查找函数的所有局部最大值

Question

I have written code to find the global minimum of a function using the simulated annealing algorithm — down below — but how to use the same algorithm to find all local maxima of a function ?

My code for finding the local minimum of a function, note that i know nothing about the function I am asking the interactor for the f(x) at x ie the cost of the function in a particular point.

#include <bits/stdc++.h>

using namespace std;

double myRand(double fMin, double fMax)
{
    double f = (double)rand() / RAND_MAX;
    return fMin + f * (fMax - fMin);
}


int main()
{
    cout.flush();


    double x,fx,xMin;
    double fMin;

    cout << "? "<<fixed << setprecision(6) << -1<<endl;
    cin>>fMin;


    for(double T = 1000; T>1; T*=.995)
    {
        x=myRand(-100,100);
        cout << "? "<<fixed << setprecision(6) << x <<endl;
        cin>>fx;

        if (fx<fMin)
        {
            fMin=fx;
            xMin = x;
        }
        else
        {
            double P=exp((fMin-fx)/T);

            if (P>myRand(1,100))
            {
                fMin=fx;
                xMin=x;
            }
        }
    }

    cout << "! "<<fixed << setprecision(6)<<xMin<<endl;

    return 0;

} 

my attempt to find the local maxima is

#include <bits/stdc++.h>

using namespace std;

double myRand(double fMin, double fMax)
{
    double f = (double)rand() / RAND_MAX;
    return fMin + f * (fMax - fMin);
}


int main()
{
    cout.flush();


    double x,fx,xMax;
    double fMax;
    int n;
    double a,b;
    cin>>n>>a>>b;

    double answer[n];




    for(int i=0; i<n; i++)
    {
        cout << "? "<<fixed << setprecision(6) << a+i/5 <<endl;
        cin>>fMax;

        for(double T = 1000; T>1; T*=.995)
        {
            x=myRand(a,b);


// i am avoiding to get the same local max twice
            while(i>0&&answer[i-1]==x)
                x=myRand(a,b);
            cout << "? "<<fixed << setprecision(6) << x <<endl;
            cin>>fx;
            if (fx>fMax)
            {
                fMax=fx;
                xMax = x;
            }
            else
            {
                double P=exp((fMax-fx)/T);

                if (P<myRand(0,1))
                {
                    fMax=fx;
                    xMax=x;
                }
            }
        }
        answer[i]=xMax;
    }
    cout << "!";
    for(int i=0; i<n; i++)
    {
        cout<<" "<<fixed << setprecision(6)<<answer[i];
    }

    return 0;

}

Answer 1

1. Place the algorithm inside a function:

    double my_unknown_function(double x) { cout << "? " << fixed << setprecision(6) << x << endl; cin >> fx; return fx; } using function = double(double); double minimum(function func) { double x, fx, xMin; /* ... */ for(double T = 1000; T>1; T*=.995) { x = myRand(-100,100); fx = func(x); /* ... */ } return xMin; }

   In this way you can simply get multiple local minima:

    std::vector<double> lm; for (int i(0); i < 100; ++i) lm.push_back(minimum(my_unknown_function));

   As explained in the comments, simulated annealing is an optimization heuristic. It's not an exhaustive search and it doesn't find all minima .

   Anyway calling minimum multiple times you can get different results, since it's stochastic. In expectation, with a large enough number of restarts , any local search method will someday give you the actual global minimum.

2. Do not rewrite the algorithm for the maximization task: you could introduce bugs and testing is harder.

   Just take the opposite of your function:

    double my_unknown_function(double x) { cout << "? " << fixed << setprecision(6) << x << endl; cin >> fx; return -fx; }

Also consider:

• Why should I not #include <bits/stdc++.h>?
• C++: "std::endl" vs "\\n"
• Why is "using namespace std;" considered bad practice?
• Why is the use of rand() considered bad?