update metric

git-svn-id: svn://scm.gforge.inria.fr/svnroot/paradiseo@264 331e1502-861f-0410-8da2-ba01fb791d7f

trunk/paradiseo-moeo/src/metric/moeoNormalizedSolutionVsSolutionBinaryMetric.h

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+// -*- mode: c++; c-indent-level: 4; c++-member-init-indent: 8; comment-column: 35; -*-
+
+//-----------------------------------------------------------------------------
+// moeoNormalizedSolutionVsSolutionBinaryMetric.h
+// (c) OPAC Team (LIFL), Dolphin Project (INRIA), 2007
+/*
+    This library...
+
+    Contact: paradiseo-help@lists.gforge.inria.fr, http://paradiseo.gforge.inria.fr
+ */
+//-----------------------------------------------------------------------------
+
+#ifndef MOEONORMALIZEDSOLUTIONVSSOLUTIONBINARYMETRIC_H_
+#define MOEONORMALIZEDSOLUTIONVSSOLUTIONBINARYMETRIC_H_
+
+#include <stdexcept>
+#include <metric/moeoMetric.h>
+
+
+/**
+ * Base class for binary metrics dedicated to the performance comparison between two solutions's objective vectors using normalized values.
+ * Then, indicator values lie in the interval [-1,1].
+ * Note that you have to set the bounds for every objective before using the operator().
+ */
+template < class ObjectiveVector, class R >
+class moeoNormalizedSolutionVsSolutionBinaryMetric : public moeoSolutionVsSolutionBinaryMetric < ObjectiveVector, R >
+{
+public:
+
+    /**
+     * Default ctr for any moeoNormalizedSolutionVsSolutionBinaryMetric object
+     */
+    moeoNormalizedSolutionVsSolutionBinaryMetric()
+    {
+        bounds.resize(ObjectiveVector::Traits::nObjectives());
+    }
+
+
+    /**
+     * Sets the lower bound (_min) and the upper bound (_max) for the objective _obj
+     * _min lower bound
+     * _max upper bound
+     * _obj the objective index
+     */
+    void setup(double _min, double _max, unsigned _obj)
+    {
+        if (_min == _max)
+        {
+            _min -= tiny();
+            _max += tiny();
+        }
+        bounds[_obj] = eoRealInterval(_min, _max);
+    }
+
+    /**
+     * Sets the lower bound and the upper bound for the objective _obj using a eoRealInterval object
+     * _realInterval the eoRealInterval object
+     * _obj the objective index
+     */
+    virtual void setup(eoRealInterval _realInterval, unsigned _obj)
+    {
+        bounds[_obj] = _realInterval;
+    }
+
+
+    /**
+     * Returns a very small value that can be used to avoid extreme cases (where the min bound == the max bound)
+     */
+    static double tiny()
+    {
+        return 1e-6;
+    }
+
+
+protected:
+
+    /** the bounds for every objective (bounds[i] = bounds for the objective i) */
+    std::vector < eoRealInterval > bounds;
+
+};
+
+
+/**
+ * Additive epsilon binary metric allowing to compare two objective vectors as proposed in
+ * Zitzler E., Thiele L., Laumanns M., Fonseca C. M., Grunert da Fonseca V.:
+ * Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), pp.117–132 (2003).
+ */
+template < class ObjectiveVector >
+class moeoAdditiveEpsilonBinaryMetric : public moeoNormalizedSolutionVsSolutionBinaryMetric < ObjectiveVector, double >
+{
+public:
+
+    /**
+     * Returns the minimal distance by which the objective vector _o1 must be translated in all objectives 
+     * so that it weakly dominates the objective vector _o2	
+     * @warning don't forget to set the bounds for every objective before the call of this function
+     * @param _o1 the first objective vector
+     * @param _o2 the second objective vector
+     */
+    double operator()(const ObjectiveVector & _o1, const ObjectiveVector & _o2)
+    {
+        // computation of the epsilon value for the first objective
+        double result = epsilon(_o1, _o2, 0);
+        // computation of the epsilon value for the other objectives
+        double tmp;
+        for (unsigned i=1; i<ObjectiveVector::Traits::nObjectives(); i++)
+        {
+            tmp = epsilon(_o1, _o2, i);
+            result = std::max(result, tmp);
+        }
+        // returns the maximum epsilon value
+        return result;
+    }
+
+
+private:
+
+    /** the bounds for every objective */
+    using moeoNormalizedSolutionVsSolutionBinaryMetric < ObjectiveVector, double > :: bounds;
+
+
+    /**
+     * Returns the epsilon value by which the objective vector _o1 must be translated in the objective _obj 
+     * so that it dominates the objective vector _o2
+     * @param _o1 the first objective vector
+     * @param _o2 the second objective vector
+     * @param _obj the index of the objective
+     */
+    double epsilon(const ObjectiveVector & _o1, const ObjectiveVector & _o2, const unsigned _obj)
+    {
+        double result;
+        // if the objective _obj have to be minimized
+        if (ObjectiveVector::Traits::minimizing(_obj))
+        {
+            // _o1[_obj] - _o2[_obj]
+            result = ( (_o1[_obj] - bounds[_obj].minimum()) / bounds[_obj].range() ) - ( (_o2[_obj] - bounds[_obj].minimum()) / bounds[_obj].range() );
