EE6227 Homework

EE6227 Homework (2023S2)

*All submissions are to be handwritten*

1.   Assume that you are required to minimize the Ackley function benchmark below for n=4 using 16-bit binary string representation. The bound for the variables is [-2,2].

Write the objective values for the following strings:

a)   1011110010110010

b)   0011110010110010

c)   1111110110010011

d)   0000000000000001

Note: You may opt to upload program or spreadsheet as part of your online submission if you do not wish to present the detail workings in your handwritten submission.

2.   An evolutionary algorithm uses permutation string coding for a 12-city closed-loop travelling salesman problem. The visitation sequence is coded as permutation string denoted as . Assume that the distance between any two nodes i and j denoted as dij is specified by the equation below, where the symbol “%” denotes the modulo operation.

For the pair of chosen parents shown below in Figure 1, show the offspring produced for the three types of recombination operations:

a.   Partially matched crossover (PMX) where the shaded cells indicate the sub-string chosen for the PMX.

b.    Cycle recombination

c.    Edge recombination crossover, constructing the two offspring starting from node 1 and node 7.

Figure 1