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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.Arrays;<a name="line.20"></a> <FONT color="green">021</FONT> import java.util.Comparator;<a name="line.21"></a> <FONT color="green">022</FONT> <a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.MaxEvaluationsExceededException;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.MaxIterationsExceededException;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.analysis.MultivariateRealFunction;<a name="line.27"></a> <FONT color="green">028</FONT> import org.apache.commons.math.optimization.GoalType;<a name="line.28"></a> <FONT color="green">029</FONT> import org.apache.commons.math.optimization.MultivariateRealOptimizer;<a name="line.29"></a> <FONT color="green">030</FONT> import org.apache.commons.math.optimization.OptimizationException;<a name="line.30"></a> <FONT color="green">031</FONT> import org.apache.commons.math.optimization.RealConvergenceChecker;<a name="line.31"></a> <FONT color="green">032</FONT> import org.apache.commons.math.optimization.RealPointValuePair;<a name="line.32"></a> <FONT color="green">033</FONT> import org.apache.commons.math.optimization.SimpleScalarValueChecker;<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /**<a name="line.35"></a> <FONT color="green">036</FONT> * This class implements simplex-based direct search optimization<a name="line.36"></a> <FONT color="green">037</FONT> * algorithms.<a name="line.37"></a> <FONT color="green">038</FONT> *<a name="line.38"></a> <FONT color="green">039</FONT> * <p>Direct search methods only use objective function values, they don't<a name="line.39"></a> <FONT color="green">040</FONT> * need derivatives and don't either try to compute approximation of<a name="line.40"></a> <FONT color="green">041</FONT> * the derivatives. According to a 1996 paper by Margaret H. Wright<a name="line.41"></a> <FONT color="green">042</FONT> * (<a href="http://cm.bell-labs.com/cm/cs/doc/96/4-02.ps.gz">Direct<a name="line.42"></a> <FONT color="green">043</FONT> * Search Methods: Once Scorned, Now Respectable</a>), they are used<a name="line.43"></a> <FONT color="green">044</FONT> * when either the computation of the derivative is impossible (noisy<a name="line.44"></a> <FONT color="green">045</FONT> * functions, unpredictable discontinuities) or difficult (complexity,<a name="line.45"></a> <FONT color="green">046</FONT> * computation cost). In the first cases, rather than an optimum, a<a name="line.46"></a> <FONT color="green">047</FONT> * <em>not too bad</em> point is desired. In the latter cases, an<a name="line.47"></a> <FONT color="green">048</FONT> * optimum is desired but cannot be reasonably found. In all cases<a name="line.48"></a> <FONT color="green">049</FONT> * direct search methods can be useful.</p><a name="line.49"></a> <FONT color="green">050</FONT> *<a name="line.50"></a> <FONT color="green">051</FONT> * <p>Simplex-based direct search methods are based on comparison of<a name="line.51"></a> <FONT color="green">052</FONT> * the objective function values at the vertices of a simplex (which is a<a name="line.52"></a> <FONT color="green">053</FONT> * set of n+1 points in dimension n) that is updated by the algorithms<a name="line.53"></a> <FONT color="green">054</FONT> * steps.<p><a name="line.54"></a> <FONT color="green">055</FONT> *<a name="line.55"></a> <FONT color="green">056</FONT> * <p>The initial configuration of the simplex can be set using either<a name="line.56"></a> <FONT color="green">057</FONT> * {@link #setStartConfiguration(double[])} or {@link<a name="line.57"></a> <FONT color="green">058</FONT> * #setStartConfiguration(double[][])}. If neither method has been called<a name="line.58"></a> <FONT color="green">059</FONT> * before optimization is attempted, an explicit call to the first method<a name="line.59"></a> <FONT color="green">060</FONT> * with all steps set to +1 is triggered, thus building a default<a name="line.60"></a> <FONT color="green">061</FONT> * configuration from a unit hypercube. Each call to {@link<a name="line.61"></a> <FONT color="green">062</FONT> * #optimize(MultivariateRealFunction, GoalType, double[]) optimize} will reuse<a name="line.62"></a> <FONT color="green">063</FONT> * the current start configuration and move it such that its first vertex<a name="line.63"></a> <FONT color="green">064</FONT> * is at the provided start point of the optimization. If the same optimizer<a name="line.64"></a> <FONT color="green">065</FONT> * is used to solve different problems and the number of parameters change,<a name="line.65"></a> <FONT color="green">066</FONT> * the start configuration <em>must</em> be reset or a dimension mismatch<a name="line.66"></a> <FONT color="green">067</FONT> * will occur.