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This paper extends the study of the continuous Berth Allocation Problem to the case of multiple quays, which is found in many container terminals around the world. Considering multiple quays adds a problem of assigning vessels to quays to the problem of determining berthing times and positions for each incoming vessel. This problem has not been considered in the literature at the operational level addressed in this study. In order to solve it, we have developed first an integer linear model and then a genetic algorithm which works on sequences of vessels that are decoded by a constructive algorithm. A local search procedure helps to improve further the solutions produced by the genetic algorithm. We have conducted an extensive computational experiment, adapting existing instances to the case of multiple quays. We have also adapted our genetic algorithm to the case of a single quay and tested it on previously reported instances, showing its superior performance compared with existing approaches. Finally, we have developed a random instance generator for the problem with multiple quays, enabling us to conduct a systematic study of the factors affecting the complexity of the problem. [ABSTRACT FROM AUTHOR]