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
|
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.optim;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.random.RandomVectorGenerator;
/**
* Base class multi-start optimizer for a multivariate function. <br>
* This class wraps an optimizer in order to use it several times in turn with different starting
* points (trying to avoid being trapped in a local extremum when looking for a global one). <em>It
* is not a "user" class.</em>
*
* @param <PAIR> Type of the point/value pair returned by the optimization algorithm.
* @since 3.0
*/
public abstract class BaseMultiStartMultivariateOptimizer<PAIR>
extends BaseMultivariateOptimizer<PAIR> {
/** Underlying classical optimizer. */
private final BaseMultivariateOptimizer<PAIR> optimizer;
/** Number of evaluations already performed for all starts. */
private int totalEvaluations;
/** Number of starts to go. */
private int starts;
/** Random generator for multi-start. */
private RandomVectorGenerator generator;
/** Optimization data. */
private OptimizationData[] optimData;
/**
* Location in {@link #optimData} where the updated maximum number of evaluations will be
* stored.
*/
private int maxEvalIndex = -1;
/** Location in {@link #optimData} where the updated start value will be stored. */
private int initialGuessIndex = -1;
/**
* Create a multi-start optimizer from a single-start optimizer.
*
* <p>Note that if there are bounds constraints (see {@link #getLowerBound()} and {@link
* #getUpperBound()}), then a simple rejection algorithm is used at each restart. This implies
* that the random vector generator should have a good probability to generate vectors in the
* bounded domain, otherwise the rejection algorithm will hit the {@link #getMaxEvaluations()}
* count without generating a proper restart point. Users must be take great care of the <a
* href="http://en.wikipedia.org/wiki/Curse_of_dimensionality">curse of dimensionality</a>.
*
* @param optimizer Single-start optimizer to wrap.
* @param starts Number of starts to perform. If {@code starts == 1}, the {@link
* #optimize(OptimizationData[]) optimize} will return the same solution as the given {@code
* optimizer} would return.
* @param generator Random vector generator to use for restarts.
* @throws NotStrictlyPositiveException if {@code starts < 1}.
*/
public BaseMultiStartMultivariateOptimizer(
final BaseMultivariateOptimizer<PAIR> optimizer,
final int starts,
final RandomVectorGenerator generator) {
super(optimizer.getConvergenceChecker());
if (starts < 1) {
throw new NotStrictlyPositiveException(starts);
}
this.optimizer = optimizer;
this.starts = starts;
this.generator = generator;
}
/** {@inheritDoc} */
@Override
public int getEvaluations() {
return totalEvaluations;
}
/**
* Gets all the optima found during the last call to {@code optimize}. The optimizer stores all
* the optima found during a set of restarts. The {@code optimize} method returns the best point
* only. This method returns all the points found at the end of each starts, including the best
* one already returned by the {@code optimize} method. <br>
* The returned array as one element for each start as specified in the constructor. It is
* ordered with the results from the runs that did converge first, sorted from best to worst
* objective value (i.e in ascending order if minimizing and in descending order if maximizing),
* followed by {@code null} elements corresponding to the runs that did not converge. This means
* all elements will be {@code null} if the {@code optimize} method did throw an exception. This
* also means that if the first element is not {@code null}, it is the best point found across
* all starts. <br>
* The behaviour is undefined if this method is called before {@code optimize}; it will likely
* throw {@code NullPointerException}.
*
* @return an array containing the optima sorted from best to worst.
*/
public abstract PAIR[] getOptima();
/**
* {@inheritDoc}
*
* @throws MathIllegalStateException if {@code optData} does not contain an instance of {@link
* MaxEval} or {@link InitialGuess}.
*/
@Override
public PAIR optimize(OptimizationData... optData) {
// Store arguments in order to pass them to the internal optimizer.
optimData = optData;
// Set up base class and perform computations.
return super.optimize(optData);
}
/** {@inheritDoc} */
@Override
protected PAIR doOptimize() {
// Remove all instances of "MaxEval" and "InitialGuess" from the
// array that will be passed to the internal optimizer.
// The former is to enforce smaller numbers of allowed evaluations
// (according to how many have been used up already), and the latter
// to impose a different start value for each start.
for (int i = 0; i < optimData.length; i++) {
if (optimData[i] instanceof MaxEval) {
optimData[i] = null;
maxEvalIndex = i;
}
if (optimData[i] instanceof InitialGuess) {
optimData[i] = null;
initialGuessIndex = i;
continue;
}
}
if (maxEvalIndex == -1) {
throw new MathIllegalStateException();
}
if (initialGuessIndex == -1) {
throw new MathIllegalStateException();
}
RuntimeException lastException = null;
totalEvaluations = 0;
clear();
final int maxEval = getMaxEvaluations();
final double[] min = getLowerBound();
final double[] max = getUpperBound();
final double[] startPoint = getStartPoint();
// Multi-start loop.
for (int i = 0; i < starts; i++) {
// CHECKSTYLE: stop IllegalCatch
try {
// Decrease number of allowed evaluations.
optimData[maxEvalIndex] = new MaxEval(maxEval - totalEvaluations);
// New start value.
double[] s = null;
if (i == 0) {
s = startPoint;
} else {
int attempts = 0;
while (s == null) {
if (attempts++ >= getMaxEvaluations()) {
throw new TooManyEvaluationsException(getMaxEvaluations());
}
s = generator.nextVector();
for (int k = 0; s != null && k < s.length; ++k) {
if ((min != null && s[k] < min[k]) || (max != null && s[k] > max[k])) {
// reject the vector
s = null;
}
}
}
}
optimData[initialGuessIndex] = new InitialGuess(s);
// Optimize.
final PAIR result = optimizer.optimize(optimData);
store(result);
} catch (RuntimeException mue) {
lastException = mue;
}
// CHECKSTYLE: resume IllegalCatch
totalEvaluations += optimizer.getEvaluations();
}
final PAIR[] optima = getOptima();
if (optima.length == 0) {
// All runs failed.
throw lastException; // Cannot be null if starts >= 1.
}
// Return the best optimum.
return optima[0];
}
/**
* Method that will be called in order to store each found optimum.
*
* @param optimum Result of an optimization run.
*/
protected abstract void store(PAIR optimum);
/** Method that will called in order to clear all stored optima. */
protected abstract void clear();
}
|
