Application of Genetic Algorithms in Combinatorial Optimization Problems and Algorithm Analysis

In combinatorial optimization problems, traditional optimization algorithms are often difficult to efficiently find the global optimal solution. This paper studies the application of genetic algorithms in combinatorial optimization problems and its performance analysis. First, the combinatorial optimization problem is defined and a mathematical model is established. Secondly, the operation process of the genetic algorithm is designed, and the fitness function is set to evaluate the quality of the solution. Then, the algorithm parameters are adjusted through multiple experiments to optimize the algorithm performance. Finally, experiments are conducted on the classic traveling salesman problem (TSP) and knapsack problem. In the experiment, different population sizes and iteration times are set, and the shortest path length calculated by the algorithm on the TSP problem in 10 cities is 101km, which is close to the known optimal solution. The genetic algorithm has good global search capabilities and flexibility in combinatorial optimization problems. Through appropriate improvements, its solving efficiency and solution quality can be significantly improved.