</p><a name="line.67"></a> <FONT color="green">068</FONT> *<a name="line.68"></a> <FONT color="green">069</FONT> * <p>If {@link #setConvergenceChecker(RealConvergenceChecker)} is not called,<a name="line.69"></a> <FONT color="green">070</FONT> * a default {@link SimpleScalarValueChecker} is used.</p><a name="line.70"></a> <FONT color="green">071</FONT> *<a name="line.71"></a> <FONT color="green">072</FONT> * <p>Convergence is checked by providing the <em>worst</em> points of<a name="line.72"></a> <FONT color="green">073</FONT> * previous and current simplex to the convergence checker, not the best ones.</p><a name="line.73"></a> <FONT color="green">074</FONT> *<a name="line.74"></a> <FONT color="green">075</FONT> * <p>This class is the base class performing the boilerplate simplex<a name="line.75"></a> <FONT color="green">076</FONT> * initialization and handling. The simplex update by itself is<a name="line.76"></a> <FONT color="green">077</FONT> * performed by the derived classes according to the implemented<a name="line.77"></a> <FONT color="green">078</FONT> * algorithms.</p><a name="line.78"></a> <FONT color="green">079</FONT> *<a name="line.79"></a> <FONT color="green">080</FONT> * implements MultivariateRealOptimizer since 2.0<a name="line.80"></a> <FONT color="green">081</FONT> *<a name="line.81"></a> <FONT color="green">082</FONT> * @see MultivariateRealFunction<a name="line.82"></a> <FONT color="green">083</FONT> * @see NelderMead<a name="line.83"></a> <FONT color="green">084</FONT> * @see MultiDirectional<a name="line.84"></a> <FONT color="green">085</FONT> * @version $Revision: 885278 $ $Date: 2009-11-29 16:47:51 -0500 (Sun, 29 Nov 2009) $<a name="line.85"></a> <FONT color="green">086</FONT> * @since 1.2<a name="line.86"></a> <FONT color="green">087</FONT> */<a name="line.87"></a> <FONT color="green">088</FONT> public abstract class DirectSearchOptimizer implements MultivariateRealOptimizer {<a name="line.88"></a> <FONT color="green">089</FONT> <a name="line.89"></a> <FONT color="green">090</FONT> /** Message for equal vertices. */<a name="line.90"></a> <FONT color="green">091</FONT> private static final String EQUAL_VERTICES_MESSAGE =<a name="line.91"></a> <FONT color="green">092</FONT> "equal vertices {0} and {1} in simplex configuration";<a name="line.92"></a> <FONT color="green">093</FONT> <a name="line.93"></a> <FONT color="green">094</FONT> /** Message for dimension mismatch. */<a name="line.94"></a> <FONT color="green">095</FONT> private static final String DIMENSION_MISMATCH_MESSAGE =<a name="line.95"></a> <FONT color="green">096</FONT> "dimension mismatch {0} != {1}";<a name="line.96"></a> <FONT color="green">097</FONT> <a name="line.97"></a> <FONT color="green">098</FONT> /** Simplex. */<a name="line.98"></a> <FONT color="green">099</FONT> protected RealPointValuePair[] simplex;<a name="line.99"></a> <FONT color="green">100</FONT> <a name="line.100"></a> <FONT color="green">101</FONT> /** Objective function. */<a name="line.101"></a> <FONT color="green">102</FONT> private MultivariateRealFunction f;<a name="line.102"></a> <FONT color="green">103</FONT> <a name="line.103"></a> <FONT color="green">104</FONT> /** Convergence checker. */<a name="line.104"></a> <FONT color="green">105</FONT> private RealConvergenceChecker checker;<a name="line.105"></a> <FONT color="green">106</FONT> <a name="line.106"></a> <FONT color="green">107</FONT> /** Maximal number of iterations allowed. */<a name="line.107"></a> <FONT color="green">108</FONT> private int maxIterations;<a name="line.108"></a> <FONT color="green">109</FONT> <a name="line.109"></a> <FONT color="green">110</FONT> /** Number of iterations already performed. */<a name="line.110"></a> <FONT color="green">111</FONT> private int iterations;<a name="line.111"></a> <FONT color="green">112</FONT> <a name="line.112"></a> <FONT color="green">113</FONT> /** Maximal