Java tutorial
/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math3.optim.nonlinear.scalar; import org.apache.commons.math3.analysis.MultivariateFunction; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.util.MathUtils; /** * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded * domain using a penalty function.</p> * * <p> * This adapter can be used to wrap functions subject to simple bounds on * parameters so they can be used by optimizers that do <em>not</em> directly * support simple bounds. * </p> * <p> * The principle is that the user function that will be wrapped will see its * parameters bounded as required, i.e when its {@code value} method is called * with argument array {@code point}, the elements array will fulfill requirement * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components * may be unbounded or bounded only on one side if the corresponding bound is * set to an infinite value. The optimizer will not manage the user function by * itself, but it will handle this adapter and it is this adapter that will take * care the bounds are fulfilled. The adapter {@link #value(double[])} method will * be called by the optimizer with unbound parameters, and the adapter will check * if the parameters is within range or not. If it is in range, then the underlying * user function will be called, and if it is not the value of a penalty function * will be returned instead. * </p> * <p> * This adapter is only a poor-man's solution to simple bounds optimization * constraints that can be used with simple optimizers like * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.SimplexOptimizer * SimplexOptimizer}. * A better solution is to use an optimizer that directly supports simple bounds like * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.CMAESOptimizer * CMAESOptimizer} or * {@link org.apache.commons.math3.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer * BOBYQAOptimizer}. * One caveat of this poor-man's solution is that if start point or start simplex * is completely outside of the allowed range, only the penalty function is used, * and the optimizer may converge without ever entering the range. * </p> * * @see MultivariateFunctionMappingAdapter * * @version $Id: MultivariateFunctionPenaltyAdapter.java 1416643 2012-12-03 19:37:14Z tn $ * @since 3.0 */ public class MultivariateFunctionPenaltyAdapter implements MultivariateFunction { /** Underlying bounded function. */ private final MultivariateFunction bounded; /** Lower bounds. */ private final double[] lower; /** Upper bounds. */ private final double[] upper; /** Penalty offset. */ private final double offset; /** Penalty scales. */ private final double[] scale; /** * Simple constructor. * <p> * When the optimizer provided points are out of range, the value of the * penalty function will be used instead of the value of the underlying * function. In order for this penalty to be effective in rejecting this * point during the optimization process, the penalty function value should * be defined with care. This value is computed as: * <pre> * penalty(point) = offset + ∑<sub>i</sub>[scale[i] * √|point[i]-boundary[i]|] * </pre> * where indices i correspond to all the components that violates their boundaries. * </p> * <p> * So when attempting a function minimization, offset should be larger than * the maximum expected value of the underlying function and scale components * should all be positive. When attempting a function maximization, offset * should be lesser than the minimum expected value of the underlying function * and scale components should all be negative. * minimization, and lesser than the minimum expected value of the underlying * function when attempting maximization. * </p> * <p> * These choices for the penalty function have two properties. First, all out * of range points will return a function value that is worse than the value * returned by any in range point. Second, the penalty is worse for large * boundaries violation than for small violations, so the optimizer has an hint * about the direction in which it should search for acceptable points. * </p> * @param bounded bounded function * @param lower lower bounds for each element of the input parameters array * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for * unbounded values) * @param upper upper bounds for each element of the input parameters array * (some elements may be set to {@code Double.POSITIVE_INFINITY} for * unbounded values) * @param offset base offset of the penalty function * @param scale scale of the penalty function * @exception DimensionMismatchException if lower bounds, upper bounds and * scales are not consistent, either according to dimension or to bounadary * values */ public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded, final double[] lower, final double[] upper, final double offset, final double[] scale) { // safety checks MathUtils.checkNotNull(lower); MathUtils.checkNotNull(upper); MathUtils.checkNotNull(scale); if (lower.length != upper.length) { throw new DimensionMismatchException(lower.length, upper.length); } if (lower.length != scale.length) { throw new DimensionMismatchException(lower.length, scale.length); } for (int i = 0; i < lower.length; ++i) { // note the following test is written in such a way it also fails for NaN if (!(upper[i] >= lower[i])) { throw new NumberIsTooSmallException(upper[i], lower[i], true); } } this.bounded = bounded; this.lower = lower.clone(); this.upper = upper.clone(); this.offset = offset; this.scale = scale.clone(); } /** * Computes the underlying function value from an unbounded point. * <p> * This method simply returns the value of the underlying function * if the unbounded point already fulfills the bounds, and compute * a replacement value using the offset and scale if bounds are * violated, without calling the function at all. * </p> * @param point unbounded point * @return either underlying function value or penalty function value */ public double value(double[] point) { for (int i = 0; i < scale.length; ++i) { if ((point[i] < lower[i]) || (point[i] > upper[i])) { // bound violation starting at this component double sum = 0; for (int j = i; j < scale.length; ++j) { final double overshoot; if (point[j] < lower[j]) { overshoot = scale[j] * (lower[j] - point[j]); } else if (point[j] > upper[j]) { overshoot = scale[j] * (point[j] - upper[j]); } else { overshoot = 0; } sum += FastMath.sqrt(overshoot); } return offset + sum; } } // all boundaries are fulfilled, we are in the expected // domain of the underlying function return bounded.value(point); } }