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 */ 017package org.apache.commons.math3.optim.nonlinear.scalar; 018 019import org.apache.commons.math3.analysis.MultivariateFunction; 020import org.apache.commons.math3.exception.DimensionMismatchException; 021import org.apache.commons.math3.exception.NumberIsTooSmallException; 022import org.apache.commons.math3.util.FastMath; 023import 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 * @since 3.0 066 */ 067public class MultivariateFunctionPenaltyAdapter 068 implements MultivariateFunction { 069 /** Underlying bounded function. */ 070 private final MultivariateFunction bounded; 071 /** Lower bounds. */ 072 private final double[] lower; 073 /** Upper bounds. */ 074 private final double[] upper; 075 /** Penalty offset. */ 076 private final double offset; 077 /** Penalty scales. */ 078 private final double[] scale; 079 080 /** 081 * Simple constructor. 082 * <p> 083 * When the optimizer provided points are out of range, the value of the 084 * penalty function will be used instead of the value of the underlying 085 * function. In order for this penalty to be effective in rejecting this 086 * point during the optimization process, the penalty function value should 087 * be defined with care. This value is computed as: 088 * <pre> 089 * penalty(point) = offset + ∑<sub>i</sub>[scale[i] * √|point[i]-boundary[i]|] 090 * </pre> 091 * where indices i correspond to all the components that violates their boundaries. 092 * </p> 093 * <p> 094 * So when attempting a function minimization, offset should be larger than 095 * the maximum expected value of the underlying function and scale components 096 * should all be positive. When attempting a function maximization, offset 097 * should be lesser than the minimum expected value of the underlying function 098 * and scale components should all be negative. 099 * minimization, and lesser than the minimum expected value of the underlying 100 * function when attempting maximization. 101 * </p> 102 * <p> 103 * These choices for the penalty function have two properties. First, all out 104 * of range points will return a function value that is worse than the value 105 * returned by any in range point. Second, the penalty is worse for large 106 * boundaries violation than for small violations, so the optimizer has an hint 107 * about the direction in which it should search for acceptable points. 108 * </p> 109 * @param bounded bounded function 110 * @param lower lower bounds for each element of the input parameters array 111 * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for 112 * unbounded values) 113 * @param upper upper bounds for each element of the input parameters array 114 * (some elements may be set to {@code Double.POSITIVE_INFINITY} for 115 * unbounded values) 116 * @param offset base offset of the penalty function 117 * @param scale scale of the penalty function 118 * @exception DimensionMismatchException if lower bounds, upper bounds and 119 * scales are not consistent, either according to dimension or to bounadary 120 * values 121 */ 122 public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded, 123 final double[] lower, final double[] upper, 124 final double offset, final double[] scale) { 125 126 // safety checks 127 MathUtils.checkNotNull(lower); 128 MathUtils.checkNotNull(upper); 129 MathUtils.checkNotNull(scale); 130 if (lower.length != upper.length) { 131 throw new DimensionMismatchException(lower.length, upper.length); 132 } 133 if (lower.length != scale.length) { 134 throw new DimensionMismatchException(lower.length, scale.length); 135 } 136 for (int i = 0; i < lower.length; ++i) { 137 // note the following test is written in such a way it also fails for NaN 138 if (!(upper[i] >= lower[i])) { 139 throw new NumberIsTooSmallException(upper[i], lower[i], true); 140 } 141 } 142 143 this.bounded = bounded; 144 this.lower = lower.clone(); 145 this.upper = upper.clone(); 146 this.offset = offset; 147 this.scale = scale.clone(); 148 } 149 150 /** 151 * Computes the underlying function value from an unbounded point. 152 * <p> 153 * This method simply returns the value of the underlying function 154 * if the unbounded point already fulfills the bounds, and compute 155 * a replacement value using the offset and scale if bounds are 156 * violated, without calling the function at all. 157 * </p> 158 * @param point unbounded point 159 * @return either underlying function value or penalty function value 160 */ 161 public double value(double[] point) { 162 163 for (int i = 0; i < scale.length; ++i) { 164 if ((point[i] < lower[i]) || (point[i] > upper[i])) { 165 // bound violation starting at this component 166 double sum = 0; 167 for (int j = i; j < scale.length; ++j) { 168 final double overshoot; 169 if (point[j] < lower[j]) { 170 overshoot = scale[j] * (lower[j] - point[j]); 171 } else if (point[j] > upper[j]) { 172 overshoot = scale[j] * (point[j] - upper[j]); 173 } else { 174 overshoot = 0; 175 } 176 sum += FastMath.sqrt(overshoot); 177 } 178 return offset + sum; 179 } 180 } 181 182 // all boundaries are fulfilled, we are in the expected 183 // domain of the underlying function 184 return bounded.value(point); 185 } 186}