Ballast water management and the method chosen to achieve it is a key issue and concerns key technologies in ship design If the sequential exchange method is the chosen method, the sequence chosen to perform the exchange is very important and affects many aspects including ships' stability, structural strength, maneuverability, operational expenses and building cost, and so forth In this paper, based on the multiple risk assessment criteria of the sequential method, the problem of finding a feasible and optimum exchange sequence is boiled down to a multiobjective combinatorial optimization problem with multiple nonlinear constraints The diagonal exchange strategy was adopted, and the diagonal exchange mathematical model was built, taking into consideration the ship's intact stability, structural strength, trims, draughts, and bridge vision In order to find a set of Pareto solutions, a multiobjective genetic algorithm (MOGA) was used In the algorithm, a constraint-domination principle was adopted to handle the multiple constraints, and a nondominated sorting method was used to perform the selection of the Pareto solutions Using the proposed mathematic model and the MOGA, a Pareto solution set that met all the design criteria could be efficiently and accurately obtained for the engineers to choose from within short running times Compared with the traditional symmetrical exchanging method, the simulation results showed that the proposed method can produce more and better solutions with smaller trims, smaller bridge blind vision range, and better structural strength performances