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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * 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 and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math3.optimization.direct;
19  
20  import org.apache.commons.math3.analysis.MultivariateFunction;
21  import org.apache.commons.math3.exception.DimensionMismatchException;
22  import org.apache.commons.math3.exception.NumberIsTooSmallException;
23  import org.apache.commons.math3.util.FastMath;
24  import org.apache.commons.math3.util.MathUtils;
25  
26  /**
27   * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded
28   * domain using a penalty function.</p>
29   *
30   * <p>
31   * This adapter can be used to wrap functions subject to simple bounds on
32   * parameters so they can be used by optimizers that do <em>not</em> directly
33   * support simple bounds.
34   * </p>
35   * <p>
36   * The principle is that the user function that will be wrapped will see its
37   * parameters bounded as required, i.e when its {@code value} method is called
38   * with argument array {@code point}, the elements array will fulfill requirement
39   * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
40   * may be unbounded or bounded only on one side if the corresponding bound is
41   * set to an infinite value. The optimizer will not manage the user function by
42   * itself, but it will handle this adapter and it is this adapter that will take
43   * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
44   * be called by the optimizer with unbound parameters, and the adapter will check
45   * if the parameters is within range or not. If it is in range, then the underlying
46   * user function will be called, and if it is not the value of a penalty function
47   * will be returned instead.
48   * </p>
49   * <p>
50   * This adapter is only a poor man solution to simple bounds optimization constraints
51   * that can be used with simple optimizers like {@link SimplexOptimizer} with {@link
52   * NelderMeadSimplex} or {@link MultiDirectionalSimplex}. A better solution is to use
53   * an optimizer that directly supports simple bounds like {@link CMAESOptimizer} or
54   * {@link BOBYQAOptimizer}. One caveat of this poor man solution is that if start point
55   * or start simplex is completely outside of the allowed range, only the penalty function
56   * is used, and the optimizer may converge without ever entering the range.
57   * </p>
58   *
59   * @see MultivariateFunctionMappingAdapter
60   *
61   * @deprecated As of 3.1 (to be removed in 4.0).
62   * @since 3.0
63   */
64  
65  @Deprecated
66  public class MultivariateFunctionPenaltyAdapter implements MultivariateFunction {
67  
68      /** Underlying bounded function. */
69      private final MultivariateFunction bounded;
70  
71      /** Lower bounds. */
72      private final double[] lower;
73  
74      /** Upper bounds. */
75      private final double[] upper;
76  
77      /** Penalty offset. */
78      private final double offset;
79  
80      /** Penalty scales. */
81      private final double[] scale;
82  
83      /** Simple constructor.
84       * <p>
85       * When the optimizer provided points are out of range, the value of the
86       * penalty function will be used instead of the value of the underlying
87       * function. In order for this penalty to be effective in rejecting this
88       * point during the optimization process, the penalty function value should
89       * be defined with care. This value is computed as:
90       * <pre>
91       *   penalty(point) = offset + &sum;<sub>i</sub>[scale[i] * &radic;|point[i]-boundary[i]|]
92       * </pre>
93       * where indices i correspond to all the components that violates their boundaries.
94       * </p>
95       * <p>
96       * So when attempting a function minimization, offset should be larger than
97       * the maximum expected value of the underlying function and scale components
98       * should all be positive. When attempting a function maximization, offset
99       * 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 }