Function Minimisation using Simulated Annealing Algorithm

[starxxx]

I need help n writing a simulated annealing algorithm that is able to maximize f(x)=sin(0.15*x)+cos(x) defined on the interval 0<= x <= 40 using the cooling schedule

[JosAH]

What do you mean by 'the cooling schedule'? As long as you get the temperature
T down at each iteration it will be fine theoretically. Have a look here.

kind regards,

Jos

[starxxx]

Thank You...

Yes I know about the temperature change. I have not done the f(x) functions for along time and have forgotten how they work and how to implement them and the connection between the temperature and the graph. It needs to be coded in Java to find the optimal point.

Regards

[JosAH]

Thank You...

Yes I know about the temperature change. I have not done the f(x) functions for along time and have forgotten how they work and how to implement them and the connection between the temperature and the graph. It needs to be coded in Java to find the optimal point.

Regards

You have to come up with a value x' for a given value x. if f(x') > f(x) you've found
a better approximation so you accept it.

If deltaE = f(x)-f(x') > 0 then you only accept the worse step x' over x iff p*exp(deltaE/T)
is smaller than a pseudo random value q in [0,1]. Note that p is in [0,1]
as well and represents the probability of taking an 'uphill' step at T == infinite.

This is basically the metropolis algorithm.

For the java source code check the API documentation for the Math class and
its static functions. We don't hand out boiler plate Java source code; we are
willing to help you to solve your problem(s) though but you have to give it a try first.

kind regards,

Jos

[starxxx]

Thank you

I have come up with the following code but it seems to be wrong.

 import java.io.*;
import java.lang.*;
import java.awt.*;
import java.awt.event.*;
import java.util.*;
import java.io.Serializable;
 
public class sim
 
{
// Initialize variables
          Random random = new Random(); // set up random number generator
    protected static double temperature = 0.95; // annealing adjustments
           protected static double a,y = 0,k = 0,temp = 0; // Variables
    protected static double minx = 0; // Constrain of x
    protected static double maxx = 40; // Constrain of x
    //public boolean anneal(double d);
 
public static void main( String args[] )
 
 { 
 
double r[]=new double[10];
Random random = new Random(); // How are the inputs will be randomized
 
// Generate initial x[i] values 
 
        //System.out.println("\nx[i] values");
        //System.out.println("==================");
 
       for(int i=0;i<10;i++)
       {
 
       a = random.nextDouble(); // How are the inputs will be randomized
 
       if((a<maxx) || (a>minx))
 
       {
 
         r[i] = a;  
 
       }
        //    System.out.println(""+r[i]);
        //    System.out.println("Random number printing");
       } 
 
    //    System.out.println("\nf(x) values");
    //    System.out.println("==================");
 
      for(int i = 0;i<10;i++)
    {
 
    //y = r[i]*r[i]-10*Math.cos(2*3.142*r[i]); // Calculate probabilities
      y = Math.sin(0.15*r[i])+ Math.cos(r[i]);   
    //f(x)=sin(0.15*x)+cos(x)          
    k = k + y;
 
         //    System.out.println(+k);
        //   System.out.println("Addition formula out come");
    }
 
    k = 10*10+k;
 
    //    System.out.println("\nf(x) + 10 values returns");
    //         System.out.println("\n"+k);
//
   int l = 1;
   while(l != 4) // loop
 
   {
 
double r1[]=new double[10];
 
    //    System.out.println("\nx[i] values");
//        System.out.println("==================");
 
       for(int i = 0;i<10;i++)
       {
 
       a = Math.random();
 
       if((a<maxx) || (a>minx))
       {
    //       System.out.println("<" + maxx+"Maxx"+" > " + minx + "minxx");
         r[i] = a;
 
       }
    //        System.out.println(""+r[i]);
       } 
 
//        System.out.println("\nf(x) values");
//        System.out.println("==================");
 
      for(int i = 0;i<10;i++)
    {
 
    //y = r[i]*r[i]-10*Math.cos(2*3.142*r[i]); // Calculate probabilities
      y = Math.sin(0.15*r[i])+ Math.cos(r[i]);   
    //f(x)=sin(0.15*x)+cos(x)
 
    k = k + y;
//               System.out.println(+k);
 
    }
 
    k = 10*10+k;
 
//        System.out.println("\nf(x) + 10 values returns");
 //            System.out.println("\n"+k);
 
 
//Source code: http://www.heatonresearch.com/articles/9/page4.html / http://www.heatonresearch.com/code/64/SimulatedAnnealing.zip
 
{
 
if (temperature < 1.0E-4)
         {
           if (k > 0.0)
            {
              temperature = k;
            //  System.out.println("\nBetter Value = "+k);
          //    System.out.println(1.0E-4);
           }   
           }
 
           if (Math.random() < Math.exp(k / temperature))
              {
   // System.out.println(Math.exp(k / temperature)+ " Some equation");           
 
                temperature = k;
             // System.out.println("\nBetterValue = "+k + "k");
//System.out.println(temp);
System.out.println(temperature + "   Temparature");
 
// ====== 
//1) Choose a high starting temperature T and a random starting point x. T <- T0, x <- x0 
//2) Calculate the function value of the starting point. E <- f (x) 
//3) For each iteration k, k = 1 ... kf and while T is sufficiently large, do the following: 
//a) Choose a new point x', using a generating function. x' <- g(x) 
//b) Calculate the function value of x'. E' <- f (x') 
//c) Set x<-x'and E<-E'with probability determined by the acceptance function h(). //d) Reduce the temperature T by //annealing, e.g. T(k+1) <- c*T(k), 0 < c < 1. 
//4) Return x and E as the optimal point and the optimal function value. 
// ======              
 
             }
             }  
 
l++;
 
//System.out.println(l);
    }
}
}

[starxxx]

Need help ASAP...................plz help me......

[Nepomuk]

Need help ASAP...................plz help me......

What exactly DOES happen? You say it's going wrong, but what is it, that goes wrong?

Greetings,
Nepomuk