
    }

    // Compare in minimization orientation *without* materializing the two
    // oriented `Vec<f64>`s that `as_minimization` would allocate.
    // `pareto_compare` is called O(n²) times across the multi-objective
    // algorithms, so a per-call heap-allocation pair dominates the whole
    // program. For a Maximize objective, "a beats b" is just `av > bv` —
    // bit-identical to `-av < -bv` after orientation.
    let mut a_better_anywhere = false;
    let mut b_better_anywhere = false;
    for ((obj, &av), &bv) in objectives
        .objectives
        .iter()
        .zip(a.objectives.iter())
        .zip(b.objectives.iter())
    {
        let (a_better, b_better) = match obj.direction {
            Direction::Minimize => (av < bv, av > bv),
            Direction::Maximize => (av > bv, av < bv),
        };
        if a_better {
            a_better_anywhere = true;
        } else if b_better {
            b_better_anywhere = true;
        }
    }

    match (a_better_anywhere, b_better_anywhere) {
        (true, false) => Dominance::Dominates,
        (false, true) => Dominance::DominatedBy,
        (false, false) => Dominance::Equal,
        (true, true) => Dominance::NonDominated,
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::core::objective::Objective;

    fn space_min2() -> ObjectiveSpace {
        ObjectiveSpace::new(vec![Objective::minimize("f1"), Objective::minimize("f2")])
    }

    #[test]
    fn a_dominates_b() {
        let s = space_min2();
        let a = Evaluation::new(vec![1.0, 1.0]);
        let b = Evaluation::new(vec![2.0, 2.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Dominates);
    }

    #[test]
    fn a_dominated_by_b() {
        let s = space_min2();
        let a = Evaluation::new(vec![3.0, 4.0]);
        let b = Evaluation::new(vec![1.0, 2.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::DominatedBy);
    }

    #[test]
    fn non_dominated_pair() {
        let s = space_min2();
        let a = Evaluation::new(vec![1.0, 4.0]);
        let b = Evaluation::new(vec![3.0, 2.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::NonDominated);
    }

    #[test]
    fn equal_pair() {
        let s = space_min2();
        let a = Evaluation::new(vec![2.0, 2.0]);
        let b = Evaluation::new(vec![2.0, 2.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Equal);
    }

    #[test]
    fn feasible_beats_infeasible() {
        let s = space_min2();
        let a = Evaluation::new(vec![10.0, 10.0]);
        let b = Evaluation::constrained(vec![1.0, 1.0], 5.0);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Dominates);
        assert_eq!(pareto_compare(&b, &a, &s), Dominance::DominatedBy);
    }

    #[test]
    fn smaller_violation_wins_among_infeasible() {
        let s = space_min2();
        let a = Evaluation::constrained(vec![100.0, 100.0], 1.0);
        let b = Evaluation::constrained(vec![0.0, 0.0], 5.0);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Dominates);
    }

    #[test]
    fn maximize_axis_handled_correctly() {
        let s = ObjectiveSpace::new(vec![
            Objective::minimize("cost"),
            Objective::maximize("accuracy"),
        ]);
        // a: cost=1 (better), accuracy=0.9 (better) → dominates b
        let a = Evaluation::new(vec![1.0, 0.9]);
        let b = Evaluation::new(vec![2.0, 0.8]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Dominates);
    }

    /// `a` better on one axis, worse on the other → NonDominated. Pins the
    /// `av < bv` / `av > bv` comparisons in the per-objective scan.
    #[test]
    fn trade_off_is_non_dominated() {
        let s = space_min2();
        let a = Evaluation::new(vec![1.0, 5.0]);
        let b = Evaluation::new(vec![5.0, 1.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::NonDominated);
        assert_eq!(pareto_compare(&b, &a, &s), Dominance::NonDominated);
    }

    /// `a` better on one axis, equal on the other → Dominates. This is the
    /// boundary case that distinguishes `<` from `<=` in the scan.
    #[test]
    fn better_on_one_equal_on_other_dominates() {
        let s = space_min2();
        let a = Evaluation::new(vec![1.0, 2.0]);
        let b = Evaluation::new(vec![2.0, 2.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Dominates);
        assert_eq!(pareto_compare(&b, &a, &s), Dominance::DominatedBy);
    }

    /// Identical objectives → Equal (neither `<` nor `>` ever fires).
    #[test]
    fn identical_objectives_are_equal() {
        let s = space_min2();
        let a = Evaluation::new(vec![3.0, 3.0]);
        let b = Evaluation::new(vec![3.0, 3.0]);
        assert_eq!(pareto_compare(&a, &b, &s), Dominance::Equal);
    }
}