paradiseo/moeo/tutorial/Lesson1/README.md

How to run your first multi-objective EA?

In this lesson you will solve the Schaffer SCH1 bi-objective problem with NSGA-II using the ParadisEO-MOEO framework.

The SCH1 problem minimizes two objectives over a single real-valued variable x in [0, 2]:

• f1(x) = x^2
• f2(x) = (x - 2)^2

1. Running

From the build/moeo/tutorial/Lesson1 directory:

./Sch1 --help
./Sch1 --popSize=100 --maxGen=100

Parameters can also be read from a file:

./Sch1 @Sch1.param

2. Browsing the code

Open Sch1.cpp and follow along.

First, define the objective vector traits. This tells MOEO how many objectives the problem has and whether each is minimizing or maximizing:

class Sch1ObjectiveVectorTraits : public moeoObjectiveVectorTraits
{
public:
    static bool minimizing (int) { return true; }
    static bool maximizing (int) { return false; }
    static unsigned int nObjectives () { return 2; }
};

The solution class Sch1 inherits from moeoRealVector — a real-valued decision vector that also carries an objective vector:

class Sch1 : public moeoRealVector < Sch1ObjectiveVector >
{
public:
    Sch1() : moeoRealVector < Sch1ObjectiveVector > (1) {}
};

The evaluator computes both objectives and stores them via objectiveVector():

void operator () (Sch1 & _sch1)
{
    if (_sch1.invalidObjectiveVector()) {
        Sch1ObjectiveVector objVec;
        double x = _sch1[0];
        objVec[0] = x * x;
        objVec[1] = (x - 2.0) * (x - 2.0);
        _sch1.objectiveVector(objVec);
    }
}

The algorithm itself is a single line — moeoNSGAII takes the generation limit, evaluator, crossover, and mutation as constructor arguments:

moeoNSGAII < Sch1 > nsgaII (MAX_GEN, eval, xover, P_CROSS, mutation, P_MUT);

After the run, extract the Pareto front with moeoUnboundedArchive:

moeoUnboundedArchive < Sch1 > arch;
arch(pop);
arch.sortedPrintOn(cout);