On solving combinatorial optimization problems

Abstract

This work is devoted to the study of discrete optimization problems, which are widely used in industry, logistics, transport systems and information technologies. The study is important due to the complexity of such problems and the need to improve the efficiency of algorithms for their solution. One example of discrete optimization problems is the traveling salesman problem, which is used to model the processes of optimal route planning, queue management and allocation of computational resources. The aim of the work is to analyze modern methods and algorithms of discrete optimization, which can reduce computational complexity. Particular attention is paid to combinatorial methods, in particular the branch and bounds method, as well as heuristic and metaheuristic approaches, including ant and genetic algorithms. The effectiveness of discrete optimization methods for applied problems with a large number of variables and belonging to the class of NP-hard problems is noted. This makes it possible not only to reduce calculation time, but also to increase the accuracy of models in various fields – from logistics and transportation to scientific computing and resource planning.