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THE TRAVELING SALESMAN PROBLEM: MATHEMATICAL MODELING AND OPTIMAL SOLUTIONS

Mamatova Zilolakhan Khabibullokhanovna,Abdumajidova Mukaramkhan Iqbaljon kizi , Fergana​ state university

Abstract

Salesman issues trade in the field of products distribution , sales and transportation costs to calculate These issues trade representative planned routes and work efficiency increase for important is considered . Within the scope of the issue salesman work time , every one the store product sell opportunities , and various to cities to go time determination through total sold products or done affairs This type is issues not only trade representatives efficiency increase , maybe the company general business strategies to optimize help gives .

Keywords

distances matrix , route , closed route , route length , whole valuable variables , graph , Hamilton outline ( Hamilton cycle ), networks and borders method , cited matrix , backpack ( bomber aircraft (issue about ) , resources , cargo, loads transportation ( flight ).

References

Lin, S., & Kernighan, BW (1973). "An effective heuristic algorithm for the traveling salesman problem." Operations Research, 21(2), 498-516.

Applegate, DL, Bixby, RE, Chvátal , V., & Cook, WJ (2006). "The Traveling Salesman Problem: A Computational Study." Princeton University Press.

Keller, DM, & Matheson, JE (1972). "The Traveling Salesman Problem: A Survey." Management Science, 18(10), B224-B235.

Wagner, G. (1972-1973). "Foundations of operations research" (Vols. 1-3). Moscow: Mir.

Zaichenko, Yu. P. (1979). "Operations Research." Kiev: Higher School.

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THE TRAVELING SALESMAN PROBLEM: MATHEMATICAL MODELING AND OPTIMAL SOLUTIONS. (2025). International Journal of Artificial Intelligence, 5(04), 1204-1212. https://www.academicpublishers.org/journals/index.php/ijai/article/view/4062