A ``magic square'' of order n is an n-by-n matrix containing all the integers from 1 to n*n, each one exactly once, such that all row, column, and diagonal sums are the same. In other words, it is a permutation of the numbers 1 to n*n, arranged in a rectangular grid, with the property that each row sum of the matrix, each column sum, and each diagonal sum is equal to the same integer.

For example, a magic square of order 3 is 

    2  7  6
    9  5  1
    4  3  8
The three row sums, the three column sums, and the two diagonal sums are 15.

Using SGA-C, aGA.java, or simple_ga_prog from the class directory ~shartley/MCS770, generate magic squares using a genetic algorithm. Generate one magic square for as many different values of n as you can.

The major challenge in this assignment is the design of your encoding scheme and fitness function.

This programming assignment is due in class Monday, May 6, 1996.

There are three things to turn in electronically using the submit command:

  1. A listing of your objective (fitness) function from the SGA-C, aGA.java, simple_ga_prog.c or simple_ga_prog.java source code, plus any other procedures or code you change.
  2. A listing of your best runs of SGA-C, aGA.java, or simple_ga_prog. DO NOT include all generations! Use the script command and then edit out all but the first few, a middle few, and the last few generations.
  3. A write-up answering these questions describing how you optimized the function using genetic algorithms and what you learned (about one or two single-spaced page), and what problems you encountered while designing, implementing, and debugging your program and how you solved those problems.
  4. Your write-up should clearly describe your encoding scheme, fitness function, crossover operators tried, mutation operators tried, and parameters that led to successful runs (population size, crossover and mutation probabilities).

Use the submit command to turn in file copies of all of the above. Place them in the Pr3 directory of MCS770.