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 018package org.apache.commons.math3.optimization.direct; 019 020import org.apache.commons.math3.analysis.MultivariateFunction; 021import org.apache.commons.math3.exception.DimensionMismatchException; 022import org.apache.commons.math3.exception.NumberIsTooSmallException; 023import org.apache.commons.math3.util.FastMath; 024import org.apache.commons.math3.util.MathUtils; 025 026/** 027 * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded 028 * domain using a penalty function.</p> 029 * 030 * <p> 031 * This adapter can be used to wrap functions subject to simple bounds on 032 * parameters so they can be used by optimizers that do <em>not</em> directly 033 * support simple bounds. 034 * </p> 035 * <p> 036 * The principle is that the user function that will be wrapped will see its 037 * parameters bounded as required, i.e when its {@code value} method is called 038 * with argument array {@code point}, the elements array will fulfill requirement 039 * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components 040 * may be unbounded or bounded only on one side if the corresponding bound is 041 * set to an infinite value. The optimizer will not manage the user function by 042 * itself, but it will handle this adapter and it is this adapter that will take 043 * care the bounds are fulfilled. The adapter {@link #value(double[])} method will 044 * be called by the optimizer with unbound parameters, and the adapter will check 045 * if the parameters is within range or not. If it is in range, then the underlying 046 * user function will be called, and if it is not the value of a penalty function 047 * will be returned instead. 048 * </p> 049 * <p> 050 * This adapter is only a poor man solution to simple bounds optimization constraints 051 * that can be used with simple optimizers like {@link SimplexOptimizer} with {@link 052 * NelderMeadSimplex} or {@link MultiDirectionalSimplex}. A better solution is to use 053 * an optimizer that directly supports simple bounds like {@link CMAESOptimizer} or 054 * {@link BOBYQAOptimizer}. One caveat of this poor man solution is that if start point 055 * or start simplex is completely outside of the allowed range, only the penalty function 056 * is used, and the optimizer may converge without ever entering the range. 057 * </p> 058 * 059 * @see MultivariateFunctionMappingAdapter 060 * 061 * @deprecated As of 3.1 (to be removed in 4.0). 062 * @since 3.0 063 */ 064 065@Deprecated 066public class MultivariateFunctionPenaltyAdapter implements MultivariateFunction { 067 068 /** Underlying bounded function. */ 069 private final MultivariateFunction bounded; 070 071 /** Lower bounds. */ 072 private final double[] lower; 073 074 /** Upper bounds. */ 075 private final double[] upper; 076 077 /** Penalty offset. */ 078 private final double offset; 079 080 /** Penalty scales. */ 081 private final double[] scale; 082 083 /** Simple constructor. 084 * <p> 085 * When the optimizer provided points are out of range, the value of the 086 * penalty function will be used instead of the value of the underlying 087 * function. In order for this penalty to be effective in rejecting this 088 * point during the optimization process, the penalty function value should 089 * be defined with care. This value is computed as: 090 * <pre> 091 * penalty(point) = offset + ∑<sub>i</sub>[scale[i] * √|point[i]-boundary[i]|] 092 * </pre> 093 * where indices i correspond to all the components that violates their boundaries. 094 * </p> 095 * <p> 096 * So when attempting a function minimization, offset should be larger than 097 * the maximum expected value of the underlying function and scale components 098 * should all be positive. When attempting a function maximization, offset 099 * should be lesser than the minimum expected value of the underlying function 100 * and scale components should all be negative. 101 * minimization, and lesser than the minimum expected value of the underlying 102 * function when attempting maximization. 103 * </p> 104 * <p> 105 * These choices for the penalty function have two properties. First, all out 106 * of range points will return a function value that is worse than the value 107 * returned by any in range point. Second, the penalty is worse for large 108 * boundaries violation than for small violations, so the optimizer has an hint 109 * about the direction in which it should search for acceptable points. 110 * </p> 111 * @param bounded bounded function 112 * @param lower lower bounds for each element of the input parameters array 113 * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for 114 * unbounded values) 115 * @param upper upper bounds for each element of the input parameters array 116 * (some elements may be set to {@code Double.POSITIVE_INFINITY} for 117 * unbounded values) 118 * @param offset base offset of the penalty function 119 * @param scale scale of the penalty function 120 * @exception DimensionMismatchException if lower bounds, upper bounds and 121 * scales are not consistent, either according to dimension or to bounadary 122 * values 123 */ 124 public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded, 125 final double[] lower, final double[] upper, 126 final double offset, final double[] scale) { 127 128 // safety checks 129 MathUtils.checkNotNull(lower); 130 MathUtils.checkNotNull(upper); 131 MathUtils.checkNotNull(scale); 132 if (lower.length != upper.length) { 133 throw new DimensionMismatchException(lower.length, upper.length); 134 } 135 if (lower.length != scale.length) { 136 throw new DimensionMismatchException(lower.length, scale.length); 137 } 138 for (int i = 0; i < lower.length; ++i) { 139 // note the following test is written in such a way it also fails for NaN 140 if (!(upper[i] >= lower[i])) { 141 throw new NumberIsTooSmallException(upper[i], lower[i], true); 142 } 143 } 144 145 this.bounded = bounded; 146 this.lower = lower.clone(); 147 this.upper = upper.clone(); 148 this.offset = offset; 149 this.scale = scale.clone(); 150 151 } 152 153 /** Compute the underlying function value from an unbounded point. 154 * <p> 155 * This method simply returns the value of the underlying function 156 * if the unbounded point already fulfills the bounds, and compute 157 * a replacement value using the offset and scale if bounds are 158 * violated, without calling the function at all. 159 * </p> 160 * @param point unbounded point 161 * @return either underlying function value or penalty function value 162 */ 163 public double value(double[] point) { 164 165 for (int i = 0; i < scale.length; ++i) { 166 if ((point[i] < lower[i]) || (point[i] > upper[i])) { 167 // bound violation starting at this component 168 double sum = 0; 169 for (int j = i; j < scale.length; ++j) { 170 final double overshoot; 171 if (point[j] < lower[j]) { 172 overshoot = scale[j] * (lower[j] - point[j]); 173 } else if (point[j] > upper[j]) { 174 overshoot = scale[j] * (point[j] - upper[j]); 175 } else { 176 overshoot = 0; 177 } 178 sum += FastMath.sqrt(overshoot); 179 } 180 return offset + sum; 181 } 182 } 183 184 // all boundaries are fulfilled, we are in the expected 185 // domain of the underlying function 186 return bounded.value(point); 187 188 } 189 190}