Generalized assignment problem (GAP) considers finding minimum cost assignment of n tasks to m agents provided each task should be assigned to one agent only. In this study, a new Genetic Algorithm (GA) with some new methods has been proposed to solve GAPs. The agent-based crossover is based on the concept of dominant gene in genotype science and increases the fertility rate of the feasible solutions. The solutions are classified as infeasible, feasible and mature with reference to their conditions. The new local searches provide not only feasibility in high diversity but high profitability for the solutions. A solution is not given up through maturation-based replacement until it reaches its best. The computational results show that the agent-based crossover has much higher fertility rate than classical crossover. Finally, the proposed GA creates either optimal or near-optimal solutions.