Genetic algorithms have been used extensively in the studies on the Berth allocation problem (BAP). In this paper we present an optimization based genetic algorithm heuristic for the discrete and dynamic BAP that is independent of the objective function of the problem. It is evaluated by considering the problem of allocating space at a berth for vessels with the objective of minimizing the total weighted service time of all the vessels. The problem is formulated as a linear mixed integer program. Computational experiments are reported to evaluate the efficiency of the proposed heuristic.