1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.optimization.direct; 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport java.util.Comparator; 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.FunctionEvaluationException; 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.optimization.OptimizationException; 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.optimization.RealConvergenceChecker; 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.optimization.RealPointValuePair; 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * This class implements the multi-directional direct search method. 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @see NelderMead 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @since 1.2 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class MultiDirectional extends DirectSearchOptimizer { 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Expansion coefficient. */ 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final double khi; 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Contraction coefficient. */ 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private final double gamma; 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Build a multi-directional optimizer with default coefficients. 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p>The default values are 2.0 for khi and 0.5 for gamma.</p> 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public MultiDirectional() { 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.khi = 2.0; 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.gamma = 0.5; 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Build a multi-directional optimizer with specified coefficients. 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param khi expansion coefficient 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param gamma contraction coefficient 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public MultiDirectional(final double khi, final double gamma) { 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.khi = khi; 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond this.gamma = gamma; 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected void iterateSimplex(final Comparator<RealPointValuePair> comparator) 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws FunctionEvaluationException, OptimizationException, IllegalArgumentException { 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealConvergenceChecker checker = getConvergenceChecker(); 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond while (true) { 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond incrementIterationsCounter(); 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // save the original vertex 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealPointValuePair[] original = simplex; 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealPointValuePair best = original[0]; 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // perform a reflection step 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealPointValuePair reflected = evaluateNewSimplex(original, 1.0, comparator); 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (comparator.compare(reflected, best) < 0) { 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // compute the expanded simplex 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealPointValuePair[] reflectedSimplex = simplex; 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealPointValuePair expanded = evaluateNewSimplex(original, khi, comparator); 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (comparator.compare(reflected, expanded) <= 0) { 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // accept the reflected simplex 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond simplex = reflectedSimplex; 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return; 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // compute the contracted simplex 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final RealPointValuePair contracted = evaluateNewSimplex(original, gamma, comparator); 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (comparator.compare(contracted, best) < 0) { 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // accept the contracted simplex 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return; 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // check convergence 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int iter = getIterations(); 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond boolean converged = true; 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 0; i < simplex.length; ++i) { 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond converged &= checker.converged(iter, original[i], simplex[i]); 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (converged) { 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return; 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Compute and evaluate a new simplex. 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param original original simplex (to be preserved) 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param coeff linear coefficient 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param comparator comparator to use to sort simplex vertices from best to poorest 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @return best point in the transformed simplex 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @exception FunctionEvaluationException if the function cannot be evaluated at some point 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @exception OptimizationException if the maximal number of evaluations is exceeded 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private RealPointValuePair evaluateNewSimplex(final RealPointValuePair[] original, 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double coeff, 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final Comparator<RealPointValuePair> comparator) 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws FunctionEvaluationException, OptimizationException { 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] xSmallest = original[0].getPointRef(); 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final int n = xSmallest.length; 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // create the linearly transformed simplex 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond simplex = new RealPointValuePair[n + 1]; 128dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond simplex[0] = original[0]; 129dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 1; i <= n; ++i) { 130dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] xOriginal = original[i].getPointRef(); 131dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double[] xTransformed = new double[n]; 132dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int j = 0; j < n; ++j) { 133dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond xTransformed[j] = xSmallest[j] + coeff * (xSmallest[j] - xOriginal[j]); 134dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 135dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond simplex[i] = new RealPointValuePair(xTransformed, Double.NaN, false); 136dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 137dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 138dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // evaluate it 139dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond evaluateSimplex(comparator); 140dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return simplex[0]; 141dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 142dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 143dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 144dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 145