number of evaluations allowed. */<a name="line.113"></a> <FONT color="green">114</FONT> private int maxEvaluations;<a name="line.114"></a> <FONT color="green">115</FONT> <a name="line.115"></a> <FONT color="green">116</FONT> /** Number of evaluations already performed. */<a name="line.116"></a> <FONT color="green">117</FONT> private int evaluations;<a name="line.117"></a> <FONT color="green">118</FONT> <a name="line.118"></a> <FONT color="green">119</FONT> /** Start simplex configuration. */<a name="line.119"></a> <FONT color="green">120</FONT> private double[][] startConfiguration;<a name="line.120"></a> <FONT color="green">121</FONT> <a name="line.121"></a> <FONT color="green">122</FONT> /** Simple constructor.<a name="line.122"></a> <FONT color="green">123</FONT> */<a name="line.123"></a> <FONT color="green">124</FONT> protected DirectSearchOptimizer() {<a name="line.124"></a> <FONT color="green">125</FONT> setConvergenceChecker(new SimpleScalarValueChecker());<a name="line.125"></a> <FONT color="green">126</FONT> setMaxIterations(Integer.MAX_VALUE);<a name="line.126"></a> <FONT color="green">127</FONT> setMaxEvaluations(Integer.MAX_VALUE);<a name="line.127"></a> <FONT color="green">128</FONT> }<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> /** Set start configuration for simplex.<a name="line.130"></a> <FONT color="green">131</FONT> * <p>The start configuration for simplex is built from a box parallel to<a name="line.131"></a> <FONT color="green">132</FONT> * the canonical axes of the space. The simplex is the subset of vertices<a name="line.132"></a> <FONT color="green">133</FONT> * of a box parallel to the canonical axes. It is built as the path followed<a name="line.133"></a> <FONT color="green">134</FONT> * while traveling from one vertex of the box to the diagonally opposite<a name="line.134"></a> <FONT color="green">135</FONT> * vertex moving only along the box edges. The first vertex of the box will<a name="line.135"></a> <FONT color="green">136</FONT> * be located at the start point of the optimization.</p><a name="line.136"></a> <FONT color="green">137</FONT> * <p>As an example, in dimension 3 a simplex has 4 vertices. Setting the<a name="line.137"></a> <FONT color="green">138</FONT> * steps to (1, 10, 2) and the start point to (1, 1, 1) would imply the<a name="line.138"></a> <FONT color="green">139</FONT> * start simplex would be: { (1, 1, 1), (2, 1, 1), (2, 11, 1), (2, 11, 3) }.<a name="line.139"></a> <FONT color="green">140</FONT> * The first vertex would be set to the start point at (1, 1, 1) and the<a name="line.140"></a> <FONT color="green">141</FONT> * last vertex would be set to the diagonally opposite vertex at (2, 11, 3).</p><a name="line.141"></a> <FONT color="green">142</FONT> * @param steps steps along the canonical axes representing box edges,<a name="line.142"></a> <FONT color="green">143</FONT> * they may be negative but not null<a name="line.143"></a> <FONT color="green">144</FONT> * @exception IllegalArgumentException if one step is null<a name="line.144"></a> <FONT color="green">145</FONT> */<a name="line.145"></a> <FONT color="green">146</FONT> public void setStartConfiguration(final double[] steps)<a name="line.146"></a> <FONT color="green">147</FONT> throws IllegalArgumentException {<a name="line.147"></a> <FONT color="green">148</FONT> // only the relative position of the n final vertices with respect<a name="line.148"></a> <FONT color="green">149</FONT> // to the first one are stored<a name="line.149"></a> <FONT color="green">150</FONT> final int n = steps.length;<a name="line.150"></a> <FONT color="green">151</FONT> startConfiguration = new double[n][n];<a name="line.151"></a> <FONT color="green">152</FONT> for (int i = 0; i < n; ++i) {<a name="line.152"></a> <FONT color="green">153</FONT> final double[] vertexI = startConfiguration[i];<a name="line.153"></a> <FONT color="green">154</FONT> for (int j = 0; j < i + 1; ++j) {<a name="line.154"></a> <FONT color="green">155</FONT> if (steps[j] == 0.0) {<a name="line.155"></a> <FONT color="green">156</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.156"></a> <FONT color="green">157</FONT> EQUAL_VERTICES_MESSAGE, j, j + 1);<a name="line.157"></a> <FONT color="green">158</FONT> }<a name="line.158"></a> <FONT color="green">159</FONT> System.arraycopy(steps, 0, vertexI, 0, j + 1);<a name="line.159"></a> <FONT color="green">160</FONT> }<a name="line.160"></a> <FONT color="green">161</FONT> }<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> /** Set start configuration for simplex.