Balancing exploration and exploitation in genetic algorithm with a novel selection operator

The genetic algorithm (GA) is a widely recognized optimization technique for addressing complex and NP-hard problems; however, its effectiveness is often hampered by issues such as premature convergence and population diversity. The selection operator, which determines the probability of individuals being chosen for reproduction, significantly influences its performance. This study presents a novel selection operator, which is specifically designed to strike a balance between selection pressure and the preservation of population diversity. At the first stage, we derived the mathematical properties and assessed the sampling accuracy using Pearson’s chi-square test. For global investigation, we test its performance on benchmark TSPLIB instances and a real-world dataset of Pakistan's city coordinates in the context of the traveling salesman problem (TSP). The results indicate that the newly proposed operator either outperforms or equals the performance of other operators across key metrics, demonstrating superior stability as the dataset size increases. These findings suggest that our operator presents a promising solution for large-scale optimization challenges, such as TSP and other real-world applications.