Only generate sorted solutions by constraint using a ga-solver

I'm using genetic algorithm to solve an optimization problem. The input is a couple of inrrelevant constants and an 1x21 vector named x.

The ga-solver will give me a function value and a configuration of my x-vector where each entry can have the value from 1 to 7 representing different stations in a manufacturing system.

I need a constraint/rule for the solver, so it only suggest sorted solutions from left to right, where entries not used is given the value 7. Are the however an entry with 6 at some random place between 1 and 7, then it must be allowed to stay e.g.: x=[1 1 1 6 2 2 5 5 5 5 7 7 7 7 7 7 7 7 7 7 7]

I cannot use sort(x) as this would be an evaluation afterwards, and I need the solver to take the constraint into consideration.

Answer 1

[Alan Weiss]

I am not sure that I really understand what your constraints are. Do you allow more than one value of 6 to appear?

In general, if you want solutions in increasing order, you can achieve the goal with linear constraints of the form

 x(i) <= x(i+1)

for all relevant i. With 21 components this would lead to 20 linear constraints in an A matrix with rows of the form

 [0,0,...,0,1,-1,0,...,0]

and a b vector consisting of a column of zeros. See linear inequality constraints.

But for your case I do not know a good formulation, in part because I don't really understand how your "6" variables are constrained.

Alan Weiss

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