<a name="line.164"></a> <FONT color="green">165</FONT> * <p>The real initial simplex will be set up by moving the reference<a name="line.165"></a> <FONT color="green">166</FONT> * simplex such that its first point is located at the start point of the<a name="line.166"></a> <FONT color="green">167</FONT> * optimization.</p><a name="line.167"></a> <FONT color="green">168</FONT> * @param referenceSimplex reference simplex<a name="line.168"></a> <FONT color="green">169</FONT> * @exception IllegalArgumentException if the reference simplex does not<a name="line.169"></a> <FONT color="green">170</FONT> * contain at least one point, or if there is a dimension mismatch<a name="line.170"></a> <FONT color="green">171</FONT> * in the reference simplex or if one of its vertices is duplicated<a name="line.171"></a> <FONT color="green">172</FONT> */<a name="line.172"></a> <FONT color="green">173</FONT> public void setStartConfiguration(final double[][] referenceSimplex)<a name="line.173"></a> <FONT color="green">174</FONT> throws IllegalArgumentException {<a name="line.174"></a> <FONT color="green">175</FONT> <a name="line.175"></a> <FONT color="green">176</FONT> // only the relative position of the n final vertices with respect<a name="line.176"></a> <FONT color="green">177</FONT> // to the first one are stored<a name="line.177"></a> <FONT color="green">178</FONT> final int n = referenceSimplex.length - 1;<a name="line.178"></a> <FONT color="green">179</FONT> if (n < 0) {<a name="line.179"></a> <FONT color="green">180</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.180"></a> <FONT color="green">181</FONT> "simplex must contain at least one point");<a name="line.181"></a> <FONT color="green">182</FONT> }<a name="line.182"></a> <FONT color="green">183</FONT> startConfiguration = new double[n][n];<a name="line.183"></a> <FONT color="green">184</FONT> final double[] ref0 = referenceSimplex[0];<a name="line.184"></a> <FONT color="green">185</FONT> <a name="line.185"></a> <FONT color="green">186</FONT> // vertices loop<a name="line.186"></a> <FONT color="green">187</FONT> for (int i = 0; i < n + 1; ++i) {<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> final double[] refI = referenceSimplex[i];<a name="line.189"></a> <FONT color="green">190</FONT> <a name="line.190"></a> <FONT color="green">191</FONT> // safety checks<a name="line.191"></a> <FONT color="green">192</FONT> if (refI.length != n) {<a name="line.192"></a> <FONT color="green">193</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.193"></a> <FONT color="green">194</FONT> DIMENSION_MISMATCH_MESSAGE, refI.length, n);<a name="line.194"></a> <FONT color="green">195</FONT> }<a name="line.195"></a> <FONT color="green">196</FONT> for (int j = 0; j < i; ++j) {<a name="line.196"></a> <FONT color="green">197</FONT> final double[] refJ = referenceSimplex[j];<a name="line.197"></a> <FONT color="green">198</FONT> boolean allEquals = true;<a name="line.198"></a> <FONT color="green">199</FONT> for (int k = 0; k < n; ++k) {<a name="line.199"></a> <FONT color="green">200</FONT> if (refI[k] != refJ[k]) {<a name="line.200"></a> <FONT color="green">201</FONT> allEquals = false;<a name="line.201"></a> <FONT color="green">202</FONT> break;<a name="line.202"></a> <FONT color="green">203</FONT> }<a name="line.203"></a> <FONT color="green">204</FONT> }<a name="line.204"></a> <FONT color="green">205</FONT> if (allEquals) {<a name="line.205"></a> <FONT color="green">206</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.206"></a> <FONT color="green">207</FONT> EQUAL_VERTICES_MESSAGE, i, j);<a name="line.207"></a> <FONT color="green">208</FONT> }<a name="line.208"></a> <FONT color="green">209</FONT> }<a name="line.209"></a> <FONT color="green">210</FONT> <a name="line.210"></a> <FONT color="green">211</FONT> // store vertex i position relative to vertex 0 position<a name="line.211"></a> <FONT color="green">212</FONT> if (i > 0) {<a name="line.212"></a> <FONT color="green">213</FONT> final double[] confI = startConfiguration[i - 1];<a name="line.213"></a> <FONT color="green">214</FONT> for (int k = 0; k < n; ++k) {<a