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
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
use crate::point::*;
use crate::simplex::*;
use crate::search_space::*;
use priority_queue::PriorityQueue;
use ordered_float::OrderedFloat;
use num_traits::{Float, float::FloatCore};
use std::rc::Rc;
/// Stores the parameters and current state of a search.
///
/// - `ValueFloat` is the float type used to represent the evaluations (such as f64)
/// - `CoordFloat` is the float type used to represent the coordinates (such as f32)
pub struct Optimizer<F, CoordFloat, ValueFloat>
where F: FnMut(&[CoordFloat]) -> ValueFloat,
CoordFloat: Float + FloatCore,
ValueFloat: Float + FloatCore
{
exploration_depth: ValueFloat,
search_space: SearchSpace<F, CoordFloat, ValueFloat>,
best_point: Rc<Point<CoordFloat, ValueFloat>>,
min_value: ValueFloat,
queue: PriorityQueue<Simplex<CoordFloat, ValueFloat>, OrderedFloat<ValueFloat>>
}
impl<F, CoordFloat, ValueFloat> Optimizer<F, CoordFloat, ValueFloat>
where F: FnMut(&[CoordFloat]) -> ValueFloat,
CoordFloat: Float + FloatCore,
ValueFloat: Float + FloatCore
{
/// Creates a new optimizer to explore the given search space with the iterator interface.
///
/// Takes a function, a vector of intervals describing the input and a boolean describing whether it is a minimization problem (as opposed to a maximization problem).
/// Each call to the `.next()` function (cf iterator trait) will run an iteration of search and output the best result so far.
///
/// **Warning:** In d dimensions, this function will perform d+1 evaluations (calls to f) for the initialization of the search (those should be taken into account when counting iterations).
///
/// ```rust
/// # use simplers_optimization::Optimizer;
/// # fn main() {
/// let f = |v:&[f64]| v[0] * v[1];
/// let input_interval = vec![(-10., 10.), (-20., 20.)];
/// let should_minimize = true;
///
/// // runs the search for 30 iterations
/// // then waits until we find a point good enough
/// // finally stores the best value so far
/// let (min_value, coordinates) = Optimizer::new(f, &input_interval, should_minimize)
/// .skip(30)
/// .skip_while(|(value,coordinates)| *value > 1. )
/// .next().unwrap();
///
/// println!("min value: {} found in [{}, {}]", min_value, coordinates[0], coordinates[1]);
/// # }
/// ```
pub fn new(f: F, input_interval: &[(CoordFloat, CoordFloat)], should_minimize: bool) -> Self
{
// builds initial conditions
let mut search_space = SearchSpace::new(f, input_interval, should_minimize);
let initial_simplex = Simplex::initial_simplex(&mut search_space);
// various values track through the iterations
let best_point = initial_simplex.corners
.iter()
.max_by_key(|c| OrderedFloat(c.value))
.expect("You need at least one dimension!")
.clone();
let min_value = initial_simplex.corners
.iter()
.map(|c| c.value)
.min_by_key(|&v| OrderedFloat(v))
.expect("You need at least one dimension!");
// initialize priority queue
// no need to evaluate the initial simplex as it will be popped immediately
let mut queue: PriorityQueue<Simplex<CoordFloat, ValueFloat>, OrderedFloat<ValueFloat>> =
PriorityQueue::new();
queue.push(initial_simplex, OrderedFloat(ValueFloat::zero()));
let exploration_depth = ValueFloat::from(6.).unwrap();
Optimizer { exploration_depth, search_space, best_point, min_value, queue }
}
/// Predicts the objective function value at a given point using the algorithm's internal model.
///
/// The prediction uses inverse-distance-weighted interpolation from the corners of the
/// simplex containing the query point — the same interpolation scheme used internally
/// to guide the search.
///
/// The `point` should be in the original input space (the hypercube defined by `input_interval`).
/// Returns `None` if the point falls outside all current simplices (e.g. due to floating-point
/// edge cases) or if the internal geometry is degenerate.
pub fn predict(&self, point: &[CoordFloat]) -> Option<ValueFloat>
{
// Convert from hypercube to internal simplex coordinates
let internal_point = self.search_space.to_simplex(point);
// Find the containing simplex and interpolate
for (simplex, _) in self.queue.iter()
{
if simplex.contains_point(&internal_point)
{
let value = simplex.interpolate_at(&internal_point);
// Un-negate for minimization
return Some(if self.search_space.minimize { -value } else { value });
}
}
None
}
/// Returns all points evaluated so far, in evaluation order, as `(coordinates, value)` pairs.
///
/// The coordinates are in the original input space (the hypercube defined by `input_interval`),
/// and the values are the raw outputs of the objective function (not transformed for min/max).
///
/// The first `d+1` entries (where `d` is the number of input dimensions) are the initial
/// simplex vertices placed at the corners of the search space.
/// Each subsequent entry corresponds to one iteration of the optimizer,
/// evaluating the center of the most promising simplex.
///
/// This can be used to plot the optimization trajectory (value vs. iteration number)
/// or to visualize which regions of the search space have been explored.
pub fn evaluated_points(&self) -> &[(Coordinates<CoordFloat>, ValueFloat)]
{
&self.search_space.history
}
/// Sets the exploration depth for the algorithm, useful when using the iterator interface.
///
/// `exploration_depth` represents the number of splits we can exploit before requiring higher-level exploration.
