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 * https://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 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.optim.nonlinear.scalar;
23
24 import org.hipparchus.analysis.MultivariateFunction;
25 import org.hipparchus.exception.LocalizedCoreFormats;
26 import org.hipparchus.exception.MathIllegalArgumentException;
27 import org.hipparchus.util.FastMath;
28 import org.hipparchus.util.MathUtils;
29
30 /**
31 * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded
32 * domain using a penalty function.</p>
33 *
34 * <p>
35 * This adapter can be used to wrap functions subject to simple bounds on
36 * parameters so they can be used by optimizers that do <em>not</em> directly
37 * support simple bounds.
38 * </p>
39 * <p>
40 * The principle is that the user function that will be wrapped will see its
41 * parameters bounded as required, i.e when its {@code value} method is called
42 * with argument array {@code point}, the elements array will fulfill requirement
43 * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
44 * may be unbounded or bounded only on one side if the corresponding bound is
45 * set to an infinite value. The optimizer will not manage the user function by
46 * itself, but it will handle this adapter and it is this adapter that will take
47 * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
48 * be called by the optimizer with unbound parameters, and the adapter will check
49 * if the parameters is within range or not. If it is in range, then the underlying
50 * user function will be called, and if it is not the value of a penalty function
51 * will be returned instead.
52 * </p>
53 * <p>
54 * This adapter is only a poor-man's solution to simple bounds optimization
55 * constraints that can be used with simple optimizers like
56 * {@link org.hipparchus.optim.nonlinear.scalar.noderiv.SimplexOptimizer
57 * SimplexOptimizer}.
58 * A better solution is to use an optimizer that directly supports simple bounds like
59 * {@link org.hipparchus.optim.nonlinear.scalar.noderiv.CMAESOptimizer
60 * CMAESOptimizer} or
61 * {@link org.hipparchus.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
62 * BOBYQAOptimizer}.
63 * One caveat of this poor-man's solution is that if start point or start simplex
64 * is completely outside of the allowed range, only the penalty function is used,
65 * and the optimizer may converge without ever entering the range.
66 * </p>
67 *
68 * @see MultivariateFunctionMappingAdapter
69 *
70 */
71 public class MultivariateFunctionPenaltyAdapter
72 implements MultivariateFunction {
73 /** Underlying bounded function. */
74 private final MultivariateFunction bounded;
75 /** Lower bounds. */
76 private final double[] lower;
77 /** Upper bounds. */
78 private final double[] upper;
79 /** Penalty offset. */
80 private final double offset;
81 /** Penalty scales. */
82 private final double[] scale;
83
84 /**
85 * Simple constructor.
86 * <p>
87 * When the optimizer provided points are out of range, the value of the
88 * penalty function will be used instead of the value of the underlying
89 * function. In order for this penalty to be effective in rejecting this
90 * point during the optimization process, the penalty function value should
91 * be defined with care. This value is computed as:</p>
92 * <p>
93 * penalty(point) = offset + ∑<sub>i</sub>[scale[i] * √|point[i]-boundary[i]|]
94 * </p>
95 * <p>
96 * where indices i correspond to all the components that violates their boundaries.
97 * </p>
98 * <p>
99 * So when attempting a function minimization, offset should be larger than
100 * the maximum expected value of the underlying function and scale components
101 * should all be positive. When attempting a function maximization, offset
102 * should be lesser than the minimum expected value of the underlying function
103 * and scale components should all be negative.
104 * minimization, and lesser than the minimum expected value of the underlying
105 * function when attempting maximization.
106 * </p>
107 * <p>
108 * These choices for the penalty function have two properties. First, all out
109 * of range points will return a function value that is worse than the value
110 * returned by any in range point. Second, the penalty is worse for large
111 * boundaries violation than for small violations, so the optimizer has an hint
112 * about the direction in which it should search for acceptable points.
113 * </p>
114 * @param bounded bounded function
115 * @param lower lower bounds for each element of the input parameters array
116 * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
117 * unbounded values)
118 * @param upper upper bounds for each element of the input parameters array
119 * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
120 * unbounded values)
121 * @param offset base offset of the penalty function
122 * @param scale scale of the penalty function
123 * @exception MathIllegalArgumentException if lower bounds, upper bounds and
124 * scales are not consistent, either according to dimension or to bounadary
125 * values
126 */
127 public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded,
128 final double[] lower, final double[] upper,
129 final double offset, final double[] scale) {
130
131 // safety checks
132 MathUtils.checkNotNull(lower);
133 MathUtils.checkNotNull(upper);
134 MathUtils.checkNotNull(scale);
135 if (lower.length != upper.length) {
136 throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
137 lower.length, upper.length);
138 }
139 if (lower.length != scale.length) {
140 throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
141 lower.length, scale.length);
142 }
143 for (int i = 0; i < lower.length; ++i) {
144 if (!(upper[i] >= lower[i])) { // NOPMD - the test is written in such a way it also fails for NaN
145 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL,
146 upper[i], lower[i]);
147 }
148 }
149
150 this.bounded = bounded;
151 this.lower = lower.clone();
152 this.upper = upper.clone();
153 this.offset = offset;
154 this.scale = scale.clone();
155 }
156
157 /**
158 * Computes the underlying function value from an unbounded point.
159 * <p>
160 * This method simply returns the value of the underlying function
161 * if the unbounded point already fulfills the bounds, and compute
162 * a replacement value using the offset and scale if bounds are
163 * violated, without calling the function at all.
164 * </p>
165 * @param point unbounded point
166 * @return either underlying function value or penalty function value
167 */
168 @Override
169 public double value(double[] point) {
170
171 for (int i = 0; i < scale.length; ++i) {
172 if ((point[i] < lower[i]) || (point[i] > upper[i])) {
173 // bound violation starting at this component
174 double sum = 0;
175 for (int j = i; j < scale.length; ++j) {
176 final double overshoot;
177 if (point[j] < lower[j]) {
178 overshoot = scale[j] * (lower[j] - point[j]);
179 } else if (point[j] > upper[j]) {
180 overshoot = scale[j] * (point[j] - upper[j]);
181 } else {
182 overshoot = 0;
183 }
184 sum += FastMath.sqrt(overshoot);
185 }
186 return offset + sum;
187 }
188 }
189
190 // all boundaries are fulfilled, we are in the expected
191 // domain of the underlying function
192 return bounded.value(point);
193 }
194 }