name="line.214"></a> <FONT color="green">215</FONT> confI[k] = refI[k] - ref0[k];<a name="line.215"></a> <FONT color="green">216</FONT> }<a name="line.216"></a> <FONT color="green">217</FONT> }<a name="line.217"></a> <FONT color="green">218</FONT> <a name="line.218"></a> <FONT color="green">219</FONT> }<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> }<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> /** {@inheritDoc} */<a name="line.223"></a> <FONT color="green">224</FONT> public void setMaxIterations(int maxIterations) {<a name="line.224"></a> <FONT color="green">225</FONT> this.maxIterations = maxIterations;<a name="line.225"></a> <FONT color="green">226</FONT> }<a name="line.226"></a> <FONT color="green">227</FONT> <a name="line.227"></a> <FONT color="green">228</FONT> /** {@inheritDoc} */<a name="line.228"></a> <FONT color="green">229</FONT> public int getMaxIterations() {<a name="line.229"></a> <FONT color="green">230</FONT> return maxIterations;<a name="line.230"></a> <FONT color="green">231</FONT> }<a name="line.231"></a> <FONT color="green">232</FONT> <a name="line.232"></a> <FONT color="green">233</FONT> /** {@inheritDoc} */<a name="line.233"></a> <FONT color="green">234</FONT> public void setMaxEvaluations(int maxEvaluations) {<a name="line.234"></a> <FONT color="green">235</FONT> this.maxEvaluations = maxEvaluations;<a name="line.235"></a> <FONT color="green">236</FONT> }<a name="line.236"></a> <FONT color="green">237</FONT> <a name="line.237"></a> <FONT color="green">238</FONT> /** {@inheritDoc} */<a name="line.238"></a> <FONT color="green">239</FONT> public int getMaxEvaluations() {<a name="line.239"></a> <FONT color="green">240</FONT> return maxEvaluations;<a name="line.240"></a> <FONT color="green">241</FONT> }<a name="line.241"></a> <FONT color="green">242</FONT> <a name="line.242"></a> <FONT color="green">243</FONT> /** {@inheritDoc} */<a name="line.243"></a> <FONT color="green">244</FONT> public int getIterations() {<a name="line.244"></a> <FONT color="green">245</FONT> return iterations;<a name="line.245"></a> <FONT color="green">246</FONT> }<a name="line.246"></a> <FONT color="green">247</FONT> <a name="line.247"></a> <FONT color="green">248</FONT> /** {@inheritDoc} */<a name="line.248"></a> <FONT color="green">249</FONT> public int getEvaluations() {<a name="line.249"></a> <FONT color="green">250</FONT> return evaluations;<a name="line.250"></a> <FONT color="green">251</FONT> }<a name="line.251"></a> <FONT color="green">252</FONT> <a name="line.252"></a> <FONT color="green">253</FONT> /** {@inheritDoc} */<a name="line.253"></a> <FONT color="green">254</FONT> public void setConvergenceChecker(RealConvergenceChecker convergenceChecker) {<a name="line.254"></a> <FONT color="green">255</FONT> this.checker = convergenceChecker;<a name="line.255"></a> <FONT color="green">256</FONT> }<a name="line.256"></a> <FONT color="green">257</FONT> <a name="line.257"></a> <FONT color="green">258</FONT> /** {@inheritDoc} */<a name="line.258"></a> <FONT color="green">259</FONT> public RealConvergenceChecker getConvergenceChecker() {<a name="line.259"></a> <FONT color="green">260</FONT> return checker;<a name="line.260"></a> <FONT color="green">261</FONT> }<a name="line.261"></a> <FONT color="green">262</FONT> <a name="line.262"></a> <FONT color="green">263</FONT> /** {@inheritDoc} */<a name="line.263"></a> <FONT color="green">264</FONT> public RealPointValuePair optimize(final MultivariateRealFunction function,<a name="line.264"></a> <FONT color="green">265</FONT> final GoalType goalType,<a name="line.265"></a> <FONT color="green">266</FONT> final double[] startPoint)<a name="line.266"></a> <FONT color="green">267</FONT> throws FunctionEvaluationException, OptimizationException,<a name="line.267"></a> <FONT color="green">268</FONT> IllegalArgumentException {<a name="line.268"></a> <FONT color="green">269</FONT> <a name="line.269"></a> <FONT color="green">270</FONT> if (startConfiguration == null) {<a name="line.270"></a> <FONT color="green">271</FONT> // no initial configuration has been set up for simplex<a name="line.271"></a> <FONT color="green">272</FONT> // build a default one from a unit hypercube<a name="line.272"></a> <FONT color="green">273</FONT> final double[] unit = new double[startPoint.length];<a name="line.273"></a> <FONT