Dear Masoumeh Moeini ,

You could calculate the Euclidian Distance between given and target strings. Followingly, you could rank your matchings to divide into groups.

I hope it would be helpful.

with bests,

Mansurbek Abdullaev

Dear Masoumeh Moeini,

The qualitative search for the best point or the optimal point can be intuitive and will be conditioned by the minimization of a distance such that the latter represents the minimum error relating to a given compromise.

To obtain practical information, i suggest you to see links on topic.

https://www.geeksforgeeks.org/find-a-fixed-point-in-a-given-array/

https://www.geeksforgeeks.org/closest-pair-of-points-using-divide-and-conquer-algorithm/

https://www.geeksforgeeks.org/kmp-algorithm-for-pattern-searching/

https://www.geeksforgeeks.org/rabin-karp-algorithm-for-pattern-searching/

https://www.hackerearth.com/practice/notes/exact-string-matching-algorithms/

https://www.cs.purdue.edu/homes/ayg/CS251/slides/chap11.pdf

https://www.php.net/manual/en/ref.array.php

Best regards

Dear Mansurbek Urol ugli Abdullaev

Thank you so much of your answer, I will surely study this topic.

Best regards,

Masoumeh Moeini

Dear Mohamed-Mourad Lafifi

Thank you so much of your answer, I will surely study these topics.

Best regards,

Masoumeh Moeini

Dear Masoumeh Moeini

In a typical optimal control problem, the optimal-point associated with the optimal solution, might not be necessarily unique (it could be multi-modal). Non-uniqueness of the optimal-point poses a challenge to find the optimal solution, even for the exactly the same cost function (performance index) associated with the optimal control problem at hand.

Dear Saeb AmirAhmadi Chomachar

Thanks a lot, what's the solution for that? what topics shoud I study about? I mean Greedy algorithm, dynamic programming , ... ,which one can help me?

Dear Masoumeh Moeini

The experts in control community, are still unable to find the globally optimal solution, in case the optimal control problem is nonlinear or non-scalar (multi-dimensional). The Hamilton-Jacobi-Bellman (HJB) equation is almost impossible to be solved analytically for non-scalar systems, and Dynamic-programming is also hurdled by extra-large amount of numerical data or in the specific terminology, the "curse of dimensionality", and both are computationally highly expensive. Hence, the experts in control society do not still know how to solve an optimal control problem in its global sense. All the available methods, ultimately incorporate some type of quasi-linearization and find the local solution, NOT the global solution. The Maximum Principle is also such a local method. All the available optimal methodologies as the one you mentioned as "Greedy-algorithm", are actually a contraption and remedy, not a cure. Therefore, the experts compromise and come to terms with these obstacle and unfairly are convinced to use these methodologies, although they know the disadvantages but the problem could not be perfectly coped with, since other options and alternatives do not yet exist in the existing literature, and the question has been left open for researchers.

I suggest you to linearize your problem (if it is nonlinear), then solve it for a local optimal solution. If the problem is with constraints, then you may utilize "The Maximum Principle".

Dear Saeb AmirAhmadi Chomachar

Thank you so much of your answer.

Dear Masoumeh Moeini

You are most welcome.