Question

Write a computer program to implement a generational GA for the One-Max problem:

Use the following parameters:
• Representation: binary strings of length L=25;
• Initialization: random

• Parent selection: fitness proportionate, implemented using roulette wheel;
• Recombination: one-point crossover with probability pc= 0.7;
• Mutation: bit-flip with probability pm= 1/L;
• Population size = 100;
• Termination condition: 100 generation or optimum found.
After every generation find the best, worst, and mean fitness in the population and (possibly) plot then on a graph with time (generation) on the x axis.
Do 10 run and find the mean and standard deviation of the time (generations) taken to find the optimum.
Solution
Given the specification of the problem, it is rather simple to write a Java program.

Answer 1

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mod (ll)(1e9 + 7)

// Iterative Function to calculate (x^y)%p in O(log y)
ll power(ll x, ll y, ll p)
{
   ll res = 1; // Initialize result

   x = x % p; // Update x if it is more than or
   // equal to p

   while (y > 0) {

       // If y is odd, multiply x with result
       if (y & 1)
           res = (res * x) % p;

       // y must be even now
       y = y >> 1; // y = y/2
       x = (x * x) % p;
   }
   return res;
}

// Function to count the number of binary
// strings of length N having only 0's and 1's
ll findCount(ll N)
{
   int count = power(2, N, mod);
   return count;
}

// Driver code
int main()
{
   ll N = 25;

   cout << findCount(N);

   return 0;
}