color="green">274</FONT> Arrays.fill(unit, 1.0);<a name="line.274"></a> <FONT color="green">275</FONT> setStartConfiguration(unit);<a name="line.275"></a> <FONT color="green">276</FONT> }<a name="line.276"></a> <FONT color="green">277</FONT> <a name="line.277"></a> <FONT color="green">278</FONT> this.f = function;<a name="line.278"></a> <FONT color="green">279</FONT> final Comparator<RealPointValuePair> comparator =<a name="line.279"></a> <FONT color="green">280</FONT> new Comparator<RealPointValuePair>() {<a name="line.280"></a> <FONT color="green">281</FONT> public int compare(final RealPointValuePair o1,<a name="line.281"></a> <FONT color="green">282</FONT> final RealPointValuePair o2) {<a name="line.282"></a> <FONT color="green">283</FONT> final double v1 = o1.getValue();<a name="line.283"></a> <FONT color="green">284</FONT> final double v2 = o2.getValue();<a name="line.284"></a> <FONT color="green">285</FONT> return (goalType == GoalType.MINIMIZE) ?<a name="line.285"></a> <FONT color="green">286</FONT> Double.compare(v1, v2) : Double.compare(v2, v1);<a name="line.286"></a> <FONT color="green">287</FONT> }<a name="line.287"></a> <FONT color="green">288</FONT> };<a name="line.288"></a> <FONT color="green">289</FONT> <a name="line.289"></a> <FONT color="green">290</FONT> // initialize search<a name="line.290"></a> <FONT color="green">291</FONT> iterations = 0;<a name="line.291"></a> <FONT color="green">292</FONT> evaluations = 0;<a name="line.292"></a> <FONT color="green">293</FONT> buildSimplex(startPoint);<a name="line.293"></a> <FONT color="green">294</FONT> evaluateSimplex(comparator);<a name="line.294"></a> <FONT color="green">295</FONT> <a name="line.295"></a> <FONT color="green">296</FONT> RealPointValuePair[] previous = new RealPointValuePair[simplex.length];<a name="line.296"></a> <FONT color="green">297</FONT> while (true) {<a name="line.297"></a> <FONT color="green">298</FONT> <a name="line.298"></a> <FONT color="green">299</FONT> if (iterations > 0) {<a name="line.299"></a> <FONT color="green">300</FONT> boolean converged = true;<a name="line.300"></a> <FONT color="green">301</FONT> for (int i = 0; i < simplex.length; ++i) {<a name="line.301"></a> <FONT color="green">302</FONT> converged &= checker.converged(iterations, previous[i], simplex[i]);<a name="line.302"></a> <FONT color="green">303</FONT> }<a name="line.303"></a> <FONT color="green">304</FONT> if (converged) {<a name="line.304"></a> <FONT color="green">305</FONT> // we have found an optimum<a name="line.305"></a> <FONT color="green">306</FONT> return simplex[0];<a name="line.306"></a> <FONT color="green">307</FONT> }<a name="line.307"></a> <FONT color="green">308</FONT> }<a name="line.308"></a> <FONT color="green">309</FONT> <a name="line.309"></a> <FONT color="green">310</FONT> // we still need to search<a name="line.310"></a> <FONT color="green">311</FONT> System.arraycopy(simplex, 0, previous, 0, simplex.length);<a name="line.311"></a> <FONT color="green">312</FONT> iterateSimplex(comparator);<a name="line.312"></a> <FONT color="green">313</FONT> <a name="line.313"></a> <FONT color="green">314</FONT> }<a name="line.314"></a> <FONT color="green">315</FONT> <a name="line.315"></a> <FONT color="green">316</FONT> }<a name="line.316"></a> <FONT color="green">317</FONT> <a name="line.317"></a> <FONT color="green">318</FONT> /** Increment the iterations counter by 1.<a name="line.318"></a> <FONT color="green">319</FONT> * @exception OptimizationException if the maximal number<a name="line.319"></a> <FONT color="green">320</FONT> * of iterations is exceeded<a name="line.320"></a> <FONT color="green">321</FONT> */<a name="line.321"></a> <FONT color="green">322</FONT> protected void incrementIterationsCounter()<a name="line.322"></a> <FONT color="green">323</FONT> throws OptimizationException {<a name="line.323"></a> <FONT color="green">324</FONT> if (++iterations > maxIterations) {<a name="line.324"></a> <FONT color="green">325</FONT> throw new OptimizationException(new MaxIterationsExceededException(maxIterations));<a name="line.325"></a> <FONT color="green">326</FONT> }<a name="line.326"></a> <FONT color="green">327</FONT> }<a name="line.327"></a> <FONT color="green">328</FONT> <a name="line.328"></a> <FONT color="green">329</FONT> /** Compute the next simplex of the algorithm.