The dynamic memory manager (DMM) is a key element whose customization for a target application reports great benefits in terms of execution time, memory usage and energy consumption. Previous works presented algorithms to automatically obtain custom DMMs for a given application. Nevertheless, those approaches are based on grammatical evolution where the fitness is built as an aggregate objective function, which does not completely exploit the search space, returning the designer the DMM solution with best fitness. However, this approach may not find solutions that could fit in a concrete hardware platform due to a very low value of one of the objectives while the others remain high, which may represent a high fitness. In this work we present the first multi-objective optimization methodology applied to DMM optimization where the Pareto dominance is considered, thus providing the designer with a set of non-dominated DMM implementations on each optimization run. Our results show that the multi-objective optimization provides Pareto-optimal alternatives due to a better exploitation of the search space obtaining better hypervolume values than the aggregate objective function approach.