/// As long as one stays in a reasonable range (5-10), the algorithm should not be very sensitive to the parameter :
///
/// - 0 represents full exploration (similar to grid search)
/// - high numbers focus on exploitation (no need to go very high)
/// - 5 appears to be a good default value
///
/// **WARNING**: this function should only be used before the first iteration
/// (as it will not update the score of already computed points for the next iterations
/// which will degrade the quality of the algorithm)
///
/// ```rust
/// # use simplers_optimization::Optimizer;
/// # fn main() {
/// let f = |v:&[f64]| v[0] * v[1];
/// let input_interval = vec![(-10., 10.), (-20., 20.)];
/// let should_minimize = true;
///
/// // sets exploration_depth to be very greedy
/// let (min_value_greedy, _) = Optimizer::new(f, &input_interval, should_minimize)
/// .set_exploration_depth(20)
/// .skip(100)
/// .next().unwrap();
///
/// // sets exploration_depth to focus on exploration
/// let (min_value_explore, _) = Optimizer::new(f, &input_interval, should_minimize)
/// .set_exploration_depth(0)
/// .skip(100)
/// .next().unwrap();
///
/// println!("greedy result : {} vs exploration result : {}", min_value_greedy, min_value_explore);
/// # }
/// ```
pub fn set_exploration_depth(mut self, exploration_depth: usize) -> Self
{
self.exploration_depth = ValueFloat::from(exploration_depth + 1).unwrap();
self
}
/// Self contained optimization algorithm.
///
/// Takes a function to maximize, a vector of intervals describing the input and a number of iterations.
///
/// ```rust
/// # use simplers_optimization::Optimizer;
/// # fn main() {
/// let f = |v:&[f64]| v[0] + v[1];
/// let input_interval = vec![(-10., 10.), (-20., 20.)];
/// let nb_iterations = 100;
///
/// let (max_value, coordinates) = Optimizer::maximize(f, &input_interval, nb_iterations);
/// println!("max value: {} found in [{}, {}]", max_value, coordinates[0], coordinates[1]);
/// # }
/// ```
pub fn maximize(f: F,
input_interval: &[(CoordFloat, CoordFloat)],
nb_iterations: usize)
-> (ValueFloat, Coordinates<CoordFloat>)
{
let initial_iteration_number = input_interval.len() + 1;
let should_minimize = false;
Optimizer::new(f, input_interval, should_minimize).nth(nb_iterations - initial_iteration_number)
.unwrap()
}
/// Self contained optimization algorithm.
///
/// Takes a function to minimize, a vector of intervals describing the input and a number of iterations.
///
/// ```rust
/// # use simplers_optimization::Optimizer;
/// # fn main() {
/// let f = |v:&[f64]| v[0] * v[1];
/// let input_interval = vec![(-10., 10.), (-20., 20.)];
/// let nb_iterations = 100;
///
/// let (min_value, coordinates) = Optimizer::minimize(f, &input_interval, nb_iterations);
/// println!("min value: {} found in [{}, {}]", min_value, coordinates[0], coordinates[1]);
/// # }
/// ```
pub fn minimize(f: F,
input_interval: &[(CoordFloat, CoordFloat)],
nb_iterations: usize)
-> (ValueFloat, Coordinates<CoordFloat>)
{
let initial_iteration_number = input_interval.len() + 1;
let should_minimize = true;
Optimizer::new(f, input_interval, should_minimize).nth(nb_iterations - initial_iteration_number)
.unwrap()
}
}
/// implements iterator for the Optimizer to give full control on the stopping condition to the user
impl<F, CoordFloat, ValueFloat> Iterator for Optimizer<F, CoordFloat, ValueFloat>
where F: FnMut(&[CoordFloat]) -> ValueFloat,
CoordFloat: Float + FloatCore,
ValueFloat: Float + FloatCore
{
type Item = (ValueFloat, Coordinates<CoordFloat>);
/// runs an iteration of the optimization algorithm and returns the best result so far
fn next(&mut self) -> Option<Self::Item>
{
// gets the exploration depth for later use
let exploration_depth = self.exploration_depth;
// gets an up to date simplex
let mut simplex = self.queue.pop().expect("Impossible: The queue cannot be empty!").0;
let current_difference = self.best_point.value - self.min_value;
while simplex.difference != current_difference
{
// updates the simplex and pushes it back into the queue
simplex.difference = current_difference;
let new_evaluation = simplex.evaluate(exploration_depth);
self.queue.push(simplex, OrderedFloat(new_evaluation));
// pops a new simplex
simplex = self.queue.pop().expect("Impossible: The queue cannot be empty!").0;
}
// evaluate the center of the simplex
let coordinates = simplex.center.clone();
let value = self.search_space.evaluate(&coordinates);
let new_point = Rc::new(Point { coordinates, value });
// splits the simplex around its center and push the subsimplex into the queue
simplex.split(new_point.clone(), current_difference)
.into_iter()
.map(|s| (OrderedFloat(s.evaluate(exploration_depth)), s))
.for_each(|(e, s)| {
self.queue.push(s, e);
});
// updates the difference
if value > self.best_point.value
{
self.best_point = new_point;
}
else if value < self.min_value
{
self.min_value = value;
}
// gets the best value so far
let best_value =
if self.search_space.minimize { -self.best_point.value } else { self.best_point.value };
let best_coordinate = self.search_space.to_hypercube(&self.best_point.coordinates);
Some((best_value, best_coordinate))
}
}