+        }
+        // if the objective _obj have to be maximized
+        else
+        {
+            // _o2[_obj] - _o1[_obj]
+            result = ( (_o2[_obj] - bounds[_obj].minimum()) / bounds[_obj].range() ) - ( (_o1[_obj] - bounds[_obj].minimum()) / bounds[_obj].range() );
+        }
+        return result;
+    }
+
+};
+
+
+/**
+ * Hypervolume binary metric allowing to compare two objective vectors as proposed in
+ * Zitzler E., Künzli S.: Indicator-Based Selection in Multiobjective Search. In Parallel Problem Solving from Nature (PPSN VIII).
+ * Lecture Notes in Computer Science 3242, Springer, Birmingham, UK pp.832–842 (2004).
+ * This indicator is based on the hypervolume concept introduced in
+ * Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study.
+ * Parallel Problem Solving from Nature (PPSN-V), pp.292-301 (1998).
+ */
+template < class ObjectiveVector >
+class moeoHypervolumeBinaryMetric : public moeoNormalizedSolutionVsSolutionBinaryMetric < ObjectiveVector, double >
+{
+public:
+
+    /**
+     * Ctor
+     * @param _rho value used to compute the reference point from the worst values for each objective (default : 1.1)
+     */
+    moeoHypervolumeBinaryMetric(double _rho = 1.1) : rho(_rho)
+    {
+        // not-a-maximization problem check
+        for (unsigned i=0; i<ObjectiveVector::Traits::nObjectives(); i++)
+        {
+            if (ObjectiveVector::Traits::maximizing(i))
+            {
+                throw std::runtime_error("Hypervolume binary metric not yet implemented for a maximization problem in moeoHypervolumeBinaryMetric");
+            }
+        }
+        // consistency check
+        if (rho < 1)
+        {
+            cout << "Warning, value used to compute the reference point rho for the hypervolume calculation must not be smaller than 1" << endl;
+            cout << "Adjusted to 1" << endl;
+            rho = 1;
+        }
+    }
+
+
+    /**
+     * Returns the volume of the space that is dominated by _o2 but not by _o1 with respect to a reference point computed using rho.
+     * @warning don't forget to set the bounds for every objective before the call of this function
+     * @param _o1 the first objective vector
+     * @param _o2 the second objective vector
+     */
+    double operator()(const ObjectiveVector & _o1, const ObjectiveVector & _o2)
+    {
+        double result;
+        // if _o1 dominates _o2
+        if ( paretoComparator(_o1,_o2) )
+        {
+            result = - hypervolume(_o1, _o2, ObjectiveVector::Traits::nObjectives()-1);
+        }
+        else
+        {
+            result = hypervolume(_o2, _o1, ObjectiveVector::Traits::nObjectives()-1);
+        }
+        return result;
+    }
+
+
+private:
+
+    /** value used to compute the reference point from the worst values for each objective */
+    double rho;
+    /** the bounds for every objective */
+    using moeoNormalizedSolutionVsSolutionBinaryMetric < ObjectiveVector, double > :: bounds;
+    /** Functor to compare two objective vectors according to Pareto dominance relation */
+    moeoParetoObjectiveVectorComparator < ObjectiveVector > paretoComparator;
+
+    /**
+     * Returns the volume of the space that is dominated by _o2 but not by _o1 with respect to a reference point computed using rho for the objective _obj.
+     * @param _o1 the first objective vector
+     * @param _o2 the second objective vector
+     * @param _obj the objective index
+     * @param _flag used for iteration, if _flag=true _o2 is not talen into account (default : false)
+     */
+    double hypervolume(const ObjectiveVector & _o1, const ObjectiveVector & _o2, const unsigned _obj, const bool _flag = false)
+    {
+        double result;
+        double range = rho * bounds[_obj].range();
+        double max = bounds[_obj].minimum() + range;
+        // value of _1 for the objective _obj
+        double v1 = _o1[_obj];
+        // value of _2 for the objective _obj (if _flag=true, v2=max)
+        double v2;
+        if (_flag)
+        {
+            v2 = max;
+        }
+        else
+        {
+            v2 = _o2[_obj];
+        }
+        // computation of the volume
+        if (_obj == 0)
+        {
+            if (v1 < v2)
+            {
+                result = (v2 - v1) / range;
+            }
+            else
+            {
+                result = 0;
+            }
+        }
+        else
+        {
+            if (v1 < v2)
+            {
+                result = ( hypervolume(_o1, _o2, _obj-1, true) * (v2 - v1) / range ) + ( hypervolume(_o1, _o2, _obj-1) * (max - v2) / range );
+            }
+            else
+            {
+                result = hypervolume(_o1, _o2, _obj-1) * (max - v2) / range;
+            }
+        }
+        return result;
+    }
+
+};
+
+
+#endif /*MOEONORMALIZEDSOLUTIONVSSOLUTIONBINARYMETRIC_H_*/