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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.linear;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.util.ArrayList;<a name="line.20"></a> <FONT color="green">021</FONT> import java.util.List;<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.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> import org.apache.commons.math.util.MathUtils;<a name="line.25"></a> <FONT color="green">026</FONT> <a name="line.26"></a> <FONT color="green">027</FONT> <a name="line.27"></a> <FONT color="green">028</FONT> /**<a name="line.28"></a> <FONT color="green">029</FONT> * Solves a linear problem using the Two-Phase Simplex Method.<a name="line.29"></a> <FONT color="green">030</FONT> * @version $Revision: 812831 $ $Date: 2009-09-09 04:48:03 -0400 (Wed, 09 Sep 2009) $<a name="line.30"></a> <FONT color="green">031</FONT> * @since 2.0<a name="line.31"></a> <FONT color="green">032</FONT> */<a name="line.32"></a> <FONT color="green">033</FONT> public class SimplexSolver extends AbstractLinearOptimizer {<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /** Default amount of error to accept in floating point comparisons. */<a name="line.35"></a> <FONT color="green">036</FONT> private static final double DEFAULT_EPSILON = 1.0e-6;<a name="line.36"></a> <FONT color="green">037</FONT> <a name="line.37"></a> <FONT color="green">038</FONT> /** Amount of error to accept in floating point comparisons. */<a name="line.38"></a> <FONT color="green">039</FONT> protected final double epsilon;<a name="line.39"></a> <FONT color="green">040</FONT> <a name="line.40"></a> <FONT color="green">041</FONT> /**<a name="line.41"></a> <FONT color="green">042</FONT> * Build a simplex solver with default settings.<a name="line.42"></a> <FONT color="green">043</FONT> */<a name="line.43"></a> <FONT color="green">044</FONT> public SimplexSolver() {<a name="line.44"></a> <FONT color="green">045</FONT> this(DEFAULT_EPSILON);<a name="line.45"></a> <FONT color="green">046</FONT> }<a name="line.46"></a> <FONT color="green">047</FONT> <a name="line.47"></a> <FONT color="green">048</FONT> /**<a name="line.48"></a> <FONT color="green">049</FONT> * Build a simplex solver with a specified accepted amount of error<a name="line.49"></a> <FONT color="green">050</FONT> * @param epsilon the amount of error to accept in floating point comparisons<a name="line.50"></a> <FONT color="green">051</FONT> */<a name="line.51"></a> <FONT color="green">052</FONT> public SimplexSolver(final double epsilon) {<a name="line.52"></a> <FONT color="green">053</FONT> this.epsilon = epsilon;<a name="line.53"></a> <FONT color="green">054</FONT> }<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /**<a name="line.56"></a> <FONT color="green">057</FONT> * Returns the column with the most negative coefficient in the objective function row.<a name="line.57"></a> <FONT color="green">058</FONT> * @param tableau simple tableau for the problem<a name="line.58"></a> <FONT color="green">059</FONT> * @return column with the most negative coefficient<a name="line.59"></a> <FONT color="green">060</FONT> */<a name="line.60"></a> <FONT color="green">061</FONT> private Integer getPivotColumn(SimplexTableau tableau) {<a name="line.61"></a> <FONT color="green">062</FONT> double minValue = 0;<a name="line.62"></a> <FONT color="green">063</FONT> Integer minPos = null;<a name="line.63"></a> <FONT color="green">064</FONT> for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getWidth() - 1; i++) {<a name="line.64"></a> <FONT color="green">065</FONT> if (MathUtils.compareTo(tableau.getEntry(0, i), minValue, epsilon) < 0) {<a name="line.65"></a> <FONT color="green">066</FONT> minValue = tableau.getEntry(0, i);<a name="line.66"></a> <FONT color="green">067</FONT> minPos = i;<a name="line.67"></a> <FONT color="green">068</FONT> }<a name="line.68"></a> <FONT color="green">069</FONT> }<a name="line.69"></a> <FONT color="green">070</FONT> return minPos;<a name="line.70"></a> <FONT color="green">071</FONT> }<a name="line.71"></a> <FONT color="green">072</FONT> <a name="line.72"></a> <FONT color="green">073</FONT> /**<a name="line.73"></a> <FONT color="green">074</FONT> * Returns the row with the minimum ratio as given by the minimum ratio test (MRT).