1/*2* Licensed to the Apache Software Foundation (ASF) under one or more3* contributor license agreements. See the NOTICE file distributed with4* this work for additional information regarding copyright ownership.5* The ASF licenses this file to You under the Apache License, Version 2.06* (the "License"); you may not use this file except in compliance with7* the License. You may obtain a copy of the License at8*9* http://www.apache.org/licenses/LICENSE-2.010*11* Unless required by applicable law or agreed to in writing, software12* distributed under the License is distributed on an "AS IS" BASIS,13* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.14* See the License for the specific language governing permissions and15* limitations under the License.16*/17 18packageorg.apache.commons.math3.optimization.direct; 19 20importorg.apache.commons.math3.analysis.MultivariateFunction; 21importorg.apache.commons.math3.exception.DimensionMismatchException; 22importorg.apache.commons.math3.exception.NumberIsTooSmallException; 23importorg.apache.commons.math3.util.FastMath; 24importorg.apache.commons.math3.util.MathUtils; 25 26/**27* <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded28* domain using a penalty function.</p>29*30* <p>31* This adapter can be used to wrap functions subject to simple bounds on32* parameters so they can be used by optimizers that do <em>not</em> directly33* support simple bounds.34* </p>35* <p>36* The principle is that the user function that will be wrapped will see its37* parameters bounded as required, i.e when its {@code value} method is called38* with argument array {@code point}, the elements array will fulfill requirement39* {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components40* may be unbounded or bounded only on one side if the corresponding bound is41* set to an infinite value. The optimizer will not manage the user function by42* itself, but it will handle this adapter and it is this adapter that will take43* care the bounds are fulfilled. The adapter {@link #value(double[])} method will44* be called by the optimizer with unbound parameters, and the adapter will check45* if the parameters is within range or not. If it is in range, then the underlying46* user function will be called, and if it is not the value of a penalty function47* will be returned instead.48* </p>49* <p>50* This adapter is only a poor man solution to simple bounds optimization constraints51* that can be used with simple optimizers like {@link SimplexOptimizer} with {@link52* NelderMeadSimplex} or {@link MultiDirectionalSimplex}. A better solution is to use53* an optimizer that directly supports simple bounds like {@link CMAESOptimizer} or54* {@link BOBYQAOptimizer}. One caveat of this poor man solution is that if start point55* or start simplex is completely outside of the allowed range, only the penalty function56* is used, and the optimizer may converge without ever entering the range.57* </p>58*59* @see MultivariateFunctionMappingAdapter60*61* @version $Id: MultivariateFunctionPenaltyAdapter.java 1422230 2012-12-15 12:11:13Z erans $62* @deprecated As of 3.1 (to be removed in 4.0).63* @since 3.064*/65 66 @Deprecated 67publicclassMultivariateFunctionPenaltyAdapterimplementsMultivariateFunction { 68 69/**Underlying bounded function. */70privatefinalMultivariateFunction bounded; 71 72/**Lower bounds. */73privatefinaldouble[] lower; 74 75/**Upper bounds. */76privatefinaldouble[] upper; 77 78/**Penalty offset. */79privatefinaldoubleoffset; 80 81/**Penalty scales. */82privatefinaldouble[] scale; 83 84/**Simple constructor.85* <p>86* When the optimizer provided points are out of range, the value of the87* penalty function will be used instead of the value of the underlying88* function. In order for this penalty to be effective in rejecting this89* point during the optimization process, the penalty function value should90* be defined with care. This value is computed as:91* <pre>92* penalty(point) = offset + ∑<sub>i</sub>[scale[i] * √|point[i]-boundary[i]|]93* </pre>94* where indices i correspond to all the components that violates their boundaries.95* </p>96* <p>97* So when attempting a function minimization, offset should be larger than98* the maximum expected value of the underlying function and scale components99* should all be positive. When attempting a function maximization, offset100* should be lesser than the minimum expected value of the underlying function101* and scale components should all be negative.102* minimization, and lesser than the minimum expected value of the underlying103* function when attempting maximization.104* </p>105* <p>106* These choices for the penalty function have two properties. First, all out107* of range points will return a function value that is worse than the value108* returned by any in range point. Second, the penalty is worse for large109* boundaries violation than for small violations, so the optimizer has an hint110* about the direction in which it should search for acceptable points.111* </p>112* @param bounded bounded function113* @param lower lower bounds for each element of the input parameters array114* (some elements may be set to {@code Double.NEGATIVE_INFINITY} for115* unbounded values)116* @param upper upper bounds for each element of the input parameters array117* (some elements may be set to {@code Double.POSITIVE_INFINITY} for118* unbounded values)119* @param offset base offset of the penalty function120* @param scale scale of the penalty function121* @exception DimensionMismatchException if lower bounds, upper bounds and122* scales are not consistent, either according to dimension or to bounadary123* values124*/125publicMultivariateFunctionPenaltyAdapter(finalMultivariateFunction bounded, 126finaldouble[] lower,finaldouble[] upper, 127finaldoubleoffset,finaldouble[] scale) { 128 129// safety checks130 MathUtils.checkNotNull(lower); 131 MathUtils.checkNotNull(upper); 132 MathUtils.checkNotNull(scale); 133if(lower.length != upper.length) { 134thrownewDimensionMismatchException(lower.length, upper.length); 135 } 136if(lower.length != scale.length) { 137thrownewDimensionMismatchException(lower.length, scale.length); 138 } 139for(inti = 0; i < lower.length; ++i) { 140// note the following test is written in such a way it also fails for NaN141if(!(upper[i] >= lower[i])) { 142thrownewNumberIsTooSmallException(upper[i], lower[i],true); 143 } 144 } 145 146this.bounded = bounded; 147this.lower = lower.clone(); 148this.upper = upper.clone(); 149this.offset = offset; 150this.scale = scale.clone(); 151 152 } 153 154/**Compute the underlying function value from an unbounded point.155* <p>156* This method simply returns the value of the underlying function157* if the unbounded point already fulfills the bounds, and compute158* a replacement value using the offset and scale if bounds are159* violated, without calling the function at all.160* </p>161* @param point unbounded point162* @return either underlying function value or penalty function value163*/164publicdoublevalue(double[] point) { 165 166for(inti = 0; i < scale.length; ++i) { 167if((point[i] < lower[i]) || (point[i] > upper[i])) { 168// bound violation starting at this component169doublesum = 0; 170for(intj = i; j < scale.length; ++j) { 171finaldoubleovershoot; 172if(point[j] < lower[j]) { 173 overshoot = scale[j] * (lower[j] - point[j]); 174 }elseif(point[j] > upper[j]) { 175 overshoot = scale[j] * (point[j] - upper[j]); 176 }else{ 177 overshoot = 0; 178 } 179 sum += FastMath.sqrt(overshoot); 180 } 181returnoffset + sum; 182 } 183 } 184 185// all boundaries are fulfilled, we are in the expected186// domain of the underlying function187returnbounded.value(point); 188 189 } 190 191 }