This problem is to solve the Magic Square Problem (constrained and unconstrained versions), a combinatorial optimization problem, using modern heuristic methods.

Magic squares have been a source of fascination since ancient times, over 4,000 years. A magic square is a square matrix of size *n*, containing each of the numbers 1 to *n*^{2} exactly once, in which each column, each row, and both diagonals add up to the same magic number.

It is possible to impose many different constraints on a standard magic square problem. Here the constrained version stipulates that the solution matrix must have a pre-defined contiguous sub-matrix.

Here is the binary code, and here is the readme file. As the 2nd runner-up, this program solved the constrained version of 400 x 400 magic square within a minute in the 2011 International Optimisation Competition.

- X. Xie, “Meta-LS Solver for Magic Square Competition,” International Optimisation Competition, 2011.

`@TechReport{xie2011tr00, Title = {Meta-LS Solver for Magic Square Competition}, Author = {Xiao-Feng Xie}, Code={http://www.wiomax.com/team/xie/project/magic/MagicSquare.jar}, PDF={http://www.wiomax.com/team/xie/project/magic/IOC_readme.pdf}, Institution={International Optimisation Competition}, Year = {2011} }`