<a name="line.74"></a> <FONT color="green">075</FONT> * @param tableau simple tableau for the problem<a name="line.75"></a> <FONT color="green">076</FONT> * @param col the column to test the ratio of. See {@link #getPivotColumn(SimplexTableau)}<a name="line.76"></a> <FONT color="green">077</FONT> * @return row with the minimum ratio<a name="line.77"></a> <FONT color="green">078</FONT> */<a name="line.78"></a> <FONT color="green">079</FONT> private Integer getPivotRow(SimplexTableau tableau, final int col) {<a name="line.79"></a> <FONT color="green">080</FONT> // create a list of all the rows that tie for the lowest score in the minimum ratio test<a name="line.80"></a> <FONT color="green">081</FONT> List<Integer> minRatioPositions = new ArrayList<Integer>();<a name="line.81"></a> <FONT color="green">082</FONT> double minRatio = Double.MAX_VALUE;<a name="line.82"></a> <FONT color="green">083</FONT> for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getHeight(); i++) {<a name="line.83"></a> <FONT color="green">084</FONT> final double rhs = tableau.getEntry(i, tableau.getWidth() - 1);<a name="line.84"></a> <FONT color="green">085</FONT> final double entry = tableau.getEntry(i, col);<a name="line.85"></a> <FONT color="green">086</FONT> if (MathUtils.compareTo(entry, 0, epsilon) > 0) {<a name="line.86"></a> <FONT color="green">087</FONT> final double ratio = rhs / entry;<a name="line.87"></a> <FONT color="green">088</FONT> if (MathUtils.equals(ratio, minRatio, epsilon)) {<a name="line.88"></a> <FONT color="green">089</FONT> minRatioPositions.add(i);<a name="line.89"></a> <FONT color="green">090</FONT> } else if (ratio < minRatio) {<a name="line.90"></a> <FONT color="green">091</FONT> minRatio = ratio;<a name="line.91"></a> <FONT color="green">092</FONT> minRatioPositions = new ArrayList<Integer>();<a name="line.92"></a> <FONT color="green">093</FONT> minRatioPositions.add(i);<a name="line.93"></a> <FONT color="green">094</FONT> }<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> <a name="line.97"></a> <FONT color="green">098</FONT> if (minRatioPositions.size() == 0) {<a name="line.98"></a> <FONT color="green">099</FONT> return null;<a name="line.99"></a> <FONT color="green">100</FONT> } else if (minRatioPositions.size() > 1) {<a name="line.100"></a> <FONT color="green">101</FONT> // there's a degeneracy as indicated by a tie in the minimum ratio test<a name="line.101"></a> <FONT color="green">102</FONT> // check if there's an artificial variable that can be forced out of the basis<a name="line.102"></a> <FONT color="green">103</FONT> for (Integer row : minRatioPositions) {<a name="line.103"></a> <FONT color="green">104</FONT> for (int i = 0; i < tableau.getNumArtificialVariables(); i++) {<a name="line.104"></a> <FONT color="green">105</FONT> int column = i + tableau.getArtificialVariableOffset();<a name="line.105"></a> <FONT color="green">106</FONT> if (MathUtils.equals(tableau.getEntry(row, column), 1, epsilon) &&<a name="line.106"></a> <FONT color="green">107</FONT> row.equals(tableau.getBasicRow(column))) {<a name="line.107"></a> <FONT color="green">108</FONT> return row;<a name="line.108"></a> <FONT color="green">109</FONT> }<a name="line.109"></a> <FONT color="green">110</FONT> }<a name="line.110"></a> <FONT color="green">111</FONT> }<a name="line.111"></a> <FONT color="green">112</FONT> }<a name="line.112"></a> <FONT color="green">113</FONT> return minRatioPositions.get(0);<a name="line.113"></a> <FONT color="green">114</FONT> }<a name="line.114"></a> <FONT color="green">115</FONT> <a name="line.115"></a> <FONT color="green">116</FONT> /**<a name="line.116"></a> <FONT color="green">117</FONT> * Runs one iteration of the Simplex method on the given model.<a name="line.117"></a> <FONT color="green">118</FONT> * @param tableau simple tableau for the problem<a name="line.118"></a> <FONT color="green">119</FONT> * @throws OptimizationException if the maximal iteration count has been<a name="line.119"></a> <FONT color="green">120</FONT> * exceeded or if the model is found not to have a bounded solution<a name="line.120"></a> <FONT color="green">121</FONT> */<a name="line.121"></a> <FONT color="green">122</FONT> protected void doIteration(final SimplexTableau tableau)<a name="line.122"></a> <FONT color="green">123</FONT> throws OptimizationException {<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> incrementIterationsCounter();<a name="line.125"></a> <FONT color="green">126</FONT> <a name="line.126"></a> <FONT color="green">127</FONT> Integer