This work deals with the problem of a nozzle design addressed through a multi-objective optimization strategy where governing equations of fluid dynamics model the phenomena. The liquid flow rate and the nozzle length are considered as the design criteria. Two Differential Evolution variants are proposed to obtain a set of design configurations that presents numerous and different synergies between the design criteria. The first variant is based on the Hypervolume performance metric (MODE-HVR) and the second one includes the-dominance concept (MODE-HV R). A comparative study is performed with other optimizers from well-established search approaches for multi-objective optimization such as algorithms based on Pareto dominance (NSGA-II and SPEA2), decomposition (MOEA/D), metric (SMS-EMOA) and hybrid (NSGA-III). Based on the Spacing and Hypervolume indicators of the obtained Pareto fronts, the proposed optimization algorithms can provide more design solutions, promoting the reconfigurability (synergy) in the nozzle design. Hence, the multi-objective design strategy allows the designer to have a wide range of solutions and to choose the most suitable one for a particular application, compared with a traditional design where both design criteria are considered as a single aggregate function. INDEX TERMS Optimum nozzle design, multi-objective optimization, multi-objective search approaches, optimization.

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