Multi-objective optimization (MOO) that accounts for several distinct, possibly conflicting, objectives is expected to be capable of providing improved reservoir management (RM) solutions for efficient oil field development owing to the overall optimization of subsurface flow. Considering the complexity and diversity of MOO problems in model-based RM, we develop three MOO methods (MOAdjoint, MOGA, and MOPSO) in this work to address various oil field development problems. MOAdjoint combines a weighted sum technique with a gradient-based method for solving large-scale continuous problems that have thousands of variables. An adjoint method is used to compute efficiently the derivatives of objective functions with respect to decision variables and a sequential quadratic programming method is used for optimization search. MOGA is a population-based method, which combines a Pareto-ranking technique with genetic algorithm (GA) to address small-scale discrete problems. MOPSO is another population-based method, which combines a Pareto-ranking technique with particle swarm optimization (PSO) for a wide spectrum of optimization problems. Their advantages and disadvantages are highlighted. An example is used to compare the three methods. Results show that MOPSO seems particularly suitable for medium-scale RM problems, mainly because of its relatively high rate of convergence and efficient recovery of Pareto front.