What is the kind of this algorithm;
Input : square matrix
Objective function = minimization of total movements cost of matrix based on permutative manner
Constrains : Lower and upper bound of the objective function
The optimal solution lies between the estimated lower and upper bound obtaining before beginning the permutative manner for computing the objective function of the matrix.
How does the algorithm work to reach the known feasible space? does it need a random operator?
Is this algorithm a hybrid approach of exact and metaheuristic? or what is it?
Probably more information required about function, otherwise, it's a probe algorithm with decision on type of function from permutation (increasing or decreasing)
It seems to me you are facing a combinatorial problem. If this is right, then you must to code the decisions variables possible values. In this case different admissible permutations, and to make evolve its by some algorithm, by example GA, minimizing your objective function.
Dear Gamiel Saeed,
I agree with our colleague José Arzola-Ruiz that this can be considered as a combinatorial optimization problem from which we can use metaheuristic algorithms such as GA, PSO ...
Here are two sample references that address a similar problem.
https://tel.archives-ouvertes.fr/tel-01355746v2/document
https://www.whitman.edu/Documents/Academics/Mathematics/2014/carrjk.pdf
Best regards
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