One-point cross over in genetic algorithm

Question

I am using one point cross over to cross two individual. Assume that I have two individual such as

I1='10010011' 
I2='11001101'

tmp_P is vector store two individual I1 and I2. I want to implement one point cross over in C++. Is it right?

This is algorithm description

fori=1 to N/2 (N is number of individual=2 in my case)
   if random[0,1]<=Pc //cross prob.
       pos=random_int[1,n-1]
       for k=pos+1 to n //Length of individual=8 in my case
          aux=tmp_P_i[k]
          tmp_P_i[k]=tmp_P_(i+N/2)[k]
          tmp_P_(i+N/2)[k]=aux;
       end
   end
end

My problem is I am confusing the index of pos. Is it get random from [0 to n-2]. Is it right?

 //Random integer in range [min max]
int random_int(int min, int max) //range : [min, max]
{
    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_int_distribution<> dis(min, max);
    return dis(gen);
}
//One-point Crossover
vector< vector<int> > crossover(vector< vector<int> > tmp_P)
{
    int pos=0;
    for (int i=0;i<N/2;i++)
    {
        //If random number smaller than crossover probability then do Crossover
        if(RND()<=Pc)
        {
            pos=random_int(0,n-2);//Index in C++ from 0
            int aux=0;
            for (int k=pos+1;k<n;k++)
            {
                //swat
                aux=tmp_P[i][k];
                tmp_P[i][k]=tmp_P[i+N/2][k];
                tmp_P[i+N/2][k]=aux;
            }
        }
    }
    return tmp_P;
}

Answer 1

• random_int

  For debugging purpose (repeatability) you shouldn't always call rd(). Moreover you are recreating the pseudo-RNG at every call.

  Call the random device just once and do everything else with a (randomly) seeded pseudo-RNG. As a bonus, you should store the seed value in a log file so you can later replay the pseudo-random sequence.

  It should be something like:

  int random_int(int min, int max)
  {
  #if defined(NDEBUG)
    static std::mt19937 gen(std::random_device());  // or thread_local  
  #else
    static std::mt19937 gen(1234);  // or, better, thread_local
  #endif
  
    std::uniform_int_distribution<> dis(min, max);
    return dis(gen);
  }
  

• crossover

  • pos is correct (it's in the [0;n-2] range); the actual crossover position is in the [1;n-1] range (skipping the 0 index is correct since it would swap the entire genome).

    You can directly initialize pos with:

     unsigned pos = random_int(1, n-1);
    
     for (unsigned k = pos; k < n; ++k)
     { /* ... */ }
    

    this is simpler.

  • you could use the std::swap function

  • if variables are habitually assigned a meaningful value when they first appear in the code then there's no chance of them accidentally being used with a meaningless or uninitialised value (e.g. pos / aux, see Why declare a variable in one line, and assign to it in the next?)
  • if the individuals' length is fixed you can also consider std::bitset to store the genome

---

So something like this should work:

unsigned random_int(unsigned min, unsigned max)
{
#if defined(NDEBUG)
  static std::mt19937 gen(std::random_device());
#else
  static std::mt19937 gen(1234u);
#endif

  std::uniform_int_distribution<> dis(min, max);
  return dis(gen);
}

std::vector<std::vector<int>> crossover(std::vector<std::vector<int>> tmp_P)
{
  const auto N = tmp_P.size();
  const auto n = tmp_P[0].size();

  for (unsigned i = 0; i < N/2; ++i)
  {
    assert(tmp_P[i].size() == n);

    // If random number smaller than crossover probability then do Crossover
    if (RND() <= Pc)
      for (unsigned k = random_int(1, n-1); k < n; ++k)
        std::swap(tmp_P[i][k], tmp_P[i + N/2][k]);
  }

  return tmp_P;
}