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 * @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 3.0
64 */
65
66 @Deprecated
67 public class MultivariateFunctionPenaltyAdapter implements MultivariateFunction {
68
69 /** Underlying bounded function. */
70 private final MultivariateFunction bounded;
71
72 /** Lower bounds. */
73 private final double[] lower;
74
75 /** Upper bounds. */
76 private final double[] upper;
77
78 /** Penalty offset. */
79 private final double offset;
80
81 /** Penalty scales. */
82 private final double[] scale;
83
84 /** Simple constructor.
85 * <p>
86 * When the optimizer provided points are out of range, the value of the
87 * penalty function will be used instead of the value of the underlying
88 * function. In order for this penalty to be effective in rejecting this
89 * point during the optimization process, the penalty function value should
90 * 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 than
98 * the maximum expected value of the underlying function and scale components
99 * should all be positive. When attempting a function maximization, offset
100 * should be lesser than the minimum expected value of the underlying function
101 * and scale components should all be negative.
102 * minimization, and lesser than the minimum expected value of the underlying
103 * function when attempting maximization.
104 * </p>
105 * <p>
106 * These choices for the penalty function have two properties. First, all out
107 * of range points will return a function value that is worse than the value
108 * returned by any in range point. Second, the penalty is worse for large
109 * boundaries violation than for small violations, so the optimizer has an hint
110 * about the direction in which it should search for acceptable points.
111 * </p>
112 * @param bounded bounded function
113 * @param lower lower bounds for each element of the input parameters array
114 * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
115 * unbounded values)
116 * @param upper upper bounds for each element of the input parameters array
117 * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
118 * unbounded values)
119 * @param offset base offset of the penalty function
120 * @param scale scale of the penalty function
121 * @exception DimensionMismatchException if lower bounds, upper bounds and
122 * scales are not consistent, either according to dimension or to bounadary
123 * values
124 */
125 public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded,
126 final double[] lower, final double[] upper,
127 final double offset, final double[] scale) {
128
129 // safety checks
130 MathUtils.checkNotNull(lower);
131 MathUtils.checkNotNull(upper);
132 MathUtils.checkNotNull(scale);
133 if (lower.length != upper.length) {
134 throw new DimensionMismatchException(lower.length, upper.length);
135 }
136 if (lower.length != scale.length) {
137 throw new DimensionMismatchException(lower.length, scale.length);
138 }
139 for (int i = 0; i < lower.length; ++i) {
140 // note the following test is written in such a way it also fails for NaN
141 if (!(upper[i] >= lower[i])) {
142 throw new NumberIsTooSmallException(upper[i], lower[i], true);
143 }
144 }
145
146 this.bounded = bounded;
147 this.lower = lower.clone();
148 this.upper = upper.clone();
149 this.offset = offset;
150 this.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 function
157 * if the unbounded point already fulfills the bounds, and compute
158 * a replacement value using the offset and scale if bounds are
159 * violated, without calling the function at all.
160 * </p>
161 * @param point unbounded point
162 * @return either underlying function value or penalty function value
163 */
164 public double value(double[] point) {
165
166 for (int i = 0; i < scale.length; ++i) {
167 if ((point[i] < lower[i]) || (point[i] > upper[i])) {
168 // bound violation starting at this component
169 double sum = 0;
170 for (int j = i; j < scale.length; ++j) {
171 final double overshoot;
172 if (point[j] < lower[j]) {
173 overshoot = scale[j] * (lower[j] - point[j]);
174 } else if (point[j] > upper[j]) {
175 overshoot = scale[j] * (point[j] - upper[j]);
176 } else {
177 overshoot = 0;
178 }
179 sum += FastMath.sqrt(overshoot);
180 }
181 return offset + sum;
182 }
183 }
184
185 // all boundaries are fulfilled, we are in the expected
186 // domain of the underlying function
187 return bounded.value(point);
188
189 }
190
191 }