Question

Discuss the challenges of a system whose fitness function is J= 1+sinax

When and the solution of space has 15 values which are represented by a 4 digit binary string ranging from 0000 to 1111. If the initial population has four members 0010 1111 0001 1000, Determine the offspring of the initial and first generation.

Answer 1

The fitness function determines the offspring of a system. For the given initial population, members 1111 and 1000 have the highest fitness values and will be the offspring of the initial and first generation.

Step-by-step explanation:

The fitness function of the given system is given by J = 1 + sin(ax).

Given that the solution space has 15 values represented by a 4-digit binary string ranging from 0000 to 1111 and the initial population has four members: 0010, 1111, 0001, and 1000.

To determine the offspring of the initial and first generation, we need to evaluate the fitness function for each member of the initial population and select the members with the highest fitness value to create the offspring.

Calculating the fitness values for the given initial population:

1. Member 0010: J = 1 + sin(a(0) * 0) = 1
   This member has a fitness value of 1.
2. Member 1111: J = 1 + sin(a(1) * 1) = 1 + sin(a)
   This member has a fitness value of 1 + sin(a).
3. Member 0001: J = 1 + sin(a(0) * 0) = 1
   This member has a fitness value of 1.
4. Member 1000: J = 1 + sin(a(0) * 1) = 1 + sin(a)
   This member has a fitness value of 1 + sin(a).

Since members 1111 and 1000 have the highest fitness values, they will be selected as the offspring of the initial and first generation.