APPLICATION OF MATHEMATICAL MODELS AND OPTIMIZATION APPROACHES IN TOURISM FIRMS ISSUE KOMMIVOYAJYOR

Аннотация

The issue of Kommivoyajer (Travel sales I am the problem — TSP) is one of the issues expansions for eigenvalues of classic discrete optimization, if the minimum distance to all the cities with the cost or one-time visit, return to the starting point requires. The tsp's mathematical formulalashuvi in this article, the main methods or specific (bruteforce, dynamic programming, tarmoqlash-limiting) and approximate (genetic algorithm, near methods) approaches will be covered. Also, the practical issue is to be applied and the complexity is analyzed.TSP his full kombinatorika features and high-level complexity is popular. Kommivoyajer expansions for the eigenvalues of discrete optimization problems is one of the classic issues, if the minimum distance to all the cities with the cost or one-time visit,return tothe starting pointrequires. The tsp's mathematical formulalashuvi in this article, the main methods or specific (bruteforce, dynamic programming, tarmoqlash-limiting) and approximate (genetic algorithm, near methods) approaches will be covered. Also, the complexity of the issue is to be practical and applied analysis this problem is np-complete problem, that is, find its exact solution, it becomes very complicated as the number of issues have increased. The computer algorithm is developed to find the solution through the different, in particular, network search algorithm of genetic algorithm and simulation annealing methods been.Kommivoyajyor the issue of in practice in many areas, for example, logistics, transportation, robotics, and is used in the management of different resources. It also used as a means to increase productivity, optimize and theoretical issues is very important. Annotation:I am the travel your sales problem (TSP) is one of the most well-known and studied problem in computer science and mathematical optimization. The objective of the problem is to find theshortest possibletravel router that allows a specified set of your sales to page557 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue05,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai the city that I visit, your visit each city only once, and return to its ultimate point your lovely starti. Is famous for its high combinatorial complexity of nature and a full TSP. It is classified as an np-problem, completed me that technique becomes increasingly difficult as the number grows of the city that you find an exact solution. Various algorithms have been using computers to find solutions developer, including network search algorithms, genetic algorithms, simulated annealing and the metho. I applied in many practical problem is the travel of your sales area, such as logistics, transportation, robotics, and various resource management systems. It is also of great theoretical importance for use as a tool for improving theoptimizationand premium. Annotasiya:kommivoyajera far zada president (TSP) — I v matematicheskoy zada president has features to track an samix izvestnix izuchennix when I optimizasii computer science. Zada president who tselsiy — nayti kratchayshiy route, posetit pozvolyayutshiy kommivoyajeru zadannie much more productive, posetiv kajdiy odin tolko raz gorod, v I v to a section isxodnuyu tochka konsov kontserni. TSP izvestna I svoystva I polnostyu svoimi kombinator visokoy slojnostyu. Zada president will far yavlyaetsya NP-polnoy, chto oznachaet, chto vsyo po naxojdenie tochno cargo resheniya stanovitsya slojnee uvelicheniya chislo gorodov is merry. Razlichnie kompyuterov razrabotani pomotshyu s naxojdeniya resheniy beginning of the algorithm, the algorithm vklyuchaya poisk v, a set of algorithm to simulirovannogo otj I geneticheskie method. Zada president razlichnix oblastyax far kommivoyajera primenyaetsya v, takix kak logistics, transport, robotics I sistem upravleniya of resources to me. Teoreticheskoe I znachenie imeet takje kak instrument bolshoy mother optimizasiipovisheniya effektivnosti thebeginning. Keywords:Kommivoyajer issue, TSP, optimization, kombinatorika, tarmoqlash-limiting, dynamic programming, heuristik methods, genetic algorithm, either‘lni to reduce, the calculation complexity, operations research. resources management, simulation made annealing, genetic algorithm, network search algorithm, thesolutionyou find. Keywords: travel I am your sales problem (TSP), optimization, combinatorics, NP- completed problem, shortest path algorithms, logistics, transportation, robotics, resource management, simulated annealing, genetic algorithms, network security, algorithms, please find solution. Klyuchevie slovo: kommivoyajera far zada president (TSP), optimizasiya, kombinatorika, NP-zada president polnaya far, put kratchayshiy, algorithm, logistics, transportation, robotics, resources upravlenii me, I simulirovanniy otj, geneticheskie algorithm, the algorithm in the set ofpoisk v,naxojdenieresheniya. To enter. The issue of