<a name="line.329"></a> <FONT color="green">330</FONT> * @param comparator comparator to use to sort simplex vertices from best to worst<a name="line.330"></a> <FONT color="green">331</FONT> * @exception FunctionEvaluationException if the function cannot be evaluated at<a name="line.331"></a> <FONT color="green">332</FONT> * some point<a name="line.332"></a> <FONT color="green">333</FONT> * @exception OptimizationException if the algorithm fails to converge<a name="line.333"></a> <FONT color="green">334</FONT> * @exception IllegalArgumentException if the start point dimension is wrong<a name="line.334"></a> <FONT color="green">335</FONT> */<a name="line.335"></a> <FONT color="green">336</FONT> protected abstract void iterateSimplex(final Comparator<RealPointValuePair> comparator)<a name="line.336"></a> <FONT color="green">337</FONT> throws FunctionEvaluationException, OptimizationException, IllegalArgumentException;<a name="line.337"></a> <FONT color="green">338</FONT> <a name="line.338"></a> <FONT color="green">339</FONT> /** Evaluate the objective function on one point.<a name="line.339"></a> <FONT color="green">340</FONT> * <p>A side effect of this method is to count the number of<a name="line.340"></a> <FONT color="green">341</FONT> * function evaluations</p><a name="line.341"></a> <FONT color="green">342</FONT> * @param x point on which the objective function should be evaluated<a name="line.342"></a> <FONT color="green">343</FONT> * @return objective function value at the given point<a name="line.343"></a> <FONT color="green">344</FONT> * @exception FunctionEvaluationException if no value can be computed for the<a name="line.344"></a> <FONT color="green">345</FONT> * parameters or if the maximal number of evaluations is exceeded<a name="line.345"></a> <FONT color="green">346</FONT> * @exception IllegalArgumentException if the start point dimension is wrong<a name="line.346"></a> <FONT color="green">347</FONT> */<a name="line.347"></a> <FONT color="green">348</FONT> protected double evaluate(final double[] x)<a name="line.348"></a> <FONT color="green">349</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.349"></a> <FONT color="green">350</FONT> if (++evaluations > maxEvaluations) {<a name="line.350"></a> <FONT color="green">351</FONT> throw new FunctionEvaluationException(new MaxEvaluationsExceededException(maxEvaluations),<a name="line.351"></a> <FONT color="green">352</FONT> x);<a name="line.352"></a> <FONT color="green">353</FONT> }<a name="line.353"></a> <FONT color="green">354</FONT> return f.value(x);<a name="line.354"></a> <FONT color="green">355</FONT> }<a name="line.355"></a> <FONT color="green">356</FONT> <a name="line.356"></a> <FONT color="green">357</FONT> /** Build an initial simplex.<a name="line.357"></a> <FONT color="green">358</FONT> * @param startPoint the start point for optimization<a name="line.358"></a> <FONT color="green">359</FONT> * @exception IllegalArgumentException if the start point does not match<a name="line.359"></a> <FONT color="green">360</FONT> * simplex dimension<a name="line.360"></a> <FONT color="green">361</FONT> */<a name="line.361"></a> <FONT color="green">362</FONT> private void buildSimplex(final double[] startPoint)<a name="line.362"></a> <FONT color="green">363</FONT> throws IllegalArgumentException {<a name="line.363"></a> <FONT color="green">364</FONT> <a name="line.364"></a> <FONT color="green">365</FONT> final int n = startPoint.length;<a name="line.365"></a> <FONT color="green">366</FONT> if (n != startConfiguration.length) {<a name="line.366"></a> <FONT color="green">367</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.367"></a> <FONT color="green">368</FONT> DIMENSION_MISMATCH_MESSAGE, n, startConfiguration.length);<a name="line.368"></a> <FONT color="green">369</FONT> }<a name="line.369"></a> <FONT color="green">370</FONT> <a name="line.370"></a> <FONT color="green">371</FONT> // set first vertex<a name="line.371"></a> <FONT color="green">372</FONT> simplex = new RealPointValuePair[n + 1];<a name="line.372"></a> <FONT color="green">373</FONT> simplex[0] = new RealPointValuePair(startPoint, Double.NaN);<a name="line.373"></a> <FONT color="green">374</FONT> <a name="line.374"></a> <FONT color="green">375</FONT> // set remaining vertices<a name="line.375"></a> <FONT color="green">376</FONT> for (int i = 0; i < n; ++i) {<a name="line.376"></a> <FONT