I'm trying to develop a GA to optimize a distribution problem.
Say we have products A, B, C in a storehouse. Depending on the
quantity of each product, we know to how many shops we want to send,
for example (highly simplified).
A - Qty = 108 - Should be send to 4 shops
B - Qty = 84 - Should be send to 3 shops
C - Qty = 48 - Should be send to 3 shop
Let's call the total number of shops that must receive a product is T1
(4 + 3 + 3 = 10)
On the other hand we have the shops P, Q, R, S with a certain capacity
and a ranking, eg.
P should receive 3 products - ranking 200
Q should receive 3 products - ranking 200
R should receive 2 products - ranking 150
S should receive 2 products - ranking 100
Let's call the total number of products the shops must receive is T2
(3 + 3 + 2 + 2 = 10)
We can be sure that in the input data T1 = T2
A possible solution here is
P Q R S
A x x x x
B x x x
C x x x
Another possible solution would be
P Q R S
A x x x x
B x x x
C x x x
I will consider solutions to be better when a high rank shop receives
products for which we have less quantity (ej C AND B).
I will consider solutions to be better when a low rank shop receives
products for which we have more quantity (ej. A and B).
I created a genetic algoritm that solves the x's in the above grid.
With this only objective it is prettty easy by minimizing a
differences function.
However I have to also optimize the other objectives and that is where
i need you to point me in the right direction.
I already tried to implement a multiple objective GA with pareto
ranking but with no success. My first objective (balance of x's) must
always be optimal and within these posible solutions the other
objectives must be optimized.
Any good readings, examples, web-sites, etc ?
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