Question
Do you think genetic algorithms worth trying out for the problem below, or will I hit local-minima issues?
I think maybe aspects of the problem is great for a generator / fitness-function style setup. (If you've botched a similar project I would love hear from you, and not do something similar)
Thank you for any tips on how to structure things and nail this right.
The problem
I'm searching a good scheduling algorithm to use for the following real-world problem.
I have a sequence with 15 slots like this (The digits may vary from 0 to 20) :
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(And there are in total 10 different sequences of this type)
Each sequence needs to expand into an array, where each slot can take 1 position.
1 1 0 0 1 1 1 0 0 0 1 1 1 0 0
1 1 0 0 1 1 1 0 0 0 1 1 1 0 0
0 0 1 1 0 0 0 1 1 1 0 0 0 1 1
0 0 1 1 0 0 0 1 1 1 0 0 0 1 1
The constraints on the matrix is that:
[row-wise, i.e. horizontally] The number of ones placed, must either be 11 or 111
[row-wise] The distance between two sequences of 1 needs to be a minimum of 00
The sum of each column should match the original array.
The number of rows in the matrix should be optimized.
The array then needs to allocate one of 4 different matrixes, which may have different number of rows:
A, B, C, D
A, B, C and D are real-world departments. The load needs to be placed reasonably fair during the course of a 10-day period, not to interfere with other department goals.
Each of the matrix is compared with expansion of 10 different original sequences so you have:
A1, A2, A3, A4, A5, A6, A7, A8, A9, A10
B1, B2, B3, B4, B5, B6, B7, B8, B9, B10
C1, C2, C3, C4, C5, C6, C7, C8, C9, C10
D1, D2, D3, D4, D5, D6, D7, D8, D9, D10
Certain spots on these may be reserved (Not sure if I should make it just reserved/not reserved or function-based). The reserved spots might be meetings and other events
The sum of each row (for instance all the A's) should be approximately the same within 2%. i.e. sum(A1 through A10) should be approximately the same as (B1 through B10) etc.
The number of rows can vary, so you have for instance:
A1: 5 rows
A2: 5 rows
A3: 1 row, where that single row could for instance be:
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0
etc..
Sub problem*
I'de be very happy to solve only part of the problem. For instance being able to input:
1 1 2 3 4 2 2 3 4 2 2 3 3 2 3
And get an appropriate array of sequences with 1's and 0's minimized on the number of rows following th constraints above.
