This study of a high-entropy alloy (HEA) explored two strategies to simultaneously satisfy two mechanical properties, ultimate tensile strength (UTS) and total elongation. The first strategy used inverse design based on a conditional variational autoencoder (CVAE), and the second employed multi-objective Bayesian optimization. Using a dataset of 501 literature-based HEAs, three models were trained with alloy composition and experimental conditions as inputs. Among these, extreme gradient boosting (XGBoost) exhibited the highest predictive performance for both properties and was selected as the final prediction model. CVAE was employed to generate 1,000 new samples from the latent space under the condition that both UTS and total elongation exceeded their mean values. Of these, 310 physically feasible compositions were validated using the XGBoost model, and approximately 17.7 % satisfied the target properties. Next, expected hypervolume improvement (EHVI)-based Bayesian optimization, beginning with 130 initial compositions that demonstrated superior properties, proposed five recommended candidates. These samples were found to differ in compositional characteristics from the existing dataset, which can be interpreted as exploration driven by the uncertainty of the probabilistic machine learning model. The candidate compositions generated by both methods were predicted by the XGBoost model to have the potential to achieve the target properties.