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 package org.apache.commons.math3.optim.nonlinear.scalar; 018 019 import org.apache.commons.math3.analysis.MultivariateFunction; 020 import org.apache.commons.math3.exception.DimensionMismatchException; 021 import org.apache.commons.math3.exception.NumberIsTooSmallException; 022 import org.apache.commons.math3.util.FastMath; 023 import org.apache.commons.math3.util.MathUtils; 024 025 /** 026 * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded 027 * domain using a penalty function.</p> 028 * 029 * <p> 030 * This adapter can be used to wrap functions subject to simple bounds on 031 * parameters so they can be used by optimizers that do <em>not</em> directly 032 * support simple bounds. 033 * </p> 034 * <p> 035 * The principle is that the user function that will be wrapped will see its 036 * parameters bounded as required, i.e when its {@code value} method is called 037 * with argument array {@code point}, the elements array will fulfill requirement 038 * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components 039 * may be unbounded or bounded only on one side if the corresponding bound is 040 * set to an infinite value. The optimizer will not manage the user function by 041 * itself, but it will handle this adapter and it is this adapter that will take 042 * care the bounds are fulfilled. The adapter {@link #value(double[])} method will 043 * be called by the optimizer with unbound parameters, and the adapter will check 044 * if the parameters is within range or not. If it is in range, then the underlying 045 * user function will be called, and if it is not the value of a penalty function 046 * will be returned instead. 047 * </p> 048 * <p> 049 * This adapter is only a poor-man's solution to simple bounds optimization 050 * constraints that can be used with simple optimizers like 051 * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer 052 * SimplexOptimizer}. 053 * A better solution is to use an optimizer that directly supports simple bounds like 054 * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer 055 * CMAESOptimizer} or 056 * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer 057 * BOBYQAOptimizer}. 058 * One caveat of this poor-man's solution is that if start point or start simplex 059 * is completely outside of the allowed range, only the penalty function is used, 060 * and the optimizer may converge without ever entering the range. 061 * </p> 062 * 063 * @see MultivariateFunctionMappingAdapter 064 * 065 * @version $Id: MultivariateFunctionPenaltyAdapter.java 1416643 2012-12-03 19:37:14Z tn $ 066 * @since 3.0 067 */ 068 public class MultivariateFunctionPenaltyAdapter 069 implements MultivariateFunction { 070 /** Underlying bounded function. */ 071 private final MultivariateFunction bounded; 072 /** Lower bounds. */ 073 private final double[] lower; 074 /** Upper bounds. */ 075 private final double[] upper; 076 /** Penalty offset. */ 077 private final double offset; 078 /** Penalty scales. */ 079 private final double[] scale; 080 081 /** 082 * Simple constructor. 083 * <p> 084 * When the optimizer provided points are out of range, the value of the 085 * penalty function will be used instead of the value of the underlying 086 * function. In order for this penalty to be effective in rejecting this 087 * point during the optimization process, the penalty function value should 088 * be defined with care. This value is computed as: 089 * <pre> 090 * penalty(point) = offset + ∑<sub>i</sub>[scale[i] * √|point[i]-boundary[i]|] 091 * </pre> 092 * where indices i correspond to all the components that violates their boundaries. 093 * </p> 094 * <p> 095 * So when attempting a function minimization, offset should be larger than 096 * the maximum expected value of the underlying function and scale components 097 * should all be positive. When attempting a function maximization, offset 098 * should be lesser than the minimum expected value of the underlying function 099 * and scale components should all be negative. 100 * minimization, and lesser than the minimum expected value of the underlying 101 * function when attempting maximization. 102 * </p> 103 * <p> 104 * These choices for the penalty function have two properties. First, all out 105 * of range points will return a function value that is worse than the value 106 * returned by any in range point. Second, the penalty is worse for large 107 * boundaries violation than for small violations, so the optimizer has an hint 108 * about the direction in which it should search for acceptable points. 109 * </p> 110 * @param bounded bounded function 111 * @param lower lower bounds for each element of the input parameters array 112 * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for 113 * unbounded values) 114 * @param upper upper bounds for each element of the input parameters array 115 * (some elements may be set to {@code Double.POSITIVE_INFINITY} for 116 * unbounded values) 117 * @param offset base offset of the penalty function 118 * @param scale scale of the penalty function 119 * @exception DimensionMismatchException if lower bounds, upper bounds and 120 * scales are not consistent, either according to dimension or to bounadary 121 * values 122 */ 123 public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded, 124 final double[] lower, final double[] upper, 125 final double offset, final double[] scale) { 126 127 // safety checks 128 MathUtils.checkNotNull(lower); 129 MathUtils.checkNotNull(upper); 130 MathUtils.checkNotNull(scale); 131 if (lower.length != upper.length) { 132 throw new DimensionMismatchException(lower.length, upper.length); 133 } 134 if (lower.length != scale.length) { 135 throw new DimensionMismatchException(lower.length, scale.length); 136 } 137 for (int i = 0; i < lower.length; ++i) { 138 // note the following test is written in such a way it also fails for NaN 139 if (!(upper[i] >= lower[i])) { 140 throw new NumberIsTooSmallException(upper[i], lower[i], true); 141 } 142 } 143 144 this.bounded = bounded; 145 this.lower = lower.clone(); 146 this.upper = upper.clone(); 147 this.offset = offset; 148 this.scale = scale.clone(); 149 } 150 151 /** 152 * Computes the underlying function value from an unbounded point. 153 * <p> 154 * This method simply returns the value of the underlying function 155 * if the unbounded point already fulfills the bounds, and compute 156 * a replacement value using the offset and scale if bounds are 157 * violated, without calling the function at all. 158 * </p> 159 * @param point unbounded point 160 * @return either underlying function value or penalty function value 161 */ 162 public double value(double[] point) { 163 164 for (int i = 0; i < scale.length; ++i) { 165 if ((point[i] < lower[i]) || (point[i] > upper[i])) { 166 // bound violation starting at this component 167 double sum = 0; 168 for (int j = i; j < scale.length; ++j) { 169 final double overshoot; 170 if (point[j] < lower[j]) { 171 overshoot = scale[j] * (lower[j] - point[j]); 172 } else if (point[j] > upper[j]) { 173 overshoot = scale[j] * (point[j] - upper[j]); 174 } else { 175 overshoot = 0; 176 } 177 sum += FastMath.sqrt(overshoot); 178 } 179 return offset + sum; 180 } 181 } 182 183 // all boundaries are fulfilled, we are in the expected 184 // domain of the underlying function 185 return bounded.value(point); 186 } 187 }