This paper describes a new approach to the radiological worker allocation problem using a multiple objective genetic algorithm, The worker allocation problem in radiological facilities involves various types of constraints and even mutually conflicting ones, such as individual dose limits, working time limits, etc, A major difficulty of this highly constrained problem is the way of finding an optimal solution in the huge search space where a large proportion of solutions are not feasible because some of the constraints cannot be satisfied, The paper proposes a model of evolution to establish an optimal assignment efficiently, based on the biological insights into the evolutionary process and heuristic ideas, The experimental results show a very rapid evolution to produce feasible solutions, and the application of multiple evaluation functions converges the feasible solutions to good ones, The genetic algorithm approach was found to be superior to the goal programming and simplex methods.