array(4*4) containing random elements having first row sum= 7 and column 4 element sum = 7.

each element of matrix should be in the range 0 t0 7 integer only. other constraints i want this matrix to follow are-

1. diagonal elements=0

2. first column sum=0

3. row four sum =0

4. sum of elements of row 2= sum of elements of column 2

5. sum of elements of row 3= sum of elements of column 3

[Image Analyst]

Why do you want that?

[harra]

i am representing the transhipment problem by this matrix. i want to create initial population for implementing genetic algorithm. Please help me. It will be highly appreciated.

[Adam]

That sounds like too many constraints to solve for to me, bit I may be wrong, that is just a gut instinct based on my time doing a PhD in optimisation, but I didn't work explicitly on solving problems with such a tight combination of hard constraints.

[Geoff Hayes]

harra - If each element of matrix should be in the range 0 to 7, then that must mean that negative numbers are excluded. So the first column and fourth row will always have zero elements. Is this the case?

[harra]

yes you are right sir. Basically, the logic is that i am considering first node as source and fourth node as destination. So, nothing goes into source node 1(so, column 1 elements zero) and nothing comes out of destination node 4(so, row 4 all elements zero).

so, in 4*4 matrix, i am considering rows as source and columns as destination nodes

[Adam]

Yes, looking at it more carefully (I got thrown off by having read what I'm sure was another question by you that had what looked like impossible constraints in a similar format!) the constraints are probably not impossible though whether you could call the numbers that would be generated to fit such constraints as "random" is debatable!

[Roger Stafford]

I just worked a similar problem for Reshdev at Answers thread #151552. You people ought to communicate.

Answer 1

[Jan]

So you mean a matrix of the form:

[0 a c e
 0 0 d f
 0 b 0 g
 0 0 0 0]

This means, that there are 8^7 possible combinations, which are only 2'097'152. You can simply run a brute force attack to check all possibilities, if they match you conditions.

[harra]

thank you, Jan Simon, can you please explain bit more?. i did not get you.

[Image Analyst]

I like it (+1 vote). Sometimes the brute force way is a lot simpler than some fancy hard-to-understand way. In my simple program of 7 nested for loops, and if statement and counter, I found 16640 matrices that fulfill the requirements. Took 8.9 seconds.