001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math3.optim.nonlinear.scalar;
018    
019    import org.apache.commons.math3.analysis.MultivariateFunction;
020    import org.apache.commons.math3.exception.DimensionMismatchException;
021    import org.apache.commons.math3.exception.NumberIsTooSmallException;
022    import org.apache.commons.math3.util.FastMath;
023    import org.apache.commons.math3.util.MathUtils;
024    
025    /**
026     * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded
027     * domain using a penalty function.</p>
028     *
029     * <p>
030     * This adapter can be used to wrap functions subject to simple bounds on
031     * parameters so they can be used by optimizers that do <em>not</em> directly
032     * support simple bounds.
033     * </p>
034     * <p>
035     * The principle is that the user function that will be wrapped will see its
036     * parameters bounded as required, i.e when its {@code value} method is called
037     * with argument array {@code point}, the elements array will fulfill requirement
038     * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
039     * may be unbounded or bounded only on one side if the corresponding bound is
040     * set to an infinite value. The optimizer will not manage the user function by
041     * itself, but it will handle this adapter and it is this adapter that will take
042     * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
043     * be called by the optimizer with unbound parameters, and the adapter will check
044     * if the parameters is within range or not. If it is in range, then the underlying
045     * user function will be called, and if it is not the value of a penalty function
046     * will be returned instead.
047     * </p>
048     * <p>
049     * This adapter is only a poor-man's solution to simple bounds optimization
050     * constraints that can be used with simple optimizers like
051     * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer
052     * SimplexOptimizer}.
053     * A better solution is to use an optimizer that directly supports simple bounds like
054     * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer
055     * CMAESOptimizer} or
056     * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
057     * BOBYQAOptimizer}.
058     * One caveat of this poor-man's solution is that if start point or start simplex
059     * is completely outside of the allowed range, only the penalty function is used,
060     * and the optimizer may converge without ever entering the range.
061     * </p>
062     *
063     * @see MultivariateFunctionMappingAdapter
064     *
065     * @version $Id: MultivariateFunctionPenaltyAdapter.java 1416643 2012-12-03 19:37:14Z tn $
066     * @since 3.0
067     */
068    public class MultivariateFunctionPenaltyAdapter
069        implements MultivariateFunction {
070        /** Underlying bounded function. */
071        private final MultivariateFunction bounded;
072        /** Lower bounds. */
073        private final double[] lower;
074        /** Upper bounds. */
075        private final double[] upper;
076        /** Penalty offset. */
077        private final double offset;
078        /** Penalty scales. */
079        private final double[] scale;
080    
081        /**
082         * Simple constructor.
083         * <p>
084         * When the optimizer provided points are out of range, the value of the
085         * penalty function will be used instead of the value of the underlying
086         * function. In order for this penalty to be effective in rejecting this
087         * point during the optimization process, the penalty function value should
088         * be defined with care. This value is computed as:
089         * <pre>
090         *   penalty(point) = offset + &sum;<sub>i</sub>[scale[i] * &radic;|point[i]-boundary[i]|]
091         * </pre>
092         * where indices i correspond to all the components that violates their boundaries.
093         * </p>
094         * <p>
095         * So when attempting a function minimization, offset should be larger than
096         * the maximum expected value of the underlying function and scale components
097         * should all be positive. When attempting a function maximization, offset
098         * should be lesser than the minimum expected value of the underlying function
099         * and scale components should all be negative.
100         * minimization, and lesser than the minimum expected value of the underlying
101         * function when attempting maximization.
102         * </p>
103         * <p>
104         * These choices for the penalty function have two properties. First, all out
105         * of range points will return a function value that is worse than the value
106         * returned by any in range point. Second, the penalty is worse for large
107         * boundaries violation than for small violations, so the optimizer has an hint
108         * about the direction in which it should search for acceptable points.
109         * </p>
110         * @param bounded bounded function
111         * @param lower lower bounds for each element of the input parameters array
112         * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
113         * unbounded values)
114         * @param upper upper bounds for each element of the input parameters array
115         * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
116         * unbounded values)
117         * @param offset base offset of the penalty function
118         * @param scale scale of the penalty function
119         * @exception DimensionMismatchException if lower bounds, upper bounds and
120         * scales are not consistent, either according to dimension or to bounadary
121         * values
122         */
123        public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded,
124                                                  final double[] lower, final double[] upper,
125                                                  final double offset, final double[] scale) {
126    
127            // safety checks
128            MathUtils.checkNotNull(lower);
129            MathUtils.checkNotNull(upper);
130            MathUtils.checkNotNull(scale);
131            if (lower.length != upper.length) {
132                throw new DimensionMismatchException(lower.length, upper.length);
133            }
134            if (lower.length != scale.length) {
135                throw new DimensionMismatchException(lower.length, scale.length);
136            }
137            for (int i = 0; i < lower.length; ++i) {
138                // note the following test is written in such a way it also fails for NaN
139                if (!(upper[i] >= lower[i])) {
140                    throw new NumberIsTooSmallException(upper[i], lower[i], true);
141                }
142            }
143    
144            this.bounded = bounded;
145            this.lower   = lower.clone();
146            this.upper   = upper.clone();
147            this.offset  = offset;
148            this.scale   = scale.clone();
149        }
150    
151        /**
152         * Computes the underlying function value from an unbounded point.
153         * <p>
154         * This method simply returns the value of the underlying function
155         * if the unbounded point already fulfills the bounds, and compute
156         * a replacement value using the offset and scale if bounds are
157         * violated, without calling the function at all.
158         * </p>
159         * @param point unbounded point
160         * @return either underlying function value or penalty function value
161         */
162        public double value(double[] point) {
163    
164            for (int i = 0; i < scale.length; ++i) {
165                if ((point[i] < lower[i]) || (point[i] > upper[i])) {
166                    // bound violation starting at this component
167                    double sum = 0;
168                    for (int j = i; j < scale.length; ++j) {
169                        final double overshoot;
170                        if (point[j] < lower[j]) {
171                            overshoot = scale[j] * (lower[j] - point[j]);
172                        } else if (point[j] > upper[j]) {
173                            overshoot = scale[j] * (point[j] - upper[j]);
174                        } else {
175                            overshoot = 0;
176                        }
177                        sum += FastMath.sqrt(overshoot);
178                    }
179                    return offset + sum;
180                }
181            }
182    
183            // all boundaries are fulfilled, we are in the expected
184            // domain of the underlying function
185            return bounded.value(point);
186        }
187    }