color="green">377</FONT> final double[] confI = startConfiguration[i];<a name="line.377"></a> <FONT color="green">378</FONT> final double[] vertexI = new double[n];<a name="line.378"></a> <FONT color="green">379</FONT> for (int k = 0; k < n; ++k) {<a name="line.379"></a> <FONT color="green">380</FONT> vertexI[k] = startPoint[k] + confI[k];<a name="line.380"></a> <FONT color="green">381</FONT> }<a name="line.381"></a> <FONT color="green">382</FONT> simplex[i + 1] = new RealPointValuePair(vertexI, Double.NaN);<a name="line.382"></a> <FONT color="green">383</FONT> }<a name="line.383"></a> <FONT color="green">384</FONT> <a name="line.384"></a> <FONT color="green">385</FONT> }<a name="line.385"></a> <FONT color="green">386</FONT> <a name="line.386"></a> <FONT color="green">387</FONT> /** Evaluate all the non-evaluated points of the simplex.<a name="line.387"></a> <FONT color="green">388</FONT> * @param comparator comparator to use to sort simplex vertices from best to worst<a name="line.388"></a> <FONT color="green">389</FONT> * @exception FunctionEvaluationException if no value can be computed for the parameters<a name="line.389"></a> <FONT color="green">390</FONT> * @exception OptimizationException if the maximal number of evaluations is exceeded<a name="line.390"></a> <FONT color="green">391</FONT> */<a name="line.391"></a> <FONT color="green">392</FONT> protected void evaluateSimplex(final Comparator<RealPointValuePair> comparator)<a name="line.392"></a> <FONT color="green">393</FONT> throws FunctionEvaluationException, OptimizationException {<a name="line.393"></a> <FONT color="green">394</FONT> <a name="line.394"></a> <FONT color="green">395</FONT> // evaluate the objective function at all non-evaluated simplex points<a name="line.395"></a> <FONT color="green">396</FONT> for (int i = 0; i < simplex.length; ++i) {<a name="line.396"></a> <FONT color="green">397</FONT> final RealPointValuePair vertex = simplex[i];<a name="line.397"></a> <FONT color="green">398</FONT> final double[] point = vertex.getPointRef();<a name="line.398"></a> <FONT color="green">399</FONT> if (Double.isNaN(vertex.getValue())) {<a name="line.399"></a> <FONT color="green">400</FONT> simplex[i] = new RealPointValuePair(point, evaluate(point), false);<a name="line.400"></a> <FONT color="green">401</FONT> }<a name="line.401"></a> <FONT color="green">402</FONT> }<a name="line.402"></a> <FONT color="green">403</FONT> <a name="line.403"></a> <FONT color="green">404</FONT> // sort the simplex from best to worst<a name="line.404"></a> <FONT color="green">405</FONT> Arrays.sort(simplex, comparator);<a name="line.405"></a> <FONT color="green">406</FONT> <a name="line.406"></a> <FONT color="green">407</FONT> }<a name="line.407"></a> <FONT color="green">408</FONT> <a name="line.408"></a> <FONT color="green">409</FONT> /** Replace the worst point of the simplex by a new point.<a name="line.409"></a> <FONT color="green">410</FONT> * @param pointValuePair point to insert<a name="line.410"></a> <FONT color="green">411</FONT> * @param comparator comparator to use to sort simplex vertices from best to worst<a name="line.411"></a> <FONT color="green">412</FONT> */<a name="line.412"></a> <FONT color="green">413</FONT> protected void replaceWorstPoint(RealPointValuePair pointValuePair,<a name="line.413"></a> <FONT color="green">414</FONT> final Comparator<RealPointValuePair> comparator) {<a name="line.414"></a> <FONT color="green">415</FONT> int n = simplex.length - 1;<a name="line.415"></a> <FONT color="green">416</FONT> for (int i = 0; i < n; ++i) {<a name="line.416"></a> <FONT color="green">417</FONT> if (comparator.compare(simplex[i], pointValuePair) > 0) {<a name="line.417"></a> <FONT color="green">418</FONT> RealPointValuePair tmp = simplex[i];<a name="line.418"></a> <FONT color="green">419</FONT> simplex[i] = pointValuePair;<a name="line.419"></a> <FONT color="green">420</FONT> pointValuePair = tmp;<a name="line.420"></a> <FONT color="green">421</FONT> }<a name="line.421"></a> <FONT color="green">422</FONT> }<a name="line.422"></a> <FONT color="green">423</FONT> simplex[n] = pointValuePair;<a name="line.423"></a> <FONT color="green">424</FONT> }<a name="line.424"></a> <FONT color="green">425</FONT> <a name="line.425"></a> <FONT color="green">426</FONT> }<a name="line.426"></a> </PRE> </BODY> </HTML>