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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.optimization.direct;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.util.Comparator;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.optimization.OptimizationException;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.optimization.RealPointValuePair;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * This class implements the Nelder-Mead direct search method.<a name="line.27"></a> <FONT color="green">028</FONT> *<a name="line.28"></a> <FONT color="green">029</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.29"></a> <FONT color="green">030</FONT> * @see MultiDirectional<a name="line.30"></a> <FONT color="green">031</FONT> * @since 1.2<a name="line.31"></a> <FONT color="green">032</FONT> */<a name="line.32"></a> <FONT color="green">033</FONT> public class NelderMead extends DirectSearchOptimizer {<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /** Reflection coefficient. */<a name="line.35"></a> <FONT color="green">036</FONT> private final double rho;<a name="line.36"></a> <FONT color="green">037</FONT> <a name="line.37"></a> <FONT color="green">038</FONT> /** Expansion coefficient. */<a name="line.38"></a> <FONT color="green">039</FONT> private final double khi;<a name="line.39"></a> <FONT color="green">040</FONT> <a name="line.40"></a> <FONT color="green">041</FONT> /** Contraction coefficient. */<a name="line.41"></a> <FONT color="green">042</FONT> private final double gamma;<a name="line.42"></a> <FONT color="green">043</FONT> <a name="line.43"></a> <FONT color="green">044</FONT> /** Shrinkage coefficient. */<a name="line.44"></a> <FONT color="green">045</FONT> private final double sigma;<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** Build a Nelder-Mead optimizer with default coefficients.<a name="line.47"></a> <FONT color="green">048</FONT> * <p>The default coefficients are 1.0 for rho, 2.0 for khi and 0.5<a name="line.48"></a> <FONT color="green">049</FONT> * for both gamma and sigma.</p><a name="line.49"></a> <FONT color="green">050</FONT> */<a name="line.50"></a> <FONT color="green">051</FONT> public NelderMead() {<a name="line.51"></a> <FONT color="green">052</FONT> this.rho = 1.0;<a name="line.52"></a> <FONT color="green">053</FONT> this.khi = 2.0;<a name="line.53"></a> <FONT color="green">054</FONT> this.gamma = 0.5;<a name="line.54"></a> <FONT color="green">055</FONT> this.sigma = 0.5;<a name="line.55"></a> <FONT color="green">056</FONT> }<a name="line.56"></a> <FONT color="green">057</FONT> <a name="line.57"></a> <FONT color="green">058</FONT> /** Build a Nelder-Mead optimizer with specified coefficients.<a name="line.58"></a> <FONT color="green">059</FONT> * @param rho reflection coefficient<a name="line.59"></a> <FONT color="green">060</FONT> * @param khi expansion coefficient<a name="line.60"></a> <FONT color="green">061</FONT> * @param gamma contraction coefficient<a name="line.61"></a> <FONT color="green">062</FONT> * @param sigma shrinkage coefficient<a name="line.62"></a> <FONT color="green">063</FONT> */<a name="line.63"></a> <FONT color="green">064</FONT> public NelderMead(final double rho, final double khi,<a name="line.64"></a> <FONT color="green">065</FONT> final double gamma, final double sigma) {<a name="line.65"></a> <FONT color="green">066</FONT> this.rho = rho;<a name="line.66"></a> <FONT color="green">067</FONT> this.khi = khi;<a name="line.67"></a> <FONT color="green">068</FONT> this.gamma = gamma;<a name="line.68"></a> <FONT color="green">069</FONT> this.sigma = sigma;<a name="line.69"></a> <FONT color="green">070</FONT> }<a name="line.70"></a> <FONT color="green">071</FONT> <a name="line.71"></a> <FONT color="green">072</FONT> /** {@inheritDoc} */<a name="line.72"></a> <FONT color="green">073</FONT> @Override<a name="line.73"></a> <FONT color="green">074</FONT> protected void iterateSimplex(final Comparator<RealPointValuePair> comparator)<a name="line.74"></a> <FONT