This paper proposes Genetic Algorithm with Border Trades (GAB), a novel modification of the standard genetic algorithm that enhances exploration by incorporating new chromosome patterns in the breeding process. This approach significantly mitigates premature convergence and improves search diversity. Empirically, GAB achieves up to 8x higher fitness and 10x faster convergence on complex job scheduling problems compared to standard Genetic Algorithms, reaching average fitness scores of 888 versus 106 in under 20 seconds. On the classic Flip-Flop problem, GAB consistently finds optimal or near-optimal solutions in fewer generations, even as input sizes scale to thousands of bits. These results highlight GAB as a highly effective and computationally efficient alternative for solving large-scale combinatorial optimization problems.