How to optimize a binary matrix with MILP?

Hi to all,

I'm working on my bachelor thesis what about cross kidney transplants matching algorithms.

I've a solution with genetic algorithm but i want to know 'what is the optimum?' (of course GA is %90-99 interval, not %100-optimum-)

So;

I have a binary matrix(also symetric)

for example=

1 2 3 4 5 6 7 8 9 10

1 [0 1 0 0 0 0 0 0 0 0

2 1 0 1 0 0 0 0 0 0 0

3 0 1 0 0 0 0 0 0 0 0

4 0 0 0 0 0 0 0 0 1 0

5 0 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0 0

7 0 0 0 0 0 0 0 0 0 0

8 0 0 0 0 0 0 0 0 0 0

9 0 0 0 1 0 0 0 0 0 0

10 0 0 0 0 0 0 0 0 0 0]

I want to find optimum match no. beetween column numbers.

In this case; NO2 and NO1 can match, NO9 and NO4 can match and NO2 and NO3 can match.

But when NO2 was matched with NO1, it can not match with NO1. Its kinda monogamy.

Optimum value is = 2 match.

Let's think about 1000*1000 matrix.

When i solve this matrix with genetic algortihm, i had 410 as a result. ( theoretical match number is 500 ((1000/2)), of course impossible.)

How can i solve this with using MILP?

Any little ideas will be very valuable for me...

Thanks to all