color="green">075</FONT> throws FunctionEvaluationException, OptimizationException {<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> incrementIterationsCounter();<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> // the simplex has n+1 point if dimension is n<a name="line.79"></a> <FONT color="green">080</FONT> final int n = simplex.length - 1;<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> // interesting values<a name="line.82"></a> <FONT color="green">083</FONT> final RealPointValuePair best = simplex[0];<a name="line.83"></a> <FONT color="green">084</FONT> final RealPointValuePair secondBest = simplex[n-1];<a name="line.84"></a> <FONT color="green">085</FONT> final RealPointValuePair worst = simplex[n];<a name="line.85"></a> <FONT color="green">086</FONT> final double[] xWorst = worst.getPointRef();<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> // compute the centroid of the best vertices<a name="line.88"></a> <FONT color="green">089</FONT> // (dismissing the worst point at index n)<a name="line.89"></a> <FONT color="green">090</FONT> final double[] centroid = new double[n];<a name="line.90"></a> <FONT color="green">091</FONT> for (int i = 0; i < n; ++i) {<a name="line.91"></a> <FONT color="green">092</FONT> final double[] x = simplex[i].getPointRef();<a name="line.92"></a> <FONT color="green">093</FONT> for (int j = 0; j < n; ++j) {<a name="line.93"></a> <FONT color="green">094</FONT> centroid[j] += x[j];<a name="line.94"></a> <FONT color="green">095</FONT> }<a name="line.95"></a> <FONT color="green">096</FONT> }<a name="line.96"></a> <FONT color="green">097</FONT> final double scaling = 1.0 / n;<a name="line.97"></a> <FONT color="green">098</FONT> for (int j = 0; j < n; ++j) {<a name="line.98"></a> <FONT color="green">099</FONT> centroid[j] *= scaling;<a name="line.99"></a> <FONT color="green">100</FONT> }<a name="line.100"></a> <FONT color="green">101</FONT> <a name="line.101"></a> <FONT color="green">102</FONT> // compute the reflection point<a name="line.102"></a> <FONT color="green">103</FONT> final double[] xR = new double[n];<a name="line.103"></a> <FONT color="green">104</FONT> for (int j = 0; j < n; ++j) {<a name="line.104"></a> <FONT color="green">105</FONT> xR[j] = centroid[j] + rho * (centroid[j] - xWorst[j]);<a name="line.105"></a> <FONT color="green">106</FONT> }<a name="line.106"></a> <FONT color="green">107</FONT> final RealPointValuePair reflected = new RealPointValuePair(xR, evaluate(xR), false);<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> if ((comparator.compare(best, reflected) <= 0) &&<a name="line.109"></a> <FONT color="green">110</FONT> (comparator.compare(reflected, secondBest) < 0)) {<a name="line.110"></a> <FONT color="green">111</FONT> <a name="line.111"></a> <FONT color="green">112</FONT> // accept the reflected point<a name="line.112"></a> <FONT color="green">113</FONT> replaceWorstPoint(reflected, comparator);<a name="line.113"></a> <FONT color="green">114</FONT> <a name="line.114"></a> <FONT color="green">115</FONT> } else if (comparator.compare(reflected, best) < 0) {<a name="line.115"></a> <FONT color="green">116</FONT> <a name="line.116"></a> <FONT color="green">117</FONT> // compute the expansion point<a name="line.117"></a> <FONT color="green">118</FONT> final double[] xE = new double[n];<a name="line.118"></a> <FONT color="green">119</FONT> for (int j = 0; j < n; ++j) {<a name="line.119"></a> <FONT color="green">120</FONT> xE[j] = centroid[j] + khi * (xR[j] - centroid[j]);<a name="line.120"></a> <FONT color="green">121</FONT> }<a name="line.121"></a> <FONT color="green">122</FONT> final RealPointValuePair expanded = new RealPointValuePair(xE, evaluate(xE), false);<a name="line.122"></a> <FONT color="green">123</FONT> <a name="line.123"></a> <FONT color="green">124</FONT> if (comparator.compare(expanded, reflected) < 0) {<a name="line.124"></a> <FONT color="green">125</FONT> // accept the expansion point<a name="line.125"></a> <FONT color="green">126</FONT> replaceWorstPoint(expanded, comparator);<a