pivotCol = getPivotColumn(tableau);<a name="line.127"></a> <FONT color="green">128</FONT> Integer pivotRow = getPivotRow(tableau, pivotCol);<a name="line.128"></a> <FONT color="green">129</FONT> if (pivotRow == null) {<a name="line.129"></a> <FONT color="green">130</FONT> throw new UnboundedSolutionException();<a name="line.130"></a> <FONT color="green">131</FONT> }<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> // set the pivot element to 1<a name="line.133"></a> <FONT color="green">134</FONT> double pivotVal = tableau.getEntry(pivotRow, pivotCol);<a name="line.134"></a> <FONT color="green">135</FONT> tableau.divideRow(pivotRow, pivotVal);<a name="line.135"></a> <FONT color="green">136</FONT> <a name="line.136"></a> <FONT color="green">137</FONT> // set the rest of the pivot column to 0<a name="line.137"></a> <FONT color="green">138</FONT> for (int i = 0; i < tableau.getHeight(); i++) {<a name="line.138"></a> <FONT color="green">139</FONT> if (i != pivotRow) {<a name="line.139"></a> <FONT color="green">140</FONT> double multiplier = tableau.getEntry(i, pivotCol);<a name="line.140"></a> <FONT color="green">141</FONT> tableau.subtractRow(i, pivotRow, multiplier);<a name="line.141"></a> <FONT color="green">142</FONT> }<a name="line.142"></a> <FONT color="green">143</FONT> }<a name="line.143"></a> <FONT color="green">144</FONT> }<a name="line.144"></a> <FONT color="green">145</FONT> <a name="line.145"></a> <FONT color="green">146</FONT> /**<a name="line.146"></a> <FONT color="green">147</FONT> * Solves Phase 1 of the Simplex method.<a name="line.147"></a> <FONT color="green">148</FONT> * @param tableau simple tableau for the problem<a name="line.148"></a> <FONT color="green">149</FONT> * @exception OptimizationException if the maximal number of iterations is<a name="line.149"></a> <FONT color="green">150</FONT> * exceeded, or if the problem is found not to have a bounded solution, or<a name="line.150"></a> <FONT color="green">151</FONT> * if there is no feasible solution<a name="line.151"></a> <FONT color="green">152</FONT> */<a name="line.152"></a> <FONT color="green">153</FONT> protected void solvePhase1(final SimplexTableau tableau) throws OptimizationException {<a name="line.153"></a> <FONT color="green">154</FONT> <a name="line.154"></a> <FONT color="green">155</FONT> // make sure we're in Phase 1<a name="line.155"></a> <FONT color="green">156</FONT> if (tableau.getNumArtificialVariables() == 0) {<a name="line.156"></a> <FONT color="green">157</FONT> return;<a name="line.157"></a> <FONT color="green">158</FONT> }<a name="line.158"></a> <FONT color="green">159</FONT> <a name="line.159"></a> <FONT color="green">160</FONT> while (!tableau.isOptimal()) {<a name="line.160"></a> <FONT color="green">161</FONT> doIteration(tableau);<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> // if W is not zero then we have no feasible solution<a name="line.164"></a> <FONT color="green">165</FONT> if (!MathUtils.equals(tableau.getEntry(0, tableau.getRhsOffset()), 0, epsilon)) {<a name="line.165"></a> <FONT color="green">166</FONT> throw new NoFeasibleSolutionException();<a name="line.166"></a> <FONT color="green">167</FONT> }<a name="line.167"></a> <FONT color="green">168</FONT> }<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> /** {@inheritDoc} */<a name="line.170"></a> <FONT color="green">171</FONT> @Override<a name="line.171"></a> <FONT color="green">172</FONT> public RealPointValuePair doOptimize() throws OptimizationException {<a name="line.172"></a> <FONT color="green">173</FONT> final SimplexTableau tableau =<a name="line.173"></a> <FONT color="green">174</FONT> new SimplexTableau(function, linearConstraints, goal, nonNegative, epsilon);<a name="line.174"></a> <FONT color="green">175</FONT> <a name="line.175"></a> <FONT color="green">176</FONT> solvePhase1(tableau);<a name="line.176"></a> <FONT color="green">177</FONT> tableau.dropPhase1Objective();<a name="line.177"></a> <FONT color="green">178</FONT> <a name="line.178"></a> <FONT color="green">179</FONT> while (!tableau.isOptimal()) {<a name="line.179"></a> <FONT color="green">180</FONT> doIteration(tableau);<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> return tableau.getSolution();<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> <a name="line.184"></a> <FONT color="green">185</FONT> }<a name="line.185"></a> </PRE> </BODY> </HTML>