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
|
/*
* 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.nonlinear.scalar.noderiv;
import java.util.Comparator;
import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.optim.PointValuePair;
/**
* This class implements the multi-directional direct search method.
*
* @since 3.0
*/
public class MultiDirectionalSimplex extends AbstractSimplex {
/** Default value for {@link #khi}: {@value}. */
private static final double DEFAULT_KHI = 2;
/** Default value for {@link #gamma}: {@value}. */
private static final double DEFAULT_GAMMA = 0.5;
/** Expansion coefficient. */
private final double khi;
/** Contraction coefficient. */
private final double gamma;
/**
* Build a multi-directional simplex with default coefficients.
* The default values are 2.0 for khi and 0.5 for gamma.
*
* @param n Dimension of the simplex.
*/
public MultiDirectionalSimplex(final int n) {
this(n, 1d);
}
/**
* Build a multi-directional simplex with default coefficients.
* The default values are 2.0 for khi and 0.5 for gamma.
*
* @param n Dimension of the simplex.
* @param sideLength Length of the sides of the default (hypercube)
* simplex. See {@link AbstractSimplex#AbstractSimplex(int,double)}.
*/
public MultiDirectionalSimplex(final int n, double sideLength) {
this(n, sideLength, DEFAULT_KHI, DEFAULT_GAMMA);
}
/**
* Build a multi-directional simplex with specified coefficients.
*
* @param n Dimension of the simplex. See
* {@link AbstractSimplex#AbstractSimplex(int,double)}.
* @param khi Expansion coefficient.
* @param gamma Contraction coefficient.
*/
public MultiDirectionalSimplex(final int n,
final double khi, final double gamma) {
this(n, 1d, khi, gamma);
}
/**
* Build a multi-directional simplex with specified coefficients.
*
* @param n Dimension of the simplex. See
* {@link AbstractSimplex#AbstractSimplex(int,double)}.
* @param sideLength Length of the sides of the default (hypercube)
* simplex. See {@link AbstractSimplex#AbstractSimplex(int,double)}.
* @param khi Expansion coefficient.
* @param gamma Contraction coefficient.
*/
public MultiDirectionalSimplex(final int n, double sideLength,
final double khi, final double gamma) {
super(n, sideLength);
this.khi = khi;
this.gamma = gamma;
}
/**
* Build a multi-directional simplex with default coefficients.
* The default values are 2.0 for khi and 0.5 for gamma.
*
* @param steps Steps along the canonical axes representing box edges.
* They may be negative but not zero. See
*/
public MultiDirectionalSimplex(final double[] steps) {
this(steps, DEFAULT_KHI, DEFAULT_GAMMA);
}
/**
* Build a multi-directional simplex with specified coefficients.
*
* @param steps Steps along the canonical axes representing box edges.
* They may be negative but not zero. See
* {@link AbstractSimplex#AbstractSimplex(double[])}.
* @param khi Expansion coefficient.
* @param gamma Contraction coefficient.
*/
public MultiDirectionalSimplex(final double[] steps,
final double khi, final double gamma) {
super(steps);
this.khi = khi;
this.gamma = gamma;
}
/**
* Build a multi-directional simplex with default coefficients.
* The default values are 2.0 for khi and 0.5 for gamma.
*
* @param referenceSimplex Reference simplex. See
* {@link AbstractSimplex#AbstractSimplex(double[][])}.
*/
public MultiDirectionalSimplex(final double[][] referenceSimplex) {
this(referenceSimplex, DEFAULT_KHI, DEFAULT_GAMMA);
}
/**
* Build a multi-directional simplex with specified coefficients.
*
* @param referenceSimplex Reference simplex. See
* {@link AbstractSimplex#AbstractSimplex(double[][])}.
* @param khi Expansion coefficient.
* @param gamma Contraction coefficient.
* @throws org.apache.commons.math3.exception.NotStrictlyPositiveException
* if the reference simplex does not contain at least one point.
* @throws org.apache.commons.math3.exception.DimensionMismatchException
* if there is a dimension mismatch in the reference simplex.
*/
public MultiDirectionalSimplex(final double[][] referenceSimplex,
final double khi, final double gamma) {
super(referenceSimplex);
this.khi = khi;
this.gamma = gamma;
}
/** {@inheritDoc} */
@Override
public void iterate(final MultivariateFunction evaluationFunction,
final Comparator<PointValuePair> comparator) {
// Save the original simplex.
final PointValuePair[] original = getPoints();
final PointValuePair best = original[0];
// Perform a reflection step.
final PointValuePair reflected = evaluateNewSimplex(evaluationFunction,
original, 1, comparator);
if (comparator.compare(reflected, best) < 0) {
// Compute the expanded simplex.
final PointValuePair[] reflectedSimplex = getPoints();
final PointValuePair expanded = evaluateNewSimplex(evaluationFunction,
original, khi, comparator);
if (comparator.compare(reflected, expanded) <= 0) {
// Keep the reflected simplex.
setPoints(reflectedSimplex);
}
// Keep the expanded simplex.
return;
}
// Compute the contracted simplex.
evaluateNewSimplex(evaluationFunction, original, gamma, comparator);
}
/**
* Compute and evaluate a new simplex.
*
* @param evaluationFunction Evaluation function.
* @param original Original simplex (to be preserved).
* @param coeff Linear coefficient.
* @param comparator Comparator to use to sort simplex vertices from best
* to poorest.
* @return the best point in the transformed simplex.
* @throws org.apache.commons.math3.exception.TooManyEvaluationsException
* if the maximal number of evaluations is exceeded.
*/
private PointValuePair evaluateNewSimplex(final MultivariateFunction evaluationFunction,
final PointValuePair[] original,
final double coeff,
final Comparator<PointValuePair> comparator) {
final double[] xSmallest = original[0].getPointRef();
// Perform a linear transformation on all the simplex points,
// except the first one.
setPoint(0, original[0]);
final int dim = getDimension();
for (int i = 1; i < getSize(); i++) {
final double[] xOriginal = original[i].getPointRef();
final double[] xTransformed = new double[dim];
for (int j = 0; j < dim; j++) {
xTransformed[j] = xSmallest[j] + coeff * (xSmallest[j] - xOriginal[j]);
}
setPoint(i, new PointValuePair(xTransformed, Double.NaN, false));
}
// Evaluate the simplex.
evaluate(evaluationFunction, comparator);
return getPoint(0);
}
}
|