name="line.126"></a> <FONT color="green">127</FONT> } else {<a name="line.127"></a> <FONT color="green">128</FONT> // accept the reflected point<a name="line.128"></a> <FONT color="green">129</FONT> replaceWorstPoint(reflected, comparator);<a name="line.129"></a> <FONT color="green">130</FONT> }<a name="line.130"></a> <FONT color="green">131</FONT> <a name="line.131"></a> <FONT color="green">132</FONT> } else {<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> if (comparator.compare(reflected, worst) < 0) {<a name="line.134"></a> <FONT color="green">135</FONT> <a name="line.135"></a> <FONT color="green">136</FONT> // perform an outside contraction<a name="line.136"></a> <FONT color="green">137</FONT> final double[] xC = new double[n];<a name="line.137"></a> <FONT color="green">138</FONT> for (int j = 0; j < n; ++j) {<a name="line.138"></a> <FONT color="green">139</FONT> xC[j] = centroid[j] + gamma * (xR[j] - centroid[j]);<a name="line.139"></a> <FONT color="green">140</FONT> }<a name="line.140"></a> <FONT color="green">141</FONT> final RealPointValuePair outContracted = new RealPointValuePair(xC, evaluate(xC), false);<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> if (comparator.compare(outContracted, reflected) <= 0) {<a name="line.143"></a> <FONT color="green">144</FONT> // accept the contraction point<a name="line.144"></a> <FONT color="green">145</FONT> replaceWorstPoint(outContracted, comparator);<a name="line.145"></a> <FONT color="green">146</FONT> return;<a name="line.146"></a> <FONT color="green">147</FONT> }<a name="line.147"></a> <FONT color="green">148</FONT> <a name="line.148"></a> <FONT color="green">149</FONT> } else {<a name="line.149"></a> <FONT color="green">150</FONT> <a name="line.150"></a> <FONT color="green">151</FONT> // perform an inside contraction<a name="line.151"></a> <FONT color="green">152</FONT> final double[] xC = new double[n];<a name="line.152"></a> <FONT color="green">153</FONT> for (int j = 0; j < n; ++j) {<a name="line.153"></a> <FONT color="green">154</FONT> xC[j] = centroid[j] - gamma * (centroid[j] - xWorst[j]);<a name="line.154"></a> <FONT color="green">155</FONT> }<a name="line.155"></a> <FONT color="green">156</FONT> final RealPointValuePair inContracted = new RealPointValuePair(xC, evaluate(xC), false);<a name="line.156"></a> <FONT color="green">157</FONT> <a name="line.157"></a> <FONT color="green">158</FONT> if (comparator.compare(inContracted, worst) < 0) {<a name="line.158"></a> <FONT color="green">159</FONT> // accept the contraction point<a name="line.159"></a> <FONT color="green">160</FONT> replaceWorstPoint(inContracted, comparator);<a name="line.160"></a> <FONT color="green">161</FONT> return;<a name="line.161"></a> <FONT color="green">162</FONT> }<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> }<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> // perform a shrink<a name="line.166"></a> <FONT color="green">167</FONT> final double[] xSmallest = simplex[0].getPointRef();<a name="line.167"></a> <FONT color="green">168</FONT> for (int i = 1; i < simplex.length; ++i) {<a name="line.168"></a> <FONT color="green">169</FONT> final double[] x = simplex[i].getPoint();<a name="line.169"></a> <FONT color="green">170</FONT> for (int j = 0; j < n; ++j) {<a name="line.170"></a> <FONT color="green">171</FONT> x[j] = xSmallest[j] + sigma * (x[j] - xSmallest[j]);<a name="line.171"></a> <FONT color="green">172</FONT> }<a name="line.172"></a> <FONT color="green">173</FONT> simplex[i] = new RealPointValuePair(x, Double.NaN, false);<a name="line.173"></a> <FONT color="green">174</FONT> }<a name="line.174"></a> <FONT color="green">175</FONT> evaluateSimplex(comparator);<a name="line.175"></a> <FONT color="green">176</FONT> <a name="line.176"></a> <FONT color="green">177</FONT> }<a name="line.177"></a> <FONT color="green">178</FONT> <a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> <a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> </PRE> </BODY> </HTML>