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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  package org.apache.commons.math3.optim.nonlinear.scalar;
18  
19  import org.apache.commons.math3.analysis.MultivariateFunction;
20  import org.apache.commons.math3.exception.DimensionMismatchException;
21  import org.apache.commons.math3.exception.NumberIsTooSmallException;
22  import org.apache.commons.math3.util.FastMath;
23  import org.apache.commons.math3.util.MathUtils;
24  
25  /**
26   * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded
27   * domain using a penalty function.</p>
28   *
29   * <p>
30   * This adapter can be used to wrap functions subject to simple bounds on
31   * parameters so they can be used by optimizers that do <em>not</em> directly
32   * support simple bounds.
33   * </p>
34   * <p>
35   * The principle is that the user function that will be wrapped will see its
36   * parameters bounded as required, i.e when its {@code value} method is called
37   * with argument array {@code point}, the elements array will fulfill requirement
38   * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
39   * may be unbounded or bounded only on one side if the corresponding bound is
40   * set to an infinite value. The optimizer will not manage the user function by
41   * itself, but it will handle this adapter and it is this adapter that will take
42   * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
43   * be called by the optimizer with unbound parameters, and the adapter will check
44   * if the parameters is within range or not. If it is in range, then the underlying
45   * user function will be called, and if it is not the value of a penalty function
46   * will be returned instead.
47   * </p>
48   * <p>
49   * This adapter is only a poor-man's solution to simple bounds optimization
50   * constraints that can be used with simple optimizers like
51   * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
52   * SimplexOptimizer}.
53   * A better solution is to use an optimizer that directly supports simple bounds like
54   * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer
55   * CMAESOptimizer} or
56   * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
57   * BOBYQAOptimizer}.
58   * One caveat of this poor-man's solution is that if start point or start simplex
59   * is completely outside of the allowed range, only the penalty function is used,
60   * and the optimizer may converge without ever entering the range.
61   * </p>
62   *
63   * @see MultivariateFunctionMappingAdapter
64   *
65   * @since 3.0
66   */
67  public class MultivariateFunctionPenaltyAdapter
68      implements MultivariateFunction {
69      /** Underlying bounded function. */
70      private final MultivariateFunction bounded;
71      /** Lower bounds. */
72      private final double[] lower;
73      /** Upper bounds. */
74      private final double[] upper;
75      /** Penalty offset. */
76      private final double offset;
77      /** Penalty scales. */
78      private final double[] scale;
79  
80      /**
81       * Simple constructor.
82       * <p>
83       * When the optimizer provided points are out of range, the value of the
84       * penalty function will be used instead of the value of the underlying
85       * function. In order for this penalty to be effective in rejecting this
86       * point during the optimization process, the penalty function value should
87       * be defined with care. This value is computed as:
88       * <pre>
89       *   penalty(point) = offset + &sum;<sub>i</sub>[scale[i] * &radic;|point[i]-boundary[i]|]
90       * </pre>
91       * where indices i correspond to all the components that violates their boundaries.
92       * </p>
93       * <p>
94       * So when attempting a function minimization, offset should be larger than
95       * the maximum expected value of the underlying function and scale components
96       * should all be positive. When attempting a function maximization, offset
97       * should be lesser than the minimum expected value of the underlying function
98       * and scale components should all be negative.
99       * 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 }