001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math3.optim.univariate;
019
020 import java.util.Arrays;
021 import java.util.Comparator;
022 import org.apache.commons.math3.exception.MathIllegalStateException;
023 import org.apache.commons.math3.exception.NotStrictlyPositiveException;
024 import org.apache.commons.math3.exception.util.LocalizedFormats;
025 import org.apache.commons.math3.random.RandomGenerator;
026 import org.apache.commons.math3.optim.MaxEval;
027 import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
028 import org.apache.commons.math3.optim.OptimizationData;
029
030 /**
031 * Special implementation of the {@link UnivariateOptimizer} interface
032 * adding multi-start features to an existing optimizer.
033 * <br/>
034 * This class wraps an optimizer in order to use it several times in
035 * turn with different starting points (trying to avoid being trapped
036 * in a local extremum when looking for a global one).
037 *
038 * @version $Id$
039 * @since 3.0
040 */
041 public class MultiStartUnivariateOptimizer
042 extends UnivariateOptimizer {
043 /** Underlying classical optimizer. */
044 private final UnivariateOptimizer optimizer;
045 /** Number of evaluations already performed for all starts. */
046 private int totalEvaluations;
047 /** Number of starts to go. */
048 private int starts;
049 /** Random generator for multi-start. */
050 private RandomGenerator generator;
051 /** Found optima. */
052 private UnivariatePointValuePair[] optima;
053 /** Optimization data. */
054 private OptimizationData[] optimData;
055 /**
056 * Location in {@link #optimData} where the updated maximum
057 * number of evaluations will be stored.
058 */
059 private int maxEvalIndex = -1;
060 /**
061 * Location in {@link #optimData} where the updated start value
062 * will be stored.
063 */
064 private int searchIntervalIndex = -1;
065
066 /**
067 * Create a multi-start optimizer from a single-start optimizer.
068 *
069 * @param optimizer Single-start optimizer to wrap.
070 * @param starts Number of starts to perform. If {@code starts == 1},
071 * the {@code optimize} methods will return the same solution as
072 * {@code optimizer} would.
073 * @param generator Random generator to use for restarts.
074 * @throws NotStrictlyPositiveException if {@code starts < 1}.
075 */
076 public MultiStartUnivariateOptimizer(final UnivariateOptimizer optimizer,
077 final int starts,
078 final RandomGenerator generator) {
079 super(optimizer.getConvergenceChecker());
080
081 if (starts < 1) {
082 throw new NotStrictlyPositiveException(starts);
083 }
084
085 this.optimizer = optimizer;
086 this.starts = starts;
087 this.generator = generator;
088 }
089
090 /** {@inheritDoc} */
091 @Override
092 public int getEvaluations() {
093 return totalEvaluations;
094 }
095
096 /**
097 * Gets all the optima found during the last call to {@code optimize}.
098 * The optimizer stores all the optima found during a set of
099 * restarts. The {@code optimize} method returns the best point only.
100 * This method returns all the points found at the end of each starts,
101 * including the best one already returned by the {@code optimize} method.
102 * <br/>
103 * The returned array as one element for each start as specified
104 * in the constructor. It is ordered with the results from the
105 * runs that did converge first, sorted from best to worst
106 * objective value (i.e in ascending order if minimizing and in
107 * descending order if maximizing), followed by {@code null} elements
108 * corresponding to the runs that did not converge. This means all
109 * elements will be {@code null} if the {@code optimize} method did throw
110 * an exception.
111 * This also means that if the first element is not {@code null}, it is
112 * the best point found across all starts.
113 *
114 * @return an array containing the optima.
115 * @throws MathIllegalStateException if {@link #optimize(OptimizationData[])
116 * optimize} has not been called.
117 */
118 public UnivariatePointValuePair[] getOptima() {
119 if (optima == null) {
120 throw new MathIllegalStateException(LocalizedFormats.NO_OPTIMUM_COMPUTED_YET);
121 }
122 return optima.clone();
123 }
124
125 /**
126 * {@inheritDoc}
127 *
128 * @throws MathIllegalStateException if {@code optData} does not contain an
129 * instance of {@link MaxEval} or {@link SearchInterval}.
130 */
131 @Override
132 public UnivariatePointValuePair optimize(OptimizationData... optData) {
133 // Store arguments in order to pass them to the internal optimizer.
134 optimData = optData;
135 // Set up base class and perform computations.
136 return super.optimize(optData);
137 }
138
139 /** {@inheritDoc} */
140 @Override
141 protected UnivariatePointValuePair doOptimize() {
142 // Remove all instances of "MaxEval" and "SearchInterval" from the
143 // array that will be passed to the internal optimizer.
144 // The former is to enforce smaller numbers of allowed evaluations
145 // (according to how many have been used up already), and the latter
146 // to impose a different start value for each start.
147 for (int i = 0; i < optimData.length; i++) {
148 if (optimData[i] instanceof MaxEval) {
149 optimData[i] = null;
150 maxEvalIndex = i;
151 continue;
152 }
153 if (optimData[i] instanceof SearchInterval) {
154 optimData[i] = null;
155 searchIntervalIndex = i;
156 continue;
157 }
158 }
159 if (maxEvalIndex == -1) {
160 throw new MathIllegalStateException();
161 }
162 if (searchIntervalIndex == -1) {
163 throw new MathIllegalStateException();
164 }
165
166 RuntimeException lastException = null;
167 optima = new UnivariatePointValuePair[starts];
168 totalEvaluations = 0;
169
170 final int maxEval = getMaxEvaluations();
171 final double min = getMin();
172 final double max = getMax();
173 final double startValue = getStartValue();
174
175 // Multi-start loop.
176 for (int i = 0; i < starts; i++) {
177 // CHECKSTYLE: stop IllegalCatch
178 try {
179 // Decrease number of allowed evaluations.
180 optimData[maxEvalIndex] = new MaxEval(maxEval - totalEvaluations);
181 // New start value.
182 final double s = (i == 0) ?
183 startValue :
184 min + generator.nextDouble() * (max - min);
185 optimData[searchIntervalIndex] = new SearchInterval(min, max, s);
186 // Optimize.
187 optima[i] = optimizer.optimize(optimData);
188 } catch (RuntimeException mue) {
189 lastException = mue;
190 optima[i] = null;
191 }
192 // CHECKSTYLE: resume IllegalCatch
193
194 totalEvaluations += optimizer.getEvaluations();
195 }
196
197 sortPairs(getGoalType());
198
199 if (optima[0] == null) {
200 throw lastException; // Cannot be null if starts >= 1.
201 }
202
203 // Return the point with the best objective function value.
204 return optima[0];
205 }
206
207 /**
208 * Sort the optima from best to worst, followed by {@code null} elements.
209 *
210 * @param goal Goal type.
211 */
212 private void sortPairs(final GoalType goal) {
213 Arrays.sort(optima, new Comparator<UnivariatePointValuePair>() {
214 public int compare(final UnivariatePointValuePair o1,
215 final UnivariatePointValuePair o2) {
216 if (o1 == null) {
217 return (o2 == null) ? 0 : 1;
218 } else if (o2 == null) {
219 return -1;
220 }
221 final double v1 = o1.getValue();
222 final double v2 = o2.getValue();
223 return (goal == GoalType.MINIMIZE) ?
224 Double.compare(v1, v2) : Double.compare(v2, v1);
225 }